Econ 210 Exam 4 15

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. n = 4 ΣX = 16 ΣY = 28 Σ (Y -)(X - ) = -8 Σ (X - )2 = 8 SST = 42 SSE = 34 Refer to Exhibit 12-10. The Y intercept is

11

Refer to Exhibit 12-6. The least squares estimate of b0 equals

11

30. In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is a. 0.6667 b. 0.6000 c. 0.4000 d. 1.5000

B

58. A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation = 9 - 3X The above equation implies that if the price is increased by $1, the demand is expected to a. increase by 6 units b. decrease by 3 units c. decrease by 6,000 units d. decrease by 3,000 units

D

63. Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained. = 80 + 6.2 X Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is a. $62,080 b. $142,000 c. $700 d. $700,000

D

75. Refer to Exhibit 14-3. The least squares estimate of b0 equals a. 1 b. -1 c. -11 d. 11

D

If the coefficient of determination is a positive value, then the coefficient of correlation must be

Either negative or positive

less than 0.005

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 12-5. The p-value is

In regression analysis, the variable that is being predicted is the a. dependent variable b. independent variable c. intervening variable d. is usually x

a. dependent variable

In a multiple regression model, the error term ε is assumed to

be normally distributed

Refer to Exhibit 11-6. The standard error of p1-p2 is Answers: a. 100 b. 52 c. 0.0225 d. 0.044

c

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

can be approximated by a normal distribution

The coefficient of determination

cannot be negative

In regression analysis, the response variable is the

dependent variable

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

goodness of fit test

Refer to Exhibit 11-5. The p-value is

greater than 0.1

Refer to Exhibit 11-4. The p-value is

larger than 0.1

SSE can never be

larger than SST

Larger values of r2 imply that the observations are more closely grouped about the

least squares line

Refer to Exhibit 11-8. The p-value is

less than 0.005

The least squares criterion is

min

If the coefficient of correlation is a positive value, then the slope of the regression line

must also be positive

If the coefficient of correlation is -0.4, then the slope of the regression line

must be negative

If the coefficient of correlation is a positive value, then the regression equation

must have a positive slope

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2,

n1 and n2 can be different sizes

The interval estimate of an individual value of y for a given value of x is

prediction interval estimate

Refer to Exhibit 11-7. The conclusion of the test is that the

proportions have not changed significantly

Simple linear regression

regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line

The standard error is the

square root of MSE

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4 X Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is

$900,000

Exhibit 12-7 You are given the following information about y and x. y Dependent Variable x Independent Variable 5 4 7 6 9 2 11 4 Refer to Exhibit 12-7. The least squares estimate of b1 (slope) equals

-0.5

In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is

-0.7

Exhibit 14-2 You are given the following information about y and x. y x Dependent Variable Independent Variable 5 15 7 12 9 10 11 7 Refer to Exhibit 14-2. The least squares estimate of b1 equals

-0.7647

Refer to Exhibit 12-2. The least squares estimate of b1 equals

-0.7647

Exhibit 14-2 You are given the following information about y and x. y x Dependent Variable Independent Variable 5 15 7 12 9 10 11 7 Refer to Exhibit 14-2. The coefficient of determination equals

-0.9941

Exhibit 14-2 You are given the following information about y and x. y x Dependent Variable Independent Variable 5 15 7 12 9 10 11 7 Refer to Exhibit 14-2. The sample correlation coefficient equals

-0.99705

Refer to Exhibit 12-6. The least squares estimate of b1 equals

-1

Exhibit 12-2 You are given the following information about y and x. Dependent Variable (Y) Independent Variable (X) 5 1 4 2 3 3 2 4 1 5 Refer to Exhibit 12-2. The point estimate of y when x = 10 is

-4

Refer to Exhibit 12-5. The point estimate of y when x = 10 is

-4

The test for goodness of fit

. is always a one-tail test with the rejection region occurring in the upper tail

Refer to Exhibit 11-1. The point estimate for the difference between the two population proportions in favor of this product is

0.02

Refer to Exhibit 11-1. The standard error of p bar 1 - p bar 2 is

0.0225

Refer to Exhibit 11-3. The standard error of p bar 1 - p bar 2 is

0.0243

40. SSE can never be a. larger than SST b. smaller than SST c. equal to 1 d. equal to zero

A

a time series

A group of observations measured at successive time intervals is known as

a

A least squares regression line a. may be used to predict a value of y if the corresponding x value is given b. implies a cause-effect relationship between x and y c. can only be determined if a good linear relationship exists between x and y d. None of these alternatives is correct.

Kruskal-Wallis Test

A nonparametric version of the Parametric analysis of variance test is the

should not be rejected

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis

113. Refer to Exhibit 14-10. The point estimate of Y when X = -3 is a. 11 b. 14 c. 8 d. 0

B

14. In a regression analysis the standard error is determined to be 4. In this situation the MSE a. is 2 b. is 16 c. depends on the sample size d. depends on the degrees of freedom

B

20. The equation that describes how the dependent variable (y) is related to the independent variable (x) is called a. the correlation model b. the regression model c. correlation analysis d. None of these alternatives is correct.

B

31. If the coefficient of determination is equal to 1, then the coefficient of correlation a. must also be equal to 1 b. can be either -1 or +1 c. can be any value between -1 to +1 d. must be -1

B

34. The coefficient of correlation a. is the square of the coefficient of determination b. is the square root of the coefficient of determination c. is the same as r-square d. can never be negative

B

43. It is possible for the coefficient of determination to be a. larger than 1 b. less than one c. less than -1 d. None of these alternatives is correct.

B

47. If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data is a. 0 b. 1 c. either 1 or -1, depending upon whether the relationship is positive or negative d. could be any value between -1 and 1

B

59. In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is a. 0.35 b. 0.65 c. 2.85 d. 0.45

B

62. If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 0.90% b. is 90%. c. is 81% d. 0.81%

B

68. Refer to Exhibit 14-1. The MSE is a. 1 b. 2 c. 3 d. 4

B

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

Becomes smaller

19.2

Below you are given the first two values of a time series. You are also given the first two values of the exponential smoothing forecast. If the smoothing constant equals .3, then the exponential smoothing forecast for time period three is

108. Refer to Exhibit 14-10. The Y intercept is a. -1 b. 1.0 c. 11 d. 0.0

C

112. Refer to Exhibit 14-10. The point estimate of Y when X = 3 is a. 11 b. 14 c. 8 d. 0

C

12. If only MSE is known, you can compute the a. r square b. coefficient of determination c. standard error d. all of these alternatives are correct

C

17. Regression analysis is a statistical procedure for developing a mathematical equation that describes how a. one independent and one or more dependent variables are related b. several independent and several dependent variables are related c. one dependent and one or more independent variables are related d. None of these alternatives is correct.

C

In conducting a hypothesis test about p1 - p2, any of the following approaches can be used except

Comparing the observed frequencies to the expected frequencies

The interval estimate of the mean value of y for a given value of x is the

Confidence Interval

104. Refer to Exhibit 14-9. The sum of squares due to regression (SSR) is a. 1434 b. 505.98 c. 50.598 d. 928.02

D

11. The standard error is the a. t-statistic squared b. square root of SSE c. square root of SST d. square root of MSE

D

28. In a regression and correlation analysis if r2 = 1, then a. SSE = SST b. SSE = 1 c. SSR = SSE d. SSR = SST

D

77. Refer to Exhibit 14-3. The coefficient of determination equals a. -0.4364 b. 0.4364 c. -0.1905 d. 0.1905

D

If we are testing for the equality of 3 population means, we should use the

F Statistic

1.53

For a one-tailed test (upper tail) at 93.7% confidence, Z =

1.328

For a two-tailed test, a sample of 20 at 80% confidence, t =

41

For the following time series, you are given the moving average forecast. The mean squared error equals

58.9

Given an actual demand of 61, forecast of 58, and an mc002-1.jpg of .3, what would the forecast for the next period be using simple exponential smoothing?

