Calabrese quiz 3

The following data represent the number of flash drives sold per day at a local computer shop and their prices. Price (x) Units Sold (y) $34 3 36 4 32 6 35 5 30 9 38 2 40 1 ​ ​ a. Develop a least squares regression line and explain what the slope of the line indicates. - answering the following: a. The slope indicates that as the price goes up by $1, the number of units sold per day goes down by .7286 units AND r2 = .8556; the regression equation has accounted for 85.56% of the total sum of squares b. The slope indicates that as the price goes down by $1, the number of units sold per day goes down by .7286 units AND r2 = .8556; the regression equation has accounted for 85.56% of the total sum of squares c. The slope indicates that as the price goes up by $1, the number of units sold per day goes up by .7286 units AND r2 = .8556; the regression equation has accounted for 85.56% of the total sum of squares d. The slope indicates that as the price goes up by $1, the number of units sold per day goes down by .7286 units AND r2 = - .8556; the regression equation has accounted for 85.56% of the total sum of squares

. y^ = 29.7857 - 0.7286x The slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. b. r 2 = .8556; the regression equation has accounted for 85.56% of the total sum of squares c. rxy = -0.92 t = -5.44 < -4.032 (df = 5); p-value .01; (Excel's result: p-value = .0028); reject H o , and conclude x and y are related

As the value of the coefficient of determination increases, the a. absolute value of the regression equation's slope decreases. b. total number of degrees of freedom increases. c. goodness of fit for the estimated regression equation increases. d. value of the correlation coefficient decreases.

a

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 ​ ​ The coefficient of correlation (multiple R) is a. .7906 b. -.7906 c. .625 d. .375

a) .7906

In regression analysis, the error term ε is a random variable with a mean or expected value of a. 0. b. 1. c. μ. d. .

a) 0

The error of rejecting a true null hypothesis is a. a Type I error. b. a Type II error. c. always negligible in hypothesis testing. d. never committed in hypothesis testing

a) Type 1 error

In regression analysis, the variable that is being predicted is the a. dependent variable. b. independent variable. c. intercept variable. d. error variable.

a) dependent variable

An assumption made about the value of a population parameter is called a(n) a. hypothesis. b. conclusion. c. error. d. probability.

a) hypothesis

In the hypothesis testing procedure, α is the a. level of significance. b. critical value. c. confidence level. d. p-value.

a) level of significance

The p-value is a probability that measures the support (or lack of support) for a. the null hypothesis. b. the alternative hypothesis. c. either the null or the alternative hypothesis. d. neither the null nor the alternative hypothesis

a) null hypothesis

When the p-value is used for hypothesis testing, the null hypothesis is rejected if a. p-value α. b. α < p-value. c. p-value = 1 - α/2. d. p-value = 1 - α.

a) p-value a.

From a population of cans of coffee marked "12 ounces," a sample of 50 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of .5 ounces. a. Formulate the hypotheses to test if the mean weight of the population is at least 12 ounces. b Using the p-value approach (given p = .0034), what is your conclusion? Let α = .05.

a. H0: μ 12 ounces Ha: μ < 12 ounces . b. p-value (.0034) < .005; therefore, reject H0. The coffee cans are being underfilled

Identify the null and alternative hypotheses for the following problems. a. The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch. b. Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar. c. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn

a. H0: μ 25 Ha: μ > 25 b. H0: p .9 Ha: p < .9 c. H0: p = .75 Ha: p ≠ .75

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are a. H0: μ ≥ 700 Ha: μ < 700. b. H0: μ = 700 Ha: μ ≠ 700. c. H0: μ > 700 Ha: μ ≤ 700. d. H0: μ < 700 Ha: μ ≥ 700.

a. H0: μ ≥ 700 Ha: μ < 700.

In a regression analysis, the coefficient of determination is .4225. The coefficient of correlation in this situation is a. .65 if b1 is positive. b. .1785. c. -.18 if b1 is negative. d. .4225.

a.) .65 if b1 is positive.

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 ​ ​ The least squares estimate of the slope is a. 1. b. 2. c. 3. d. 4.

a.) 1

In the following estimated regression equation = b0 + b1x, a. b1 is the slope. b. b1 is the intercept. c. b1x is the slope. d. b1x is the intercept.

a.) b1 is the slope.

