data Final Exam

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Which of the following is the correct expression for computing a 100(1 - α)% confidence interval of the expected value of y?

se(y^0)

The coefficient of determination R2 is _______________.

usually higher than adjusted R2

An real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model as Rent = β0 + β1 Bedroom + β2 Bath + β3 Sqft + ε. The following ANOVA table shows a portion of the regression results. Which of the following would be the rent for a 1,000-square-foot apartment that has two bedrooms and two bathrooms?

$ 1,130

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model: Which of the following is the monthly salary of an employee that has worked for 48 months at the bank?

$ 1,226

Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales, housing starts, and commercial construction. The regression uses lumber sales (in $100,000s) as the response variable with housing starts (in 1000s)(in 1,000s) and commercial construction (in 1000s)(in 1,000s) as the explanatory variables. The estimated model is Lumber Sales = β0 + β1 Housing Starts + β2Commercial Constructions + ε. The following ANOVA table summarizes a portion of the regression results. If Housing Starts were 17,000 and Commercial Construction was 3,200, the best estimate of Lumber Sales would be ______________.

$22,290,000

An marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the model: Sales= β0 +β1 Advertising + ε. The following ANOVA table below shows a portion of the regression results. Which of the following is the prediction of Sales for a firm with Advertising of $500?

$54,500

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the coefficient of determination?

+ 1

The variance of the rates of return is 0.25 for stock X and 0.01 for stock Y. The covariance between the returns of X and Y is -0.01. The correlation of the rates of return between X and Y is _____.

-0.20

Consider the following data: = 20, sx =2, = -5, sy =4, and b1 = -0.8. The sample correlation coefficient, rxy is equal to ____.

-0.40

The sample standard deviations for x and y are 10 and 15, respectively. The covariance between x and y is −120. The correlation coefficient between x and y is _____.

-0.8

When estimating = b0 + b1x1 + b2x2, the following regression results using ANOVA were obtained. Which of the following is the prediction of if x1 = 1 and x2 = 2?

-1.9

A regression equation was estimated as = -100 + 0.5x. If x = 20,the predicted value of y is _____.

-90

Calculate the value of R2 given the ANOVA portion of the following regression output:

.151

When estimating = β0 + β1x1 + β2x2 +ε, the following regression results using ANOVA were obtained. Which of the following is the standard error of the estimate?

.96

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the standard error of the estimate?

0.1348

Calculate the value of R2 given the ANOVA portion of the following regression output:

0.151

Consider the following data: = 20, sx = 2, = -5, sy = 4, and b1 = 0.40. The sample correlation coefficient, rxy is equal to ____.

0.20

In the estimation of a multiple regression model with four explanatory variables and 25 observations,SSE = 660 and SST = 1,000.The value of adjusted R2 is the closest to ____.

0.21

^^^ When testing whether the beta coefficient is significantly greater than one, the value of the test statistic is ____.

4.33

^^^ To determine whether abnormal returns exist, which of the following competing hypotheses do you set up?

H0:α = 0; HA:α ≠ 0

Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The coefficient of determination for this sample is equal to ________.

0.273

A simple linear regression of the return of firm A (RA)on the return of firm B (RB) based on 18 observations, is = 2.2 + 0.4 RB. If the coefficient of determination from this regression is 0.09, calculate the correlation between nRA and .

0.30

In the estimation of a multiple regression model with four explanatory variables and 25 observations,SSE = 660 and SST = 1,000. Which of the following is the correct value of R2?

0.34

In the estimation of a multiple regression model with two explanatory variables and 20 observations, SSE = 550 and SST = 1,000. The value of adjusted R2 is the closest to ____.

0.39

Over the past 30 years, the sample standard deviations of the rates of return for stock X and sStock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. The correlation of the rates of return between X and Y is the closest to ____.

0.40

In the estimation of a multiple regression model with two explanatory variables and 20 observations, SSE = 550 and SST = 1000. Which of the following is the correct value of R2?