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

Goodness of fit

37.3

In a completely randomized design involving four treatments, the following information is provided. The overall mean (the grand mean) for all treatments is

b

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is a. 0.6667 b. 0.6000 c. 0.4000 d. 1.5000

b

In a regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is a. 0.4000 b. 0.0256 c. 4 d. 2.56

a

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is a. 0.65 b. 0.1785 c. any positive value d. any value

c

In regression analysis, the unbiased estimate of the variance is a. coefficient of correlation b. coefficient of determination c. mean square error d. slope of the regression equation

a

In regression analysis, the variable that is being predicted is the a. dependent variable b. independent variable c. intervening variable d. is usually x

a

In regression and correlation analysis, if SSE and SST are known, then with this information the a. coefficient of determination can be computed b. slope of the line can be computed c. Y intercept can be computed d. x intercept can be computed

different levels of a factor

In the ANOVA, treatment refers to

the independent variable

In the analysis of variance procedure (ANOVA), "factor" refers to

If the cost of a Type I error is high, a smaller value should be chosen for the

Level of significance

The test statistic F is the ratio

MSR/MSE

An important application of the chi-square distribution is

Making inferences about a single population variance; testing for goodness of fit; testing for the independence of two variables

the mean square error

One measure of the accuracy of a forecasting model is

The degrees of freedom associated with a t distribution are a function of the

Sample size

More evidence against H0 is indicated by

Smaller p values

What is a statistical inference?

Takes the information from a sample to make a statement about the population

In a regression analysis, the variable that is being predicted

The dependent variable

In regression analysis, which of the following is not a required assumption about the error term ε?

The expected value of the error term is one.

197.6

The following linear trend expression was estimated using a time series with 17 time periods. Tt = 129.2 + 3.8t The trend projection for time period 18 is

Prediction interval

The interval estimate of an individual value of y for a given value of x

ordinal measurement

The level of measurement that allows for the rank ordering of data items is

nominal measurement

The level of measurement that is simply a label for the purpose of identifying an item is

irregular

The time series component that reflects variability due to natural disasters is called

A goodness of fit test is always conducted as a

Upper-tail test

Which of the following descriptive statistics is not measured in the same units as the data

Variance

matched samples

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

Refer to Exhibit 11-1. The conclusion of the test is that the Answers: a. distribution is uniform b. distribution is not uniform c. test is inconclusive d. None of these alternatives is correct.

a

Refer to Exhibit 11-1. The expected frequency for each group is Answers: a. 50 b. 1/3 c. 0.50 d. 0.333

a

Refer to Exhibit 11-6. At 95% confidence, the margin of error is Answers: a. 0.044 b. 0.064 c. 52 d. 0.0225

a

In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is a. -0.7 b. +0.7 c. 0.49 d. -0.49

a. -0.7

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

alternative hypothesis should state P1 - P2 > 0

The purpose of the hypothesis test for proportions of a multinomial population is to determine whether the actual proportions

are different than the hypothesized proportions

In a regression and correlation analysis if r2 = 1, then a. SSE must also be equal to one b. SSE must be equal to zero c. SSE can be any positive value d. SSE must be negative

b. SSE must be equal to zero

In regression analysis if the dependent variable is measured in dollars, the independent variable a. must also be in dollars b. must be in some units of currency c. can be any units d. cannot be in dollars

c. can be any units

If the coefficient of correlation is a negative value, then the coefficient of determination a. must also be negative b. must be zero c. can be either negative or positive d. must be positive

d. must be positive

If the coefficient of correlation is a positive value, then a. the intercept must also be positive b. the coefficient of determination can be either negative or positive, depending on the value of the slope c. the regression equation could have either a positive or a negative slope d. the slope of the line must be positive

d. the slope of the line must be positive

The model developed from sample data that has the form of is known as

estimated regression equation

An example of statistical inference is

hypothesis testing

A multiple regression model has the form = 7 + 2 x1 + 9 x2 As x1 increases by 1 unit (holding x2 constant), is expected to

increase by 2 units

Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 - 3x1 + 5x2. For this model SSR = 3500, SSE = 1500, and the sample size is 18.Refer to Exhibit 15-2. The coefficient of the unit price indicates that if the unit price is

increased by $1 (holding advertising constant), sales are expected to decrease by $3,000

Data points having high leverage are often

influential

An observation that has a strong effect on the regression results is called a(n)

influential observation

If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the estimated regression equation

is 16%

If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable

is 16%.

If a hypothesis is rejected at 95% confidence,

it must also be rejected at the 90% confidence

The mean square is the sum of squares divided by

its corresponding degrees of freedom

If a qualitative variable has k levels, the # of dummy variables required is

k − 1

The sampling distribution of is approximated by a

normal distribution

The sampling distribution of p bar 1 - p bar 2 is approximated by a

normal distribution

When conducting a good of fit test, the expected frequencies for the multinomial population are based on the

null hypothesis

Both the hypothesis test for proportions of a multinomial population and the test of independence focus on the difference between

observed frequencies and expected frequencies

The required condition for using an ANOVA procedure on data from several populations is that the

sampled populations have equal variances

Refer to Exhibit 11-5. At 95% confidence, the null hypothesis

should not be rejected

The standard error of x1 and x2 is the

standard deviation of the sampling distribution of x1 and x2

The standard error of is the

standard deviation of the sampling distribution of xbar1-xbar2

If only MSE is known, you can compute the

standard error

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the

t distribution with 58 degrees of freedom

Residual analysis

the analysis of the residuals used to determine whether the assumptions made about the regression model appear to be valid. Residual analysis is also used to identify outliers and influential observations.

Correlation analysis is used to determine

the strength of the relationship between the dependent and the independent variables

Mean Square Error (MSE)

the unbiased estimate of the variance of the error term o2. It is denoted by MSE or s2

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. = 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is

$1,300,000

Exhibit 12-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 12-4. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is

$66,000

Exhibit 14-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg= 12 + 1.8 x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 14-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is

$66,000

Refer to Exhibit 12-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is

$66,000

Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained. = 80 + 6.2 X Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

$700,000

Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. Y^ = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

$700,000

Least squares criterion

(Yi-Yhat)^2

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)

(n1 + n2 − 2) degrees of freedom

The number of degrees of freed for the appropriate chi-square distribution in a test of independence is

(number of rows minus 1)*(number of columns minus 1)

In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed as

(r - 1)(c - 1)

Refer to Exhibit 12-1. The coefficient of determination equals

+1

Refer to Exhibit 12-5. The coefficient of determination equals

+1

Refer to Exhibit 11-3. The point estimate for the difference between the proportions is

-0.02

Refer to Exhibit 11-1. The 95% confidence interval estimate for the difference between the populations favoring the products is

-0.024 to 0.064

Refer to Exhibit 11-3. The 95% confidence interval for the difference between the two proportions is

-0.068 to 0.028

Exhibit 12-7 You are given the following information about y and x. y Dependent Variable x Independent Variable 5 4 7 6 9 2 11 4 Refer to Exhibit 12-7. The sample correlation coefficient equals

-0.3162

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. n = 4 ΣX = 16 ΣY = 28 Σ (Y -)(X - ) = -8 Σ (X - )2 = 8 SST = 42 SSE = 34 Refer to Exhibit 12-10. The coefficient of correlation is

-0.4364

Exhibit 12-3 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-3. The sample correlation coefficient equals

-0.4364

Refer to Exhibit 12-6. The sample correlation coefficient equals

-0.4364

Refer to Exhibit 12-2. The sample correlation coefficient equals

-0.99705

A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 ∑x = 55 ∑y = 55 ∑x2 = 385 ∑y2 = 385 ∑xy = 220 Refer to Exhibit 14-1. The sample correlation coefficient equals

-1

Exhibit 12-3 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-3. The least squares estimate of b1 equals

-1

Refer to Exhibit 12-5. The least squares estimate of b1 (slope) equals

-1

Refer to Exhibit 12-5. The sample correlation coefficient equals

-1

Exhibit 12-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 Refer to Exhibit 12-5. The MSE is

0

Exhibit 12-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 Refer to Exhibit 12-5. The least squares estimate of the Y intercept is

0

In a regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is

0.0256

Refer to Exhibit 11-1. At 95% confidence, the margin of error is

0.044

Exhibit 12-3 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-3. The coefficient of determination equals