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 (r2). d. is always larger than the value of the coefficient of determination (r2).

a.) can be equal to the value of the coefficient of determination (r2).

A least squares regression line a. can be used to predict a value of y if the corresponding x value is given. b. implies a cause-and-effect relationship between x and y. c. can only be determined if a good linear relationship exists between x and y. d. ensures that the predictions of y outside the range of the values of x are valid.

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

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

a.) regression equation

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 a. ​horizontal band of points centered near zero. b. widening band of points around the x-axis. c. band of points having a slope consistent with that of the regression equation. d. parabolic band of points centered at the origin.

a.) ​horizontal band of points centered near zero.

Shown below is an Excel output for regression analysis relating y (dependent variable) and x (independent variable) select the best answer.. Summary Output Regression Statistics Multiple R 0.7732 R Square 0.5978 Standard Error 3.0414 Observations 10 ​ ANOVA df SS MS F Significance F Regression 1 110 110 11.89 0.009 Residual 8 74 9.25 Total 9 184 Coefficients Standard Error t Stat P-value Intercept 39.222 5.942 6.60 0.000 m -0.556 0.161 -3.45 0.009 a. X any Y are inversely related b. X and Y are not related because of a negative slope m = -0.556 c. X is approximately related to Y d. X and Y are related

b)

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. ​ = 500 + 4x ​ 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, the coefficient of correlation is .16. The coefficient of determination in this situation is a. .4000. b. .0256. c. 4.00. d. 2.56.

b) .0256

. If the null hypothesis is rejected in hypothesis testing, a. no conclusions can be drawn from the test. b. the alternative hypothesis is true. c. the data must have been accumulated incorrectly. d. the sample size has been too small.

b) alternative hypothesis is true

If the coefficient of determination is equal to 1, then the coefficient of correlation a. must also be +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

In regression analysis, the response variable is the a. independent variable. b. dependent variable. c. slope of the regression function. d. intercept.

b) dependent variable

In hypothesis testing, the tentative assumption about the population parameter is a. the alternative hypothesis. b. the null hypothesis. c. either the null or the alternative. d. neither the null nor the alternative.

b) null hypothesis

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. estimation analysis.

b) regression model

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is the​ a. ​standard error. b. ​residual. c. ​prediction interval. d. ​variance.

b) residual

In regression analysis, the independent variable is a. used to predict other independent variables. b. used to predict the dependent variable. c. the variable that is not used for prediction. d. the variable that is being predicted.

b) used to predict the dependent variable

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are a. H0: μ < 40.1 Ha: μ ≥ 40.1. b. H0: μ ≥ 40.1 Ha: μ < 40.1. c. H0: μ > 40.1 Ha: μ ≤ 40.1. d. H0: μ = 40.1 Ha: μ ≠ 40.1.

b. H0: μ ≥ 40.1 Ha: μ < 40.1.

You are given the following information about y and x. Dependent Variable (y) Independent Variable (x) 12 4 3 6 7 2 6 4 ​ The least squares estimate of the slope or b1 equals a. 1. b. -1. c. -11. d. 11.

b.) -1

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 ​ The least squares estimate of the slope or b1 equals a. 1. b. -1. c. 6. d. -5.

b.) -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 ​ ​ The least squares estimate of the y-intercept is a. 1. b. 2. c. 3. d. 4.

b.) 2

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

b.) 90%

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

b.) confidence interval estimate.

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 a. is 0. b. is 1. c. is either 1 or -1, depending upon whether the relationship is positive or negative. d. could be any value between -1 and 1.

b.) is 1

The coefficient of correlation a. is the square of the r-square. b. is the square root of the r-square. c. can never be equal to r-square. d. can never be negative.

b.) is the square root of the r-square.

Correlation analysis is used to determine a. the equation of the regression line. b. the strength of the linear 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. a cause-and-effect relationship between the dependent and the independent variables.

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

If the coefficient of correlation is -.4, then the slope of the regression line a. must also be -.4. b. can be either negative or positive. c. must be negative. d. must be .16.

c) must be negative.

The level of significance, in hypothesis testing, is the probability of a. accepting a true null hypothesis. b. accepting a false null hypothesis. c. rejecting a true null hypothesis. d. rejecting a false null hypothesis.

c) rejecting a true null hypothesis

The model developed from sample data that has the form of = b0 + b1x is known as the a. regression equation. b. correlation model. c. estimated regression equation. d. regression model.

c. estimated regression equation.