0.45

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. When testing whether the slope coefficient differs from 1, the value of the test statistic is ____.

0.66

The following table shows the number of cars sold last month by six dealers at Centreville Nissan dealership and their number of years of sales experience.

0.712

Consider the sample regression equation 100 + 10x, with an R2 value of 0.81. Which of the following is the value of the sample correlation between y and ?

0.90

When estimating = β0 + β1x1 + β2x2 +ε, the following regression results using ANOVA were obtained. Which of the following is the adjusted R2?

0.92

When estimating = β0 + β1x1 + β2x2 +ε, the following regression results using ANOVA were obtained.

0.93

The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as sx = 35.77, sy = 13.34, sxy = 447.68. Which of the following is the value of the sample correlation coefficient?

0.94

The following table shows the number of cars sold last month by six dealers at Centreville Nissan dealership and their number of years of sales experience. Management would like to use simple regression analysis to estimate monthly car sales using the number of years of sales experience. The slope of the regression equation is equal to _______.

1.00

A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the 50 states and the District of Columbia (n = 51), he collects data on the poverty rate (y, in %), the percent of the population with at least a high school education (x1), median income (x2, in $1000s), and the mortality rate per 1,000 residents (x3). He estimates the following model as y = β0 + β1 Education + β2 Income + β3 Mortality + ε. The following ANOVA table shows a portion of the regression results.

1.5

The following table shows the number of cars sold last month by six dealers at Centreville Nissan dealership and their number of years of sales experience.

1.84

^^^ When testing whether there are abnormal returns, or whether the alpha coefficient is significantly different from zero, the value of the test statistic is ____.

1.98

Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The error sum of squares for this sample is equal to ________.

13.70

A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the 50 states and the District of Columbia (n = 51), he collects data on the poverty rate (y, in %), the percent of the population with at least a high school education (x1), median income (x2, in $1000s), and the mortality rate per 1,000 residents (x3). He estimates the following model as = β0 + β1 Education + β2 Income + β3 Mortality + ε. The following ANOVA table shows a portion of the regression results. What is the poverty rate for a state where 85% of the population has at least a high school education, the median income is $50,000, and the mortality rate is 10 per 1,000 residents?

14.6 %

Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The total sum of squares for this sample is equal to ________.

18.86

An real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model as Rent = β0 + β1 Bedroom + β2 Bath + β3 Sqft + ε. The following ANOVA table shows a portion of the regression results. The standard deviation of the difference between actual rent and the estimate of rent is ____.

193

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. Which of the following is the value of the test statistic when testing whether x significantly influences y?

2.25

Given the following portion of regression results, which of the following is the value of the F(2,20) test statistic?

2.59

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model:

22.06% of the variation in Salary is explained by the variation in Service

An economist estimates the following model: y = β0 + β1x + ε. She would like to construct interval estimates for y when x equals 2. She estimates a modified model where y is the response variable and the explanatory variable is now defined as x+ = x - 2. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is the predicted value of y when x equals 2?

24.78

Consider the following sample regression equation = 200 + 10x, where y is the supply for Product A (in 1000s)(in 1,000s) and x is the price of Product A (in $). If the price of Product A is $5, then we expect supply to be _____.

250,000.

269.63

A regression equation was estimated as = 155 - 34x1 - 12x2. If x1 = 3 and x2 = 2, the predicted value of y would be _____.

Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales, housing starts, and commercial construction. The regression uses lumber sales (in $100,000s) as the response variable with housing starts (in 1000s)(in 1,000s) and commercial construction (in 1000s)(in 1,000s) as the explanatory variables. The estimated model is Lumber Sales = β0 + β1 Housing Starts + β2Commercial Contructions + ε. The following ANOVA table summarizes a portion of the regression results. The standard deviation of the difference between actual lumber sales and the estimate of those sales is ____.