0.1905

Refer to Exhibit 12-6. The coefficient of determination equals

0.1905

In a regression analysis if SSE = 500 and SSR = 300, then the coefficient of determination is

0.3750

In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is

0.40

If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is

0.6

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

0.6000

Refer to Exhibit 12-4. The coefficient of determination is

0.625

In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is

0.65

In a regression analysis if SST=4500 and SSE=1575, then the coefficient of determination is

0.65

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is

0.700

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

0.75

Exhibit 12-1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-1. The coefficient of correlation is

0.7906

Refer to Exhibit 12-4. The coefficient of correlation is

0.7906

Refer to Exhibit 12-2. The coefficient of determination equals

0.9941

Exhibit 12-1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-1. The least squares estimate of the slope is

1

Exhibit 12-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 Refer to Exhibit 12-5. The coefficient of determination is

1

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data is

1

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is

1

Refer to Exhibit 12-4. The least squares estimate of the slope is

1

Refer to Exhibit 11-5. The calculated value for the test statistic equals

1.6615

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 ΣX = 90 ΣY = 170 Σ (Y -)(X - ) = = 466 Σ (Y - )2 = = 1434 Σ (X - )2 = 234 SSE = 505.98 Refer to Exhibit 12-9. The least squares estimate of b1 equals

1.991

The degrees of freedom of a contingency table with 6 rows and 3 columns is

10

Refer to Exhibit 11-7. The expected frequency for the Business College is

105

The degrees of freedom for a contingency table with 12 rows and 12 columns is

121

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

14 and 240

Refer to Exhibit 11-8. The expected number of adults who prefer coffee is

150

Refer to Exhibit 12-2. The least squares estimate of b0 equals

16.41176

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. n = 4 ΣX = 16 ΣY = 28 Σ (Y -)(X - ) = -8 Σ (X - )2 = 8 SST = 42 SSE = 34 Refer to Exhibit 12-10. The MSE is

17

Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 - 3x1 + 5x2. For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2, the test statistic F is

17.5

Refer to Exhibit 11-4. The number of degrees of freedom associated with this problem is

2

Refer to Exhibit 12-4. The MSE is

2

Refer to Exhibit 12-4. The least squares estimate of the Y intercept is

2

Refer to Exhibit 12-3. Using a = 0.05, the critical t value for testing the significance of the slope is

2.131

Exhibit 12-6 For the following data the value of SSE = 0.4130. Dependent Variable (Y) Independent Variable (X) 15 4 17 6 23 2 17 4 Refer to Exhibit 12-6. The y intercept is

24

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

3 and 43

Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 - 3x1 + 5x2. For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2. If we want to test for the significance of the regression model, the critical value of F using alpha = .05

3.68

Exhibit 12-6 For the following data the value of SSE = 0.4130. Dependent Variable (Y) Independent Variable (X) 15 4 17 6 23 2 17 4 Refer to Exhibit 12-6. The total sum of squares (SST) equals

36

Refer to Exhibit 11-4. The calculated value for the test statistic equals

4

Refer to Exhibit 11-7. The calculated value for the test statistic equals

4.29

Refer to Exhibit 12-3. The critical F value at a = 0.05 is

4.54

Exhibit 15-3. In a regression model involving 30 observations, the following estimated regression equation was obtained y-hat = 17 + 4x1 - 3x2 + 8x3 + 8x4. For this model SSR = 700 and SSE = 100. Refer to Exhibit 15-3. The computed F statistic for testing the significance of the above model is

43.75

Exhibit 12-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 12-4. The F statistic computed from the above data is

45

Refer to Exhibit 12-3. The F statistic computed from the above data is

45

Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg= 12 + 1.8 x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 14-3. The F statistic computed from the above data is

45

Refer to Exhibit 11-7. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

5.991

Refer to Exhibit 11-4. The expected frequency for each group is

50

Exhibit 12-2 You are given the following information about y and x. Dependent Variable (Y) Independent Variable (X) 5 1 4 2 3 3 2 4 1 5 Refer to Exhibit 12-2. The least squares estimate of b0 (intercept)equals

6

Refer to Exhibit 12-5. The least squares estimate of b0 (intercept)equals

6

Exhibit 12-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 12-4. The t statistic for testing the significance of the slope is

6.708

Exhibit 14-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg= 12 + 1.8 x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 14-3. The t statistic for testing the significance of the slope is

6.709

Refer to Exhibit 12-3. The t statistic for testing the significance of the slope is

6.709

Refer to Exhibit 11-5. The expected frequency of seniors is

60

Refer to Exhibit 11-8. The test statistic for this test of independence is

62.5

Refer to Exhibit 11-8. With a .05 level of significance, the critical value for the test is

7.815

Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. y^ = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

700,000

Refer to Exhibit 11-5. The expected number of freshmen is

90

The degrees of freedom for a contingency table with 10 rows and 11 columns is

90

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. y^ = 500 + 4x Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is

900,000

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 ΣX = 90 ΣY = 170 Σ (Y -)(X - ) = = 466 Σ (Y - )2 = = 1434 Σ (X - )2 = 234 SSE = 505.98 Refer to Exhibit 12-9. The sum of squares due to regression (SSR) is

928.02

1. In a regression analysis, the error term 3 is a random variable with a mean or expected value of a. zero b. one c. any positive value d. any value

A

10. The interval estimate of an individual value of y for a given value of x is a. prediction interval estimate b. confidence interval estimate c. average regression d. x versus y correlation interval

A

101. Refer to Exhibit 14-8. The coefficient of correlation is a. -0.2295 b. 0.2295 c. 0.0527 d. -0.0572

A

105. Refer to Exhibit 14-9. The sample correlation coefficient equals a. 0.8045 b. -0.8045 c. 0 d. 1

A

106. Refer to Exhibit 14-9. The coefficient of determination equals a. 0.6472 b. -0.6472 c. 0 d. 1

A

109. Refer to Exhibit 14-10. The coefficient of determination is a. 0.1905 b. -0.1905 c. 0.4364 d. -0.4364

A

111. Refer to Exhibit 14-10. The MSE is a. 17 b. 8 c. 34 d. 42

A

13. The value of the coefficient of correlation (R) a. can be equal to the value of the coefficient of determination (R2) b. can never be equal to the value of the coefficient of determination (R2) c. is always smaller than the value of the coefficient of determination d. is always larger than the value of the coefficient of determination

A

15. In regression analysis, which of the following is not a required assumption about the error term ? a. The expected value of the error term is one. b. The variance of the error term is the same for all values of X. c. The values of the error term are independent. d. The error term is normally distributed.

A

19. In regression analysis, the variable that is being predicted is the a. dependent variable b. independent variable c. intervening variable d. is usually x

A

2. The coefficient of determination a. cannot be negative b. is the square root of the coefficient of correlation c. is the same as the coefficient of correlation d. can be negative or positive

A

23. In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is a. 0.65 b. 0.1785 c. any positive value d. any value

A

29. In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is a. -0.7 b. +0.7 c. 0.49 d. -0.49

A

35. If the coefficient of correlation is a positive value, then the regression equation a. must have a positive slope b. must have a negative slope c. could have either a positive or a negative slope d. must have a positive y intercept

A

37. In regression and correlation analysis, if SSE and SST are known, then with this information the a. coefficient of determination can be computed b. slope of the line can be computed c. Y intercept can be computed d. x intercept can be computed

A

44. If two variables, x and y, have a strong linear relationship, then a. there may or may not be any causal relationship between x and y b. x causes y to happen c. y causes x to happen d. None of these alternatives is correct.

A

46. A least squares regression line a. may be used to predict a value of y if the corresponding x value is given b. implies a cause-effect relationship between x and y c. can only be determined if a good linear relationship exists between x and y d. None of these alternatives is correct.

A

49. Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be a. narrower b. wider c. the same d. None of these alternatives is correct.

A

5. The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = 0 + 1x, is known as a. regression equation b. correlation equation c. estimated regression equation d. regression model

A

65. Refer to Exhibit 14-1. The least squares estimate of the slope is a. 1 b. 2 c. 3 d. 4

A

67. Refer to Exhibit 14-1. The coefficient of correlation is a. 0.7906 b. - 0.7906 c. 0.625 d. 0.375

A

7. In the following estimated regression equation a. b1 is the slope b. b1 is the intercept c. b0 is the slope d. None of these alternatives is correct.