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 ​ ​ The coefficient of determination (r - squared) is... a. .7906. b. -.7906. c. .625. d. .375.

c.) .625.

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 positive or negative. d. can be larger than 1.

c.) can be either positive or negative.

. 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 measured in any units. d. cannot be in dollars.

c.) can be measured in any units

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the​ a. ​correlation coefficient. b. ​standard error of the estimate. c. ​coefficient of determination. d. ​confidence interval estimate.

c.) coefficient of determination.

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 square lines

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. one dependent, one independent, and several error variables are related.

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

Which of the following tests is used to determine whether an additional variable makes a significant contribution to a multiple regression model? a. a t test b. a z test c. an F test (p-value) d. a chi-square test

d) chi square test

In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, a. a Type I error has been committed. b. a Type II error has been committed. c. either a Type I or a Type II error has been committed. d. the correct decision has been made

d) correct decision has been made

If the null hypothesis is rejected at the 5% level of significance, it a. will always be rejected at the 1% level. b. will always not be rejected at the 1% level. c. will never be tested at the 1% level. d. may be rejected or not rejected at the 1% level.

d) may be rejected or not rejected at the 1% level

The p-value is a. the same as the z statistic. b. a sample statistic. c. a distance. d. a probability.

d) probability

Regression analysis was applied between sales (y in $1000) and advertising (x in $100) and the following estimated regression equation was obtained. ​ = 80 + 6.2x ​ 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

The following information regarding a dependent variable y and an independent variable x is provided: Σx = 90 Σ(y - )(x - ) = -156 Σy = 340 Σ(x - )2 = 234 n = 4 Σ(y - )2 = 1974 ​ The total sum of squares (SST) is a. -156. b. 234. c. 1870. d. 1974.

d.) 1974

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is a. .80%. b. 80%. c. .64%. d. 64%.

d.) 64%

All the independent variables in a multiple regression analysis a. must be quantitative. b. must be either quantitative or qualitative but not a mix of both. c. must assume only positive values. d. can be either quantitative or qualitative or both.

d.) can be either be quantitative or qualitative or both

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 measured in any units.

d.) can be measured in any units.

. 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. equal to one. d. closer or equal to zero.

d.) closer or equal to zero

In simple linear regression, r2 is the​ a. ​mean square error. b. ​correlation coefficient. c. squared residual. d. ​coefficient of determination.

d.) coefficient of determination.

A descriptive measure of the strength of linear association between two variables is the​ a. ​coefficient of determination. b. ​slope b1 of the estimated regression line. c. ​standard error of the estimate. d. ​correlation coefficient.

d.) correlation coefficient

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 - 10x ​ 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. decrease 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 6000 units. d. decrease by 3000 units.

d.) decrease by 3000 units

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: ​ = 30,000 + 4x ​ The above equation implies that an a. increase of $4 in advertising is associated with an increase of $4000 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 $4000 in sales.

d.) increase of $1 in advertising is associated with an increase of $4000 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 a. increase of $1 in price is associated with a decrease of $8 in sales. b. increase of $8 in price is associated with a 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.) increase of $1 in price is associated with a decrease of $8000 in sales.

In regression analysis, the model in the form y = + x + ε is called the a. regression equation. b. correlation model. c. estimated regression equation. d. regression model

d.) regression model

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

d.) slope of the regression line must be positive.

In a simple linear 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. the estimated regression line intercepts the positive y-axis.

d.) the estimated regression line intercepts the positive y-axis.

Assume you have noted the following prices for books and the number of pages that each book contains. Plus the result of the RA for y - hat, r2, t, p, and alpha are given below (best answerJ) Book Pages (x) Price (y) A 500 $7.00 B 700 7.50 C 750 9.00 D 590 6.50 E 540 7.50 F 650 7.00 G 480 4.50 ​ a. = 1.0416 + .0099x b. r2 = .5629 c. t = 2.54; (df = 5); p-value is between .05 and .10; (Excel results in p-value of .052); reject H0, and conclude x and y are related. a. a, b, but not c are true b. a is false, b is true, c is true c. all are true (a, b, and c) d. we accept the null

no clue go with d