29.58

The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as sx = 35.77, sy = 13.34, sxy = 447.68. The competing hypotheses are . At the 5% significance level, which of the following is the critical value of the test statistic?

3.182

`````A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β0 + β1 Price + β2 Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), and Rides is the number of rides at the amusement park. The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30, respectively. The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as According to the modified model, which of the following is the predicted value for Attendance when Price and Rides equal $85 and 30, respectively?

34,410

4.68

The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as sx = 35.77, sy = 13.34, sxy = 447.68. The competing hypotheses are . Which of the following is the value of the test statistic?

4.77

^^ When testing whether the explanatory variables Temperature and Rides are jointly significant, the error sum of squares for the restricted model is SSER = 12,343.78. Which of the following is the value of the test statistic when conducting this test?

49.58

Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The regression sum of squares for this sample is equal to ________.

5.16

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of Product A is $5, then we expect demand to be ______.

50,000

^^^ Which of the following is the value of the test statistic for testing the joint significance of the linear regression model?

50.88

A statistics student is asked to estimate y = β0 + β1x + ε. She calculates the following values: = 440, , = 1,120, n = 11. Which of the following is the value of y if x equals 2?

58.22

Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The average weekly sales for the novel when priced at $10 is equal to ________.

6.45

^^^ Which of the following is the value of the test statistic for testing the joint significance of the linear regression model?

67.23

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0 + β1Age + ε. The following table summarizes a portion of the regression results. Which of the following is the estimate of Happiness for the person who is 65 years old?

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model: How much of the variation in Salary is unexplained by the model?

77.94 %

Given the following portion of regression results, which of the following is the value of the F2,20 test statistic?

8.04

An real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model as Rent = β0 + β1 Bedroom + β2 Bath + β3 Sqft + ε. The following ANOVA table shows a portion of the regression results. The coefficient of determination indicates that __________.

80.92% of the variation in Rent is explained by the variation in the explanatory variables

Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales, housing starts, and commercial construction. The regression uses lumber sales (in $100,000s) as the response variable with housing starts (in 1000s)(in 1,000s) and commercial construction (in 1000s)(in 1,000s) as the explanatory variables. The estimated model is Lumber Sales = β0 + β1 Housing Starts + β2Commercial Constructions + ε. The following ANOVA table summarizes a portion of the regression results. The explanatory variables (Housing Starts and Commercial Construction) together explained approximately _____% of the variations in the response variable (Lumber Sales).

86% of the variation in the poverty rate is explained by the regression model.

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β0 + β1 Price + β2 Temperature + β3 Rides + ε, whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $), Temperature is the average daily temperature (in oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. Which of the following is the value of the test statistic for testing the joint significance of the linear regression model?

99.78

Given the following portion of regression results, which of the following conclusions is true with regard to the F test at the 5% significance level?

At least one of the explanatory variables is significantly related to the response variable.

^^^ Using the 95% confidence interval, what is the conclusion to the following hypothesis test:

At the 5% significance level, reject H0 and conclude that service is significant.

^^^ Using the 95% confidence interval, which of the following is the conclusion to the following hypothesis test:

At the 5% significance level, reject H0 because the interval does not contain 0.

Which of the following can be used to conduct the test for individual significance of explanatory variables?

Both, p-value approach and confidence intervals.

Which of the following Excel's functions return the correlation coefficient?

CORREL

Consider the sample regression equation: = 12 + 2x1 - 6x2 + 6x3 + 2x4. When x1 increases 1 unit and x2 increases 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y?

Decrease by 10

Consider the sample regression equation = 12 + 3x1 - 5x2 + 7x3 - 2x4. When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y?

Decrease by 7

What is the name of the variable that is used to predict another variable?

Explanatory

In a simple linear regression based on 30 observations, the following information is provided: a, Construct a 95% confidence interval for E(y) if x = 20. b. Construct a 95% prediction interval for y if x = 20.

For a specific values a 100(1 - α)% confidence interval of the expected value of y is computed as where is the standard error of and df = n - k - 1. For a specific values a 100(1 - α)% prediction interval for an individual value of y is computed as where df = n - k - 1,se is the standard error of and se is the standard error of the estimate.

In a multiple regression based on 30 observations, the following information is provided: a. Construct a 90% confidence interval for E(y) if x1 = 30, x2 = 10, and x3 = 65. b. Construct a 90% prediction interval for y if x1 = 30, x2 = 10, and x3 = 65. c. Which interval is narrower? Explain.

In a multiple regression based on 30 observations, the following information is provided: a. Construct a 95% confidence interval for E(y) if x1 equals 40 and x2 equals 30. b. Construct a 95% prediction interval for y if x1 equals 40 and x2 equals 30. c. Which interval is narrower? Explain.

Over the past 30 years, the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. To determine whether the correlation coefficient is significantly different from zero, the appropriate hypotheses are: ____________.

H0: pxy = 0. HA: pxy /= 0

^^^ When testing whether or not x1 and x2 have the same influence on y, the null hypothesis is ____________.

H0: β1 = β2