A

76. Refer to Exhibit 14-3. The sample correlation coefficient equals a. -0.4364 b. 0.4364 c. -0.1905 d. 0.1905

A

84. Refer to Exhibit 14-5. The least squares estimate of the slope is a. 1 b. -1 c. 0 d. 3

A

87. Refer to Exhibit 14-5. The MSE is a. 0 b. -1 c. 1 d. 0.5

A

90. Refer to Exhibit 14-6. The total sum of squares (SST) equals a. 36 b. 18 c. 9 d. 1296

A

99. Refer to Exhibit 14-8. The slope of the regression equation is a. -0.667 b. 0.667 c. 100 d. -100

A

Exhibit 14-10 The following information regarding a dependent variable Y and an independent variable X is provided. X = 16 (X - )(Y - ) = -8 Y = 28 (X - )2 = 8 n = 4 SST = 42 SSE = 34 107. Refer to Exhibit 14-10. The slope of the regression function is a. -1 b. 1.0 c. 11 d. 0.0

A

Exhibit 14-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 78. Refer to Exhibit 14-4. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is a. $66,000 b. $5,412 c. $66 d. $17,400

A

a cyclical component

A component of the time series model that results in the multi-period above-trend and below-trend behavior of a time series is

d

A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation = 9 - 3X The above equation implies that if the price is increased by $1, the demand is expected to a. increase by 6 units b. decrease by 3 units c. decrease by 6,000 units d. decrease by 3,000 units

d

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an a. increase of $4 in advertising is associated with an increase of $4,000 in sales b. increase of $1 in advertising is associated with an increase of $4 in sales c. increase of $1 in advertising is associated with an increase of $34,000 in sales d. increase of $1 in advertising is associated with an increase of $4,000 in sales

d

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 60 - 8X The above equation implies that an a. increase of $1 in price is associated with a decrease of $8 in sales b. increase of $8 in price is associated with an decrease of $52,000 in sales c. increase of $1 in price is associated with a decrease of $52 in sales d. increase of $1 in price is associated with a decrease of $8000 in sales

In regression analysis, which of the following is not a required assumption about the error term e?

All are required assumptions about the error term.

As a general guideline, the research hypothesis should be stated as the

Alternative hypothesis

Pooled estimator of p

An estimator of a population proportion obtained by computing a weighted average of the sample proportions obtained from two independent samples

All of these alternatives are correct.

An important application of the chi-square distribution is

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be

At least 5

21. In regression analysis, the independent variable is a. used to predict other independent variables b. used to predict the dependent variable c. called the intervening variable d. the variable that is being predicted

B

24. In a regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is a. 0.4000 b. 0.0256 c. 4 d. 2.56

B

25. In simple linear regression analysis, which of the following is not true? a. The F test and the t test yield the same conclusion. b. The F test and the t test may or may not yield the same conclusion. c. The relationship between X and Y is represented by means of a straight line. d. The value of F = t2.

B

26. Correlation analysis is used to determine a. the equation of the regression line b. the strength of the relationship between the dependent and the independent variables c. a specific value of the dependent variable for a given value of the independent variable d. None of these alternatives is correct.

B

27. In a regression and correlation analysis if r2 = 1, then a. SSE must also be equal to one b. SSE must be equal to zero c. SSE can be any positive value d. SSE must be negative

B

45. If the coefficient of determination is 0.81, the coefficient of correlation a. is 0.6561 b. could be either + 0.9 or - 0.9 c. must be positive d. must be negative

B

52. Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4 X Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is a. $900 b. $900,000 c. $40,500 d. $505,000

B

53. The coefficient of correlation a. is the square of the coefficient of determination b. is the square root of the coefficient of determination c. is the same as r-square d. can never be negative

B

54. If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 40% b. is 16%. c. is 4% d. can be any positive value

B

79. Refer to Exhibit 14-4. The F statistic computed from the above data is a. 3 b. 45 c. 48 d. 50

B

82. Refer to Exhibit 14-4. The critical t value for testing the significance of the slope at 95% confidence is a. 1.753 b. 2.131 c. 1.746 d. 2.120

B

89. Refer to Exhibit 14-6. The y intercept is a. -1.5 b. 24 c. 0.50 d. -0.707

B

9. The interval estimate of the mean value of y for a given value of x is a. prediction interval estimate b. confidence interval estimate c. average regression d. x versus y correlation interval

B

93. Refer to Exhibit 14-7. The least squares estimate of b0 (intercept) equals a. -10 b. 10 c. 0.5 d. -0.5

B

94. Refer to Exhibit 14-7. The sample correlation coefficient equals a. 0.3162 b. -0.3162 c. 0.10 d. -0.10

B

Exhibit 14 - 1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 64. Refer to Exhibit 14-1. The least squares estimate of the Y intercept is a. 1 b. 2 c. 3 d. 4

B

Exhibit 14-2 You are given the following information about y and x. y Dependent Variable x Independent Variable 5 1 4 2 3 3 2 4 1 5 69. Refer to Exhibit 14-2. The least squares estimate of b1 (slope) equals a. 1 b. -1 c. 6 d. 5

B

Exhibit 14-3 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 74. Refer to Exhibit 14-3. The least squares estimate of b1 equals a. 1 b. -1 c. -11 d. 11

B

Exhibit 14-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 83. Refer to Exhibit 14-5. The least squares estimate of the Y intercept is a. 1 b. 0 c. -1 d. 3

B

Exhibit 14-9 A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). X = 90 (Y - )(X - ) = 466 Y = 170 (X - )2 = 234 n = 10 (Y - )2 = 1434 SSE = 505.98 102. Refer to Exhibit 14-9. The least squares estimate of b1 equals a. 0.923 b. 1.991 c. -1.991 d. -0.923

B

100. Refer to Exhibit 14-8. The Y intercept is a. -0.667 b. 0.667 c. 100 d. -100

C

22. Larger values of r2 imply that the observations are more closely grouped about the a. average value of the independent variables b. average value of the dependent variable c. least squares line d. Origin

C

3. If the coefficient of determination is a positive value, then the coefficient of correlation a. must also be positive b. must be zero c. can be either negative or positive d. must be larger than 1

C

32. In a regression analysis, the variable that is being predicted a. must have the same units as the variable doing the predicting b. is the independent variable c. is the dependent variable d. usually is denoted by x

C

41. If the coefficient of correlation is -0.4, then the slope of the regression line a. must also be -0.4 b. can be either negative or positive c. must be negative d. must be 0.16

C

55. In regression analysis if the dependent variable is measured in dollars, the independent variable a. must also be in dollars b. must be in some units of currency c. can be any units d. cannot be in dollars

C

6. The model developed from sample data that has the form of is known as a. regression equation b. correlation equation c. estimated regression equation d. regression model

C

66. Refer to Exhibit 14-1. The coefficient of determination is a. 0.7096 b. - 0.7906 c. 0.625 d. 0.375

C

70. Refer to Exhibit 14-2. The least squares estimate of b0 (intercept)equals a. 1 b. -1 c. 6 d. 5

C

71. Refer to Exhibit 14-2. The point estimate of y when x = 10 is a. -10 b. 10 c. -4 d. 4

C

72. Refer to Exhibit 14-2. The sample correlation coefficient equals a. 0 b. +1 c. -1 d. -0.5

C

73. Refer to Exhibit 14-2. The coefficient of determination equals a. 0 b. -1 c. +1 d. -0.5

C

8. In regression analysis, the unbiased estimate of the variance is a. coefficient of correlation b. coefficient of determination c. mean square error d. slope of the regression equation

C

81. Refer to Exhibit 14-4. The t statistic for testing the significance of the slope is a. 1.80 b. 1.96 c. 6.708 d. 0.555

C

91. Refer to Exhibit 14-6. The coefficient of determination (r2) equals a. 0.7071 b. -0.7071 c. 0.5 d. -0.5

C

95. Refer to Exhibit 14-7. The coefficient of determination equals a. 0.3162 b. -0.3162 c. 0.10 d. -0.10

C

97. Refer to Exhibit 14-8. The sum of squares due to error (SSE) is a. -156 b. 234 c. 1870 d. 1974

C

If the coefficient of determination is a positive value, then the regression equation a. must have a positive slope b. must have a negative slope c. could have either a positive or a negative slope d. must have a positive y intercept

C. could have either a positive or a negative slope

In regression analysis if the dependent variable is measured in dollars, the independent variable

Can be in any units

The sampling distribution for a goodness of fit test is the

Chi-square distribution

A measure of the strength of the relationship between two variables is the

Correlation

103. Refer to Exhibit 14-9. The least squares estimate of b0 equals a. 0.923 b. 1.991 c. -1.991 d. -0.923

D

110. Refer to Exhibit 14-10. The coefficient of correlation is a. 0.1905 b. -0.1905 c. 0.4364 d. -0.4364

D

16. A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an a. increase of $4 in advertising is associated with an increase of $4,000 in sales b. increase of $1 in advertising is associated with an increase of $4 in sales c. increase of $1 in advertising is associated with an increase of $34,000 in sales d. increase of $1 in advertising is associated with an increase of $4,000 in sales

D

18. In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then a. there is a positive correlation between X and Y b. if X is increased, Y must also increase c. if Y is increased, X must also increase d. None of these alternatives is correct.

D

33. Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained. = 120 - 10 X Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to a. increase by 120 units b. increase by 100 units c. increase by 20 units d. decease by 20 units

D

36. If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is a. 0.80% b. 80% c. 0.64% d. 64%

D

38. In regression analysis, if the independent variable is measured in pounds, the dependent variable a. must also be in pounds b. must be in some unit of weight c. cannot be in pounds d. can be any units

D

39. If there is a very weak correlation between two variables, then the coefficient of determination must be a. much larger than 1, if the correlation is positive b. much smaller than -1, if the correlation is negative c. much larger than one d. None of these alternatives is correct.

D

4. In regression analysis, the model in the form is called a. regression equation b. correlation equation c. estimated regression equation d. regression model

D

42. If the coefficient of correlation is a negative value, then the coefficient of determination a. must also be negative b. must be zero c. can be either negative or positive d. must be positive

D

48. If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is a. 0.10 b. 0.25 c. 0.40 d. 0.80

D

50. A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 60 - 8X The above equation implies that an a. increase of $1 in price is associated with a decrease of $8 in sales b. increase of $8 in price is associated with an decrease of $52,000 in sales c. increase of $1 in price is associated with a decrease of $52 in sales d. increase of $1 in price is associated with a decrease of $8000 in sales

D

51. In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is a. 0.20 b. 1.67 c. 0.60 d. 0.40

D

56. If there is a very strong correlation between two variables then the coefficient of determination must be a. much larger than 1, if the correlation is positive b. much smaller than -1, if the correlation is negative c. any value larger than 1 d. None of these alternatives is correct.

D

57. If the coefficient of correlation is 0.90, then the coefficient of determination a. is also 0.9 b. is either 0.81 or -0.81 c. can be either negative or positive d. must be 0.81

D

60. Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. = 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is a. $8,050 b. $130 c. $130,000 d. $1,300,000

D

61. If the coefficient of correlation is a positive value, then a. the intercept must also be positive b. the coefficient of determination can be either negative or positive, depending on the value of the slope c. the regression equation could have either a positive or a negative slope d. the slope of the line must be positive

D

80. Refer to Exhibit 14-4. To perform an F test, the p-value is a. less than .01 b. between .01 and .025 c. between .025 and .05 d. between .05 and 0.1

D

85. Refer to Exhibit 14-5. The coefficient of correlation is a. 0 b. -1 c. 0.5 d. 1

D

86. Refer to Exhibit 14-5. The coefficient of determination is a. 0 b. -1 c. 0.5 d. 1

D

98. Refer to Exhibit 14-8. The mean square error (MSE) is a. 1870 b. 13 c. 1974 d. 935

D

Exhibit 14-6 For the following data the value of SSE = 0.4130. y Dependent Variable x Independent Variable 15 4 17 6 23 2 17 4 88. Refer to Exhibit 14-6. The slope of the regression equation is a. 18 b. 24 c. 0.707 d. -1.5

D

Exhibit 14-7 You are given the following information about y and x. y Dependent Variable x Independent Variable 5 4 7 6 9 2 11 4 92. Refer to Exhibit 14-7. The least squares estimate of b1 (slope) equals a. -10 b. 10 c. 0.5 d. -0.5

D

Exhibit 14-8 The following information regarding a dependent variable Y and an independent variable X is provided X = 90 Y - )(X - ) = -156 Y = 340 (X - )2 = 234 n = 4 Y - )2 = 1974 SSR = 104 96. Refer to Exhibit 14-8. The total sum of squares (SST) is a. -156 b. 234 c. 1870 d. 1974

D

pu - po = 0

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 n1 = 500 Number of accidents = 180 Over Age of 18 n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is

μ1 -μ2 = 0

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 n1 = 80 MeanX1 = $10.80 Omega1= $2.00 Company 2 n2 = 60 MeanX1 = $10.00 Omega1=$1.50 Refer to Exhibit 10-13. The null hypothesis for this test is

3

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is

should not be rejected

Exhibit 10-5 The following information was obtained from matched samples. Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis

0.50

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A: Sample size 80 Sample mean $16.75 Population standard deviation $1.00 Company B: Sample size 60 Sample mean $16.25 Population standard deviation $0.95 Refer to Exhibit 10-8. A point estimate for the difference between the two sample means is

2.0

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Refer to Exhibit 10-9. The mean for the differences is

2.256

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Refer to Exhibit 10-9. The test statistic is

2.25

Exhibit 11-2 We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A has a sample standard deviation of 30 while a sample of 16 days of sales from store B has a sample standard deviation of 20. Refer to Exhibit 11-2. The test statistic is

should not be rejected

Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. Refer to Exhibit 11-3. At 95% confidence, the null hypothesis

σ2 ≤ 0.003

Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. Refer to Exhibit 11-3. The null hypothesis is

greater than 0.10

Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. Refer to Exhibit 11-3. The p-value for this test is

12.68

Exhibit 11-5 n = 14 s = 20 H0: σ2 ≤ 500 Ha: σ2 > 500 Refer to Exhibit 11-5. The test statistic for this problem equals

should be rejected

Exhibit 11-6 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. At 95% confidence, the null hypothesis

2.4

Exhibit 11-6 We want to test the hypothesis that the population variances are equal. Refer to Exhibit 11-6. The test statistic for this problem equals

0.10

Exhibit 11-7 We want to test the hypothesis that population A has a larger variance than population B. Refer to Exhibit 11-7. The p-value is approximately

90

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 12-2. The expected number of freshmen is

greater than 0.1

Exhibit 12-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 12-2. The p-value is

48

Exhibit 12-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. Refer to Exhibit 12-3. The expected frequency of those who received medication and were cured is

1

Exhibit 12-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. Refer to Exhibit 12-3. The number of degrees of freedom associated with this problem is

less than .005

Exhibit 12-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. Refer to Exhibit 12-3. The p-value is

3.84

Exhibit 12-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. We are interested in determining whether or not the medication was effective in curing the common cold. Refer to Exhibit 12-3. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

proportions have not changed significantly

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. The conclusion of the test is that the

105

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. The expected frequency for the Business College is

5.991

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

multinomial population

Exhibit 12-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. This problem is an example of a

62.5

Exhibit 12-5 The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 12-5. The test statistic for this test of independence is

2

Exhibit 12-7 You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83, and the standard deviation equals 4.53. Refer to Exhibit 12-7. The calculated value for the test statistic equals

greater than 0.1

Exhibit 12-7 You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83, and the standard deviation equals 4.53. Refer to Exhibit 12-7. The p-value is

500

Exhibit 13-1 SSTR = 6,750 H0: μ1=μ2=μ3=μ4 SSE = 8,000 Ha: at least one mean is different nT = 20 Refer to Exhibit 13-1. The mean square within treatments (MSE) equals

greater than 0.10

Exhibit 13-2 Refer to Exhibit 13-2. The null hypothesis is to be tested at the 5% level of significance. The p-value is

should not be rejected

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. Refer to Exhibit 13-3. The null hypothesis