````Tiffany & Co. has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the capital asset pricing model (CAPM) model for Tiffany's return. You would like to determine whether an investment in Tiffany's is riskier than the market. When conducting this test, you set up the following competing hypotheses: __________________.

H0:β ≤ 1; HA:β >1

````A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the following model: Salary = β0 + β1 Service + ε. The following table summarizes a portion of the regression results. Which of the following hypotheses will determine whether the intercept differs from zero?

H0:β0 = 0; HA:β0 ≠ 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ______________.

H0:β1 = 0

^^^ Which of the hypotheses will determine whether the slope differs from zero?

H0:β1 = 0; HA: β1 ≠ 0

^^^^ When defining whether age is significant in explaining happiness, the competing hypotheses are _____________________.

H0:β1 = 0; HA:β1 ≠ 0

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. Which of the following are the competing hypotheses used to test whether Advertising is significant in predicting Sales?

H0:β1 = 0; HA:β1 ≠ 0.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ______________.

H0:β1 = 1

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: Which of the following are the competing hypotheses used to test whether the slope coefficient differs from 3?

H0:β1 = 3; HA:β1 ≠ 3

A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ______________________.

H0:β1 = β2 = 0

^^^ When testing whether or not x1 and x2 are jointly significant, the null hypothesis is ____________.

H0:β1 = β2 = 0

^^^ Which of the following is the correct hypotheses for testing the joint significance?

H0:β1 = β2 = 0; HA: At least one βj ≠ 0

````A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model: Rent = β0 + β1 Bedroom + β2 Bath + β3Sqft + ε. The following table shows a portion of the regression results. When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ____.

H0:β1 = β2 = β3 = 0

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β0 + β1 Price + β2 Temperature + β3 Rides + ε, whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $), Temperature is the average daily temperature (in oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. Which of the following are the hypotheses to test if the explanatory variables Temperature and Rides are jointly significant in explaining Attendance?

H0:β2 = β3 = 0; HA: At least one of the coefficients is nonzero.

^^^ Which of the following are the hypotheses to test if the explanatory variables Bath and Sqft are jointly significant in explaining Rent?

H0:β2 = β3 = 0; HA: at least one of the coefficients is nonzero.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a NEGATIVE linear relationship between x and y, the alternative hypothesis takes the form ______________.

HA:b1 < 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a POSITIVE linear relationship between x and y, the alternative hypothesis takes the form ______________.

HA:β1 > 1

If Advertising goes up by $100, then on average, Sales go up by $2,880.

Which of the following is not true of the standard error of the estimate?

It can take on negative values.

The correlation coefficient captures only a ______ relationship.

Linear

Using the same data set, four models are estimated using the same response variable, however, the number of explanatory variables differs. Which of the following models provides the best fit?