50.00

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The mean square between treatments (MSTR) is

10

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 13-4. The mean square within treatments (MSE) is

60

Exhibit 13-5 Part of an ANOVA table is shown below. Refer to Exhibit 13-5. The mean square between treatments (MSTR) is

4

Exhibit 13-5 Part of an ANOVA table is shown below. Refer to Exhibit 13-6. The number of degrees of freedom corresponding to between treatments is

are not equal

Exhibit 13-6 Part of an ANOVA table is shown below. Refer to Exhibit 13-6. The conclusion of the test is that the means

.64

Exhibit 17-1 Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used. Refer to Exhibit 17-1. An estimate of the seasonal-irregular component for Quarter 3 of Year 1 is

22.5

Exhibit 17-2 Consider the following time series. t 1 2 3 4 Yi 4 7 9 10 Refer to Exhibit 17-2. The forecast for period 10 is

2.5

Exhibit 17-2 Consider the following time series. t 1 2 3 4 Yi 4 7 9 10 Refer to Exhibit 17-2. The intercept, b0, is

-6.7

Exhibit 17-3 Consider the following time series. Refer to Exhibit 17-3. The forecast for period 10 is

0.0074

Exhibit 18-1 Fifteen people were given two types of cereal, Brand X and Brand Y. Two people preferred Brand X and thirteen people preferred Brand Y. We want to determine whether or not customers prefer one brand over the other. Refer to Exhibit 18-1. The p-value for this test is

binomial

Exhibit 18-1 Fifteen people were given two types of cereal, Brand X and Brand Y. Two people preferred Brand X and thirteen people preferred Brand Y. We want to determine whether or not customers prefer one brand over the other. Refer to Exhibit 18-1. To test the null hypothesis, the appropriate probability distribution to use is

0.1336

Exhibit 18-3 It is believed that the median yearly income in a suburb of Atlanta is $70,000. A sample of 67 residents was taken. Thirty-eight had yearly incomes above $70,000, 26 had yearly incomes below $70,000, and 3 had yearly incomes equal to $70,000. The null hypothesis to be tested is H0: median = $70,000. Refer to Exhibit 18-3. The p-value for this test is

is a significant difference between the proportions

Exhibit 18-6 Forty-one individuals from a sample of 60 indicated they oppose legalized abortion. We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion. Refer to Exhibit 18-6. The conclusion is that there

Z=2.88

Exhibit 18-7 Two faculty members ranked 12 candidates for scholarships. Calculate the Spearman rank-correlation coefficient and test it for significance. Use a .02 level of significance. Refer to Exhibit 18-7. The value of test-statistics for testing significance of rank-correlation is

2.00

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-4. The test statistic is

0.1056

Exhibit 9-5 A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. Refer to Exhibit 9-5. The p-value is

c

If only MSE is known, you can compute the a. r square b. coefficient of determination c. standard error d. all of these alternatives are correct

c

If the coefficient of correlation is -0.4, then the slope of the regression line a. must also be -0.4 b. can be either negative or positive c. must be negative d. must be 0.16

d

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is a. 0.80% b. 80% c. 0.64% d. 64%

d

If the coefficient of correlation is 0.90, then the coefficient of determination a. is also 0.9 b. is either 0.81 or -0.81 c. can be either negative or positive d. must be 0.81

d

If the coefficient of correlation is a negative value, then the coefficient of determination a. must also be negative b. must be zero c. can be either negative or positive d. must be positive

b

If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 0.90% b. is 90%. c. is 81% d. 0.81%

c

If the coefficient of determination is a positive value, then the coefficient of correlation a. must also be positive b. must be zero c. can be either negative or positive d. must be larger than 1

b

If the coefficient of determination is equal to 1, then the coefficient of correlation a. must also be equal to 1 b. can be either -1 or +1 c. can be any value between -1 to +1 d. must be -1

will decrease

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error

a

In a regression analysis, the error term ε is a random variable with a mean or expected value of a. zero b. one c. any positive value d. any value

a

In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is a. -0.7 b. +0.7 c. 0.49 d. -0.49

c

In a regression analysis, the variable that is being predicted a. must have the same units as the variable doing the predicting b. is the independent variable c. is the dependent variable d. usually is denoted by x

d

In a regression and correlation analysis if r2 = 1, then a. SSE = SST b. SSE = 1 c. SSR = SSE d. SSR = SST

b

In a regression and correlation analysis if r2 = 1, then a. SSE must also be equal to one b. SSE must be equal to zero c. SSE can be any positive value d. SSE must be negative

d

In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then a. there is a positive correlation between X and Y b. if X is increased, Y must also increase c. if Y is increased, X must also increase d. None of these alternatives is correct.

40

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

a

In the following estimated regression equation a. b1 is the slope b. b1 is the intercept c. b0 is the slope d. None of these alternatives is correct.

b

It is possible for the coefficient of determination to be a. larger than 1 b. less than one c. less than -1 d. None of these alternatives is correct.

c

Larger values of r2 imply that the observations are more closely grouped about the a. average value of the independent variables b. average value of the dependent variable c. least squares line d. origin

A population where each element of the population is assigned to one and only one of several classes or categories is a

Multinomial population

If there is a very strong correlation between two variables then the coefficient of determination must be

None of these alternatives is correct.

In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then

None of these alternatives is correct.

If the coefficient of determination is 0.81, the coefficient of correlation

None of these answers are correct.

In a simple regression analysis (where y is a dependent and x an independent variable), if the y intercept is positive, then

None of these answers are correct.

if there is a very strong correlation between two variables, then the coefficient of correlation must be

None of these answers are correct.

In a simple regression analysis (where y is a dependent and x an independent variable), if the y intercept is positive, then

None of these answers is correct.

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is

Not enough information is provided to answer this question.

There is a statistically significant difference in the average final examination scores between the two classes.

Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.) Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

c

Regression analysis is a statistical procedure for developing a mathematical equation that describes how a. one independent and one or more dependent variables are related b. several independent and several dependent variables are related c. one dependent and one or more independent variables are related d. None of these alternatives is correct.

d

Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained. = 120 - 10 X Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to a. increase by 120 units b. increase by 100 units c. increase by 20 units d. decease by 20 units

d

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. = 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is a. $8,050 b. $130 c. $130,000 d. $1,300,000

b

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4 X Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is a. $900 b. $900,000 c. $40,500 d. $505,000

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

Residual

In analysis of variance, the dependent variable is called the

Response variable

In a regression analysis if r2 = 1, then

SSE must be equal to zero

In a regression and correlation analysis if r2 = 1, then

SSE must be equal to zero

In a regression analysis if r2 = 1, then

SSR = SST

The correct relationship between SST, SSR, and SSE is given by

SSR = SST - SSE

The multiple coefficient of determination is

SSR/SST

Which of the following is correct

SST = SSR + SSE

Which of the following is correct?

SST = SSR + SSE

Which of the following is correct? 1. SST = (SSR)2 2. SSR = SSE + SST 3. SSE = SSR + SST 4. SST = SSR + SSE

SST = SSR + SSE

In simple linear regression analysis, which of the following is not true?

The F test and the t test may or may not yield the same conclusion.

a correlation measure based on rank-ordered data for two variables

The Spearman rank-correlation coefficient is

H0: μ ≤ 21.80 Ha: μ > 21.80

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

2.45

The critical value of F at 95% confidence when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

121

The degrees of freedom for a contingency table with 12 rows and 12 columns is

10

The degrees of freedom for a contingency table with 6 rows and 3 columns is

rejecting a true null hypothesis

The level of significance in hypothesis testing is the probability of

number of rows minus 1 times number of columns minus 1

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

between 0.025 to 0.05

The producer of a certain bottling equipment claims that the variance of all their filled bottles is 0.027 or less. A sample of 30 bottles showed a standard deviation of 0.2. The p-value for the test is

ordinal scale

The scale of measurement that is used to rank order the observation for a variable is called the

d

The standard error is the a. t-statistic squared b. square root of SSE c. square root of SST d. square root of MSE

standard deviation of the sampling distribution of (Mean x)1 - (Mean x)2

The standard error of (Mean x)1 - (Mean x)2 is the

Which of the following is a characteristic of a binomial experiment

The trials are independent

Refer to Exhibit 11-6. The point estimate for the difference between the two population proportions in favor of this product is Answers: a. 0.02 b. 100 c. 52 d. 0.44

a

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

a dummy variable

The variable of interest in an ANOVA procedure is called

a factor

Scatter diagram

a graph of bi-variate data in which the independent variable is on the horizontal axis and the dependent variable is on the vertical axis

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see

a horizontal band of points centered near zero

Coefficient of determination

a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation

Correlation coefficient

a measure of the strength of the linear relationship between two variables

Multinomial population

a population in which each element is assigned to one and only one of several categories. The multinomial distribution extends the binomial distribution form two to three or more outcomes

Least squares method

a procedure used to develop the estimated regression equation. The objective is to minimize

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

a qualitative variable

Goodness of fit test

a statistical test conducted to determine whether to reject a hypothesized probability distribution for a population

Contingency table

a table used to summarize observed and expected frequencies for a test of independence

In regression analysis, which of the following is not a required assumption about the error term ε? a. The expected value of the error term is one. b. The variance of the error term is the same for all values of X. c. The values of the error term are independent. d. The error term is normally distributed.

a. The expected value of the error term is one.

The coefficient of determination a. cannot be negative b. is the square root of the coefficient of correlation c. is the same as the coefficient of correlation d. can be negative or positive

a. cannot be negative

In regression and correlation analysis, if SSE and SST are known, then with this information the a. coefficient of determination can be computed b. slope of the line can be computed c. Y intercept can be computed d. x intercept can be computed

a. coefficient of determination can be computed

SSE can never be a. larger than SST b. smaller than SST c. equal to 1 d. equal to zero

a. larger than SST

A least squares regression line a. may be used to predict a value of y if the corresponding x value is given b. implies a cause-effect relationship between x and y c. can only be determined if a good linear relationship exists between x and y d. None of these alternatives is correct.

a. may be used to predict a value of y if the corresponding x value is given

If the coefficient of correlation is a positive value, then the slope of the regression line a. must also be positive b. can be either negative or positive c. can be zero d. cannot be zero

a. must also be positive

Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be a. narrower b. wider c. the same d. None of these alternatives is correct

a. narrower

The interval estimate of an individual value of y for a given value of x is a. prediction interval estimate b. confidence interval estimate c. average regression d. x versus y correlation interval

a. prediction interval estimate

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as a. regression equation b. correlation equation c. estimated regression equation d. regression model

a. regression equation

If two variables, x and y, have a good linear relationship, then a. there may or may not be any causal relationship between x and y b. x causes y to happen c. y causes x to happen d. None of these alternatives is correct.

a. there may or may not be any causal relationship between x and y

In a regression analysis, the error term ε is a random variable with a mean or expected value of a. zero b. one c. any positive value d. any value

a. zero

If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the

alt. hypothesis should say m1-m2<0

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be

at least 5

Excel's ____ function is used to perform a test of independence. Answers: a. t-Test: Two Sample Assuming Equal Variances b. CHISQ.TEST c. NORM.S.DIST d. z-Test: Two Sample for Means

b

Refer to Exhibit 11-1. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals Answers: a. 7.81473 b. 5.99147 c. 7.37776 d. 9.34840

b

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4 X Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is a. $900 b. $900,000 c. $40,500 d. $505,000

b. $900,000

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is a. 0.6667 b. 0.6000 c. 0.4000 d. 1.5000

b. 0.6000

In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is a. 0.35 b. 0.65 c. 2.85 d. 0.45

b. 0.65

f all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is a. 0 b. 1 c. either 1 or -1, depending upon whether the relationship is positive or negative d. could be any value between -1 and 1

b. 1

In simple linear regression analysis, which of the following is not true? a. The F test and the t test yield the same conclusion. b. The F test and the t test may or may not yield the same conclusion. c. The relationship between X and Y is represented by means of a straight line. d. The value of F = t2.

b. The F test and the t test may or may not yield the same conclusion.

If the coefficient of determination is equal to 1, then the coefficient of correlation a. must also be equal to 1 b. can be either -1 or +1 c. can be any value between -1 to +1 d. must be -1

b. can be either -1 or +1

The interval estimate of the mean value of y for a given value of x is a. prediction interval estimate b. confidence interval estimate c. average regression d. x versus y correlation interval

b. confidence interval estimate

If the coefficient of determination is 0.81, the coefficient of correlation a. is 0.6561 b. could be either + 0.9 or - 0.9 c. must be positive d. must be negative

b. could be either + 0.9 or - 0.9

If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 40% b. is 16%. c. is 4% d. can be any positive value

b. is 16%.

If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable a. is 0.90% b. is 90%. c. is 81% d. 0.81%

b. is 90%.

The coefficient of correlation a. is the square of the coefficient of determination b. is the square root of the coefficient of determination c. is the same as r-square d. can never be negative

b. is the square root of the coefficient of determination

It is possible for the coefficient of determination to be a. larger than 1 b. less than one c. less than -1 d. None of these alternatives is correct.

b. less than one

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called a. the correlation model b. the regression model c. correlation analysis d. None of these alternatives is correct.

b. the regression model

Correlation analysis is used to determine a. the equation of the regression line b. the strength of the relationship between the dependent and the independent variables c. a specific value of the dependent variable for a given value of the independent variable d. None of these alternatives is correct.

b. the strength of the relationship between the dependent and the independent variables

In regression analysis, the independent variable is a. used to predict other independent variables b. used to predict the dependent variable c. called the intervening variable d. the variable that is being predicted

b. used to predict the dependent variable

Exhibit 12-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 Refer to Exhibit 12-4. To perform an F test, the p-value is

between .05 and 0.1

If the coefficient of determination is a positive value, then the coefficient of correlation a. must also be positive b. must be zero c. can be either negative or positive d. must be larger than 1

c. can be either negative or positive

The model developed from sample data that has the form of is known as a. regression equation b. correlation equation c. estimated regression equation d. regression model

c. estimated regression equation

In a regression analysis, the variable that is being predicted a. must have the same units as the variable doing the predicting b. is the independent variable c. is the dependent variable d. usually is denoted by x

c. is the dependent variable

Larger values of r2 imply that the observations are more closely grouped about the a. average value of the independent variables b. average value of the dependent variable c. least squares line d. origin

c. least squares line

In regression analysis, the unbiased estimate of the variance is a. coefficient of correlation b. coefficient of determination c. mean square error d. slope of the regression equation

c. mean square error

Regression analysis is a statistical procedure for developing a mathematical equation that describes how a. one independent and one or more dependent variables are related b. several independent and several dependent variables are related c. one dependent and one or more independent variables are related d. None of these alternatives is correct.

c. one dependent and one or more independent variables are related

If MSE is known, you can compute the a. r square b. coefficient of determination c. standard error d. all of these alternatives are correct

c. standard error

In regression analysis if the dependent variable is measured in dollars, the independent variable

can be any units

If the coefficient of determination is equal to 1, then the coefficient of correlation

can be either -1 or +1

If the coefficient of correlation is a negative value, then the coefficient of determination

can be either negative or positive

If the coefficient of determination is a positive value, then the coefficient of correlation

can be either negative or positive

The numerical value of the coefficient of determination

can be larger or smaller than the coefficient of correlation

Both the hypothesis test for proportions of a multinomial population and the test of independence employ the

chi squared

The sampling distribution for a goodness of fit test is the

chi-square distribution

In simple linear regression, r2 is the

coefficient of determination

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the

coefficient of determination

In regression and correlation analysis, if SSE and SST are known, then with this information the

coefficient of determination can be computed

The interval estimate of the mean value of y for a given value of x is the

confidence interva

The interval estimate of the mean value of y for a given value of x is the

confidence interval

A measure of the strength of the relationship between two variables is the

correlation coefficient

If the coefficient of determination is a positive value, then the regression equation

could have either a positive or a negative slope

Refer to Exhibit 11-1. The calculated value for the test statistic equals Answers: a. -2 b. 20 c. 2 d. 4

d

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is Answers: a. k-1 b. n-1 c. a chi-square distribution is not used d. number of rows minus 1 times number of columns minus 1

d

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. = 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is a. $8,050 b. $130 c. $130,000 d. $1,300,000

d. $1,300,000

Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained. = 80 + 6.2 X Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is a. $62,080 b. $142,000 c. $700 d. $700,000

d. $700,000

In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is a. 0.20 b. 1.67 c. 0.60 d. 0.40

d. 0.40

If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is a. 0.10 b. 0.25 c. 0.40 d. 0.80

d. 0.80

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is a. 0.80% b. 80% c. 0.64% d. 64%

d. 64%

If there is a very weak correlation between two variables then the coefficient of correlation must be a. much larger than 1, if the correlation is positive b. much smaller than 1, if the correlation is negative c. any value larger than 1 d. None of these alternatives is correct.

d. None of these alternatives is correct.