Model 1

Given the following portion of regression results, which of the following conclusions is true with regard to the F test at the 5% significance level?

Neither of the explanatory variables is significantly related to the response variable.

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. Is x significantly related to y at the 5% significance level?

No, because the p-value of 0.0745 is greater than 0.05.

When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = 1.95 with a corresponding p-value of [ 0.0653 ] At the 5% significance level, can you conclude that the correlation coefficient differs from zero?

No, since the p-value exceeds 0.05.

Which of the following identifies the range for a correlation coefficient?

None of these choices is correct.

A researcher studies the relationship between SAT scores, the test-taker's family income, and his or her grade point average (GPA). Data are collected from 24 students. He estimates the following model: SAT = β0 + β1 GPA + β2 Income + ε. The following table summarizes a portion of the regression results. At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

Only Income.

Which of the following is a common approach to fitting a line to the scatterplot?

Ordinary Least Squares.

The capital asset pricing model is given by R - RF = α + β(RM - Rf) + ε, where RM = expected return on the market, Rf = risk-free market return, and R = expected return on a stock or portfolio of interest. The response variable in this model is ________.

R - Rf

RM - Rf

The following data for five years of the annual returns for two of Vanguard's mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as sx = 35.77, sy = 13.34, sxy = 447.68. The competing hypotheses are . At the 5% significance level which of the following is the correct conclusion to the test?

Reject H0 and conclude that the returns of these two mutual funds are correlated.

^^^ At the 1% significance level, which of the following is correct?

Reject the null hypothesis. At 1% significance level, we conclude that Age is significant in explaining Happiness.

_______ plots can be used to detect common violations, and they can be used to detect outliers.

Residual

With the partial F test, we basically analyze the ratio of (SSER - SSEU) to ______.

SSEU

_______ correlation can make two variables appear closely related when no casual relation exists.

Spurious

The following scatterplot indicates that the relationship between the two variables x and y is _______________. (Down right) -----> \

Strong and NEGATIVE

Pfizer Inc. is the world's largest research-based pharmaceutical company. Monthly data for Pfizer's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the CAPM model for Pfizer's return. a. At the 5% significance level, is the beta coefficient less than one? Show the relevant steps of the appropriate hypothesis test. b. At the 5% significance level, are there abnormal returns? Show the relevant steps of the appropriate hypothesis test.

The CAPM expresses the risk-adjusted return of an asset R - Rf, as a function of a risk-adjusted market return RM - Rf. For empirical estimation, the CAPM is specified as R - Rf = α + β(RM - Rf) + ε. This is essentially a simple linear regression model. The slope coefficient β measures how sensitive the stock's return is to changes in the level of the overall market. The competing hypotheses are H0:β ≤ 1; HA:β > 1. The CAPM theory predicts α to be zero, and thus a nonzero estimate indicates abnormal returns. Abnormal returns are positive when α > 0, and negative when α < 0. The competing hypotheses are H0:α = 0; HA:α ≠ 0.

x 3 ... y 50 ... b)

The co-variance assesses whether POSITIVE or NEGATIVE linear relationship exists between x and y, and is computed as . rxy = sxy / SxSy

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. a. Specify the competing hypotheses to determine whether the explanatory variables are jointly significant. b. At the 5% significance level, are the explanatory variables jointly significant? Explain. c. At the 5% significance level, is x2 significant in explaining y? Explain. d. At the 5% significance level, is the slope coefficient attached to x3 different from −2?

The competing hypotheses for the test whether the explanatory variables are jointly significant, specified as H0:β1 = β2 = ... = βk = 0;HA: At least one βj ≠ 0. To conduct the test of joint significance, we employ a one-tailed F test. The value under the heading Significance F is the p-value. To test the individual significance the competing hypotheses are H0:βj = βj0; HA:βj ≠ βj0. Using the p-value approach, the decision rule is to reject the null hypothesis if the p-value is less than the significance level α; do not reject the null hypothesis if the p-value is greater than the significance level α. The test statistic for a test of individual significance is assumed to follow the tdfdistribution with df = n - k - 1 and its value is computed as Using the critical value approach, the decision rule for the two-tailed test is to reject the null hypothesis H0:βj = βj0, if the test statistic tdf is less than -tα/2,df or greater than -tα/2,df; otherwise, do not reject the null hypothesis. Use t table to get critical values.

Consider the following regression results based on 40 observations. a. Specify the hypotheses to determine if the slope differs from one. b. Calculate the value of the test statistic. c. At the 5% significance level, find the critical value(s). d. Does the slope differ from one? Explain.

The competing hypotheses when testing individual significance of explanatory variables usually are H0:βj = βj0; HA:βj ≠ βj0. The test statistic for a test of individual significance is assumed to follow the tdfdistribution with df = n - k - 1 and its value is computed as Using the critical value approach, the decision rule for the two-tailed test is to reject the null hypothesis H0:βj = βj0, if the test statistic tdf is less than -tα/2,df or greater than -tα/2,df; otherwise, do not reject the null hypothesis. Use t table to get critical values.

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. a. Specify the competing hypotheses to determine whether x is significant in y. b. At the 5% significance level, is x significant? Explain.

The competing hypotheses when testing individual significance of explanatory variables usually are H0:βj = βj0; HA:βj ≠ βj0; where βj0 = 0 Using the p-value approach, the decision rule is to reject the null hypothesis if the p-value is less than the significance level α; do not reject the null hypothesis if the p-value is greater than the significance level α

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. The following table summarizes a portion of the regression results: a. Specify the competing hypotheses to determine whether Service is significant in explaining Salary. b. At the 5% significance level, is Service significant? Explain.

The competing hypotheses when testing individual significance of explanatory variables usually are H0:βj = βj0; HA:βj ≠ βj0. Using the p-value approach, the decision rule is to reject the null hypothesis if the p-value is less than the significance level α; do not reject the null hypothesis if the p-value is greater than the significance level α.

When estimating a multiple regression model based on 30 observations, the following results were obtained. Specify the hypotheses to determine whether x1 is linearly related to y. At the 5% significance level, use the p-value approach to complete the test. Are x1 andy linearly related? b. Construct the 95% confidence interval for β2. Using this confidence interval, is x2 significant in explaining y? Explain. c. At the 5% significance level, can you conclude that β1 differs from −1? Show the relevant steps of the appropriate hypothesis test.

The competing hypotheses when testing individual significance of explanatory variables, in general, are H0:βj = βj0; HA:βj ≠ βj0. Using the p-value approach, the decision rule is to reject the null hypothesis if the p-value is less than the significance level α; do not reject the null hypothesis if the p-value is greater than the significance level α. If the confidence interval for the slope coefficient contains the value zero, then the explanatory variable associated with the regression coefficient is not significant. Conversely, if the confidence interval does not contain the value zero, then the explanatory variable associated with the regression coefficient is significant. The test statistic for a test of individual significance is assumed to follow the tdfdistribution with df = n - k - 1 and its value is computed as Using the critical value approach, the decision rule for the two-tailed test is to reject the null hypothesis H0:βj = βj0, if the test statistic tdf is less than -tα/2,df or greater than -tα/2,df; otherwise, do not reject the null hypothesis. Use t table to get critical values.

Which of the following statements is the least accurate concerning correlation analysis?

The correlation coefficient describes both the direction and strength of the relationship between two variables only if the two variables have same units of measurement.

A sample of 30 observations provides the following statistics: sx = 14;sy = 19; sxy = -150. a) Calculate and interpret the sample correlation coefficient rxy

The correlation coefficient is computed as rxy = Sxy / SxSy A two-tailed test of whether the population correlation coefficient differs from zero takes the following form .

A portfolio manager is interested in reducing the risk of a particular portfolio by including assets that have little, if any, correlation. He wonders whether the stock prices for the firms Apple and Google are correlated. As a very preliminary step, he collects the monthly closing stock price for each firm from January 2012 to April 2012. Compute the sample correlation coefficient. b. Specify the competing hypotheses in order to determine whether the stock prices are correlated. c. Calculate the value of the test statistic and approximate the corresponding p-value. d. At the 5% significance level, what is the conclusion to the test? Explain

The correlation coefficient is computed as rxy = Sxy / SxSy A two-tailed test of whether the population correlation coefficient differs from zero takes the following form . Compute the value of the test statistic as . Using the p-value approach, the decision rule is reject the null hypothesis if the p-value is less than the significance level α, do not reject the null hypothesis if the p-value is greater than the significance level α.

A statistics instructor wants to examine the relationship between the hours a student spends studying for the final exam (Hours) and a student's grade on the final exam (Grade). She takes a sample of five students. a. Compute the sample correlation coefficient. b. Specify the competing hypotheses in order to determine whether the hours spent studying and the final grade are correlated. c. Calculate the value of the test statistic and approximate the corresponding p-value. d. At the 10% significance level, what is the conclusion to the test? Explain.

Which of the following violates the assumptions of regression analysis?

The error term is correlated with an explanatory variable.

A researcher gathers data on 25 households and estimates the following model: Expenditure = β0 + β1 Income + ε. A residual plot of the estimated model is shown in the accompanying graph. Which of the following can be inferred from the residual plot?

The residuals seem to fan out across the horizontal axis.

Consider the following information regarding a response variable y and an explanatory variable x. a. Calculate b0 and b1. b. What is the sample regression equation? Predict y if x equals 10. c. Calculate the standard error of the estimate. d. Calculate and interpret the coefficient of determination.

The slope b1 and the interceptb0 of the simple regression equation are computed as b1 = (xi-x mean)(yi-y mean) / (xi-x mean)^2 and b0 = y mean - b1 * XMean The simple linear regression equation is y = b0 + b1x The standard error of the estimate, se, is a point estimate of the standard deviation of a random error, and it is computed as se=sqrt{ (yi-y^i)^2 / n - k - 1 . The coefficient of determination is the proportion of the variation in the response variable that is explained by the sample regression equation.It is computed as where the error sum of squares (SSE) is computed as R^2 = 1 - SSE / SST and the total sum of squares is computed as SST = (yi - y mean) ^2

x 22 35 14 10 y 26 55 30 12 a. Construct scatterplot. b. Calculate b1 and b0. What is the sample regression equation? c. Find the predicted value for y if x equals 10, 15, and 20.

The slope b1 and the interceptb0 of the simple regression equation are computed as b1 = (xi-xmean)(yi-ymean) / xi-xmean^2 and b0 = ymean-b1(xmean) The simple linear regression equation is y = b0 + b1x

John is an undergraduate business major studying at a local university. He wonders how his grade point average (GPA) can affect his future earnings. He asks five recent business school graduates information on their GPA and income (in $1,000s). The following table shows this information. Construct a scatterplot and verify that estimating a simple linear regression is appropriate in this case. b. Calculate b0 and b1. What is the sample regression equation? c. Interpret the coefficient for GPA. d. Find the predicted income earned if a GPA equals 3.0, 3.3, and 3.6.

The slope b1 and the interceptb0 of the simple regression equation are computed as and The simple linear regression equation is . For each explanatory variable, the corresponding slope coefficient measures the change in the predicted variable of the response variable given a unit increase in the associated explanatory variable, holding all other explanatory variables constant.

The following ANOVA table was obtained when estimating a multiple regression model. a. Calculate the standard error of the estimate. b. Calculate the coefficient of determination. c. Calculate adjusted R2

The standard error of the estimate, , is a point estimate of the standard deviation of the random error ε, and is computed as , where MSE is the mean square error for the residuals. The coefficient of determination is the proportion of the variation in the response variable that is explained by the sample regression equation, and it is computed as . The adjusted coefficient of determination is computed as Adjusted

A simple linear regression, Sales = β0 + β1 Advertising + ε, is estimated using time-series data over the last 10 years. The residuals, e, and the time variable, t, are shown in the accompanying table. a. Graph the residuals e against time and look for any discernible pattern. b. Which assumption is being violated? Discuss its consequences and suggest a possible remedy.

The wavelike movement in the residuals over time creates a pattern around the horizontal axis and we conclude that positive serial correlation is likely to be a problem

Which of the following statements in statistical terminology is equivalent to the statement: "There is no exact linear relationship among the explanatory variables"?

There is no perfect multicollinearity.

An investment analyst wants to examine the relationship between a mutual fund's return, its turnover rate, and its expense ratio. She randomly selects 10 mutual funds and estimates: Return = β0 + β1Turnover + β2Expense + ε, where Return is the average five-year return (in %), Turnover is the annual holdings turnover (in %), Expense is the annual expense ratio (in %), and ε is the random error component. A portion of the regression results is shown in the accompanying table. a. At the 10% significance level, are the explanatory variables jointly significant in explaining Return? Explain. b. At the 10% significance level, is each explanatory variable individually significant in explaining Return? Explain.

An analyst examines the effect that various variables have on crop yield. He estimates y = β0 + β1x1 + β2x2 + β3x3 + ε. where y is the average yield in bushels per acre, x1 is the amount of summer rainfall, x2 is the average daily use in machine hours of tractors on the farm, and x3 is the amount of fertilizer used per acre. The results of the regression are as follows: a. At the 10% significance level, are the explanatory variables jointly significant in explaining crop yield? Explain. b. At the 10% significance level, is fertilizer significant in explaining crop yield? Explain. c. At the 10% significance level, can you conclude that the slope coefficient attached to rainfall differs from 9? Explain.

To conduct the test of joint significance: H0:β1 = β2 = ... = βk = 0; HA: At least one βj ≠ 0, we employ a one-tailed F test. The value under the heading Significance F is the p-value. The competing hypotheses when testing individual significance of explanatory variables, in general, are H0:βj = βj0; HA:βj ≠ βj0. Using the p-value approach, the decision rule is to reject the null hypothesis if the p-value is less than the significance level α; do not reject the null hypothesis if the p-value is greater than the significance level α. The test statistic for a test of individual significance is assumed to follow the tdfdistribution with df = n - k - 1 and its value is computed as Using the critical value approach, the decision rule for the two-tailed test is to reject the null hypothesis H0:βj = βj0, if the test statistic tdf is less than -tα/2,df or greater than -tα/2,df; otherwise, do not reject the null hypothesis. Use t table to get critical values.

Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales, housing starts, and commercial construction. The regression uses Lumber Sales (in $100,000s) as the response variable with Housing Starts (in 1,000s) and Commercial Construction (in 1,000s) as the explanatory variables. The results of the regression are as follows: a. At the 5% significance level, are the explanatory variables jointly significant in explaining Lumber Sales? Explain. b. At the 5% significance level, is Commercial Construction significant in explaining Lumber Sales? Explain. c. At the 5% significance level, can you conclude that the slope coefficient attached to Housing Starts differs from 1? Explain.

Consider the following regression results based on 30 observations. - 2 equations - a. Formulate the hypotheses to determine whether the influences of x2 and x3 differ in explaining y. b. Calculate the value of the test statistic. c. At the 5% significance level, find the critical value(s). d. What is your conclusion to the test?

To test if the influence of explanatory variables is different, the competing hypotheses are H0:βi = βj; HA:βi ≠ βj. The test statistic is assumed