If there is a very weak correlation between two variables, then the coefficient of determination must be a. much larger than 1, if the correlation is positive b. much smaller than 1, if the correlation is negative c. much larger than one d. None of these alternatives is correct.

d. None of these alternatives is correct.

In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then a. there is a positive correlation between X and Y b. if X is increased, Y must also increase c. if Y is increased, X must also increase d. None of these alternatives is correct.

d. None of these alternatives is correct.

In a regression and correlation analysis if r2 = 1, then a. SSE = SST b. SSE = 1 c. SSR = SSE d. SSR = SST

d. SSR = SST

In regression analysis, if the independent variable is measured in pounds, the dependent variable a. must also be in pounds b. must be in some unit of weight c. cannot be in pounds d. can be any units

d. can be any units

Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained. = 120 - 10 X Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to a. increase by 120 units b. increase by 100 units c. increase by 20 units d. decease by 20 units

d. decease by 20 units

A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation = 9 - 3X The above equation implies that if the price is increased by $1, the demand is expected to a. increase by 6 units b. decrease by 3 units c. decrease by 6,000 units d. decrease by 3,000 units

d. decrease by 3,000 units

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an a. increase of $4 in advertising is associated with an increase of $4,000 in sales b. increase of $1 in advertising is associated with an increase of $4 in sales c. increase of $1 in advertising is associated with an increase of $34,000 in sales d. increase of $1 in advertising is associated with an increase of $4,000 in sales

d. increase of $1 in advertising is associated with an increase of $4,000 in sales

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 50,000 - 8X The above equation implies that an a. increase of $1 in price is associated with a decrease of $8 in sales b. increase of $8 in price is associated with an increase of $8,000 in sales c. increase of $1 in price is associated with a decrease of $42,000 in sales d. increase of $1 in price is associated with a decrease of $8000 in sales

d. increase of $1 in price is associated with a decrease of $8000 in sales

In regression analysis, the model in the form is called a. regression equation b. correlation equation c. estimated regression equation d. regression model

d. regression model

The standard error is the a. t-statistic squared b. square root of SSE c. square root of SST d. square root of MSE

d. square root of MSE

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation mc013-1.jpg = 9 - 3x The above equation implies that if the price is increased by $1, the demand is expected to

decrease by 3,000 units

In regression analysis, the variable that is being predicted is the

dependent variable

Refer to Exhibit 11-4. The conclusion of the test (at 95% confidence) is that the

distribution is uniform

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

dummy variable

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a contingency test probability test goodness of fit test None of these alternatives is correct.

goodness of fit test

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

goodness to fit test

Residual plot

graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid

Refer to Exhibit 11-7. The p-value is

greater than 0.1

Exhibit 15-2. A regression model between sales (y in $1,000), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function y-hat = 7 - 3x1 + 5x2. For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2. The coefficient of x2 indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to

increase by $5,000

A multiple regression model has the form y-hat = 7 + 2 x1 + 9 x2As x1 increase by 1 unit (holding x2 constant), y-hat is expected to

increase by 2 units

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an

increase of $1 in advertising is associated with an increase of $4,000 in sales

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation mc015-1.jpg = 50,000 + 6 x The above equation implies that an

increase of $1 in advertising is associated with an increase of $6,000 in sales

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 60 - 8X The above equation implies that an

increase of $1 in price is associated with a decrease of $8000 in sales

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation mc014-1.jpg = 50,000 - 8x The above equation implies that an

increase of $1 in price is associated with a decrease of $8000 in sales

The test for goodness of fit

is always a one-tail test with the rejection region occurring in the upper tail

In a regression analysis, the variable that is being predicted

is the dependent variable

The coefficient of correlation

is the square root of the coefficient of determination

If a qualitative variable has k levels, the number of dummy variables required is

k − 1

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is the

least squares method

It is possible for the coefficient of determination to be

less than one

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

matched samples

A least squares regression line

may be used to predict a value of y if the corresponding x value is given

In regression analysis, the unbiased estimate of the variance is

mean square error

A multiple regression model has

more than one independent variable

In multiple regression analysis, the correlation among the independent variables is termed

multicollinearity

A population where each element of the population is assigned to one and only one of several classes or categories is a

multinomial population

Refer to Exhibit 11-7. This problem is an example of a

multinomial population

A measure of goodness of fit for the estimated regression equation is the

multiple coefficient of determination

Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be

narrower

Application of the least squares method results in values of the y intercept and the slope that minimizes the sum of the squared deviations between the

observed values of the dependent variable and the estimated values of the dependent variable

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

one dependent and one or more independent variables are related

In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the

overall sample mean

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

residual

In regression analysis, an outlier is an observation whose

residual is much larger than the rest of the residual values

All of the following tests follow a chi-square distribution except

test for the difference between two means

All of the following tests follow a chi-square distribution except test of independence of two variables test for the difference between two proportions test for proportions of a multinomial population test for the difference between two means

test for the difference between two means

ANOVA table

the analysis of variance table used to summarize the computations associated with the F test for significance

a

the coefficient of determination a. cannot be negative b. is the square root of the coefficient of correlation c. is the same as the coefficient of correlation d. can be negative or positive

ith residual

the difference between the observed value of the dependent variable and the value predicted using the estimated regression equation; for the ith observation the ith residual is yi-y^i

Regression model

the equation describing how y is related to x and an error term; in simple linear regression, the regression model is

Regression equation

the equation that describes how the mean or expected value of the dependent variable is related to the independent variable; in simple linear regression E(y) = Bo + B1x

Estimated regression equation

the estimate of the regression equation developed from sample data by using the least squares method. For simple linear regression, the estimated regression equation is

Confidence interval

the interval estimate of the mean value of y for a given value of x

Which of the following does not need to be known in order to compute the p-value?

the level of significance

The adjusted multiple coefficient of determination is adjusted for

the number of independent variables

The properties of a multinomial experiment include all of the following except

the probability of each outcome can change from trial to trial. The probability can NOT change

What is the central limit theorem?

the random variable being observed should be the sum or mean of many independent identically distributed random variables

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

the regression model

In a multiple regression model, the variance of the error term ε is assumed to be

the same for all values of the independent variable

If the coefficient of correlation is a positive value, then

the slope of the line must be positive

To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the denominator of the test statistic should be the one with

the smaller sample variance

Standard error of the estimate

the square root of the mean square error, denoted by s. It is the estimate of o, the standard deviation of the error term e

As the goodness of fit for the estimated multiple regression equation increases

the value of the multiple coefficient of determination increases

Dependent variable

the variable that is being predicted or explained. It is denoted by y

Independent variable

the variable that is doing the predicting or explaining. It is denoted by x

The assumptions for the multinomial experiment parallel those for the binomial experiment with the exception that for the multinomial

there are three or more outcomes per trial

In multiple regression analysis

there can be several independent variables, but only one dependent variable

If two variables, x and y, have a strong linear relationship, then

there may or may not be any causal relationship between x and y

A goodness of fit test is always conducted as a

upper-tail test

In regression analysis, the independent variable is

used to predict the dependent variable

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

zero

In a regression analysis, the error term ε is a random variable with a mean or expected value of

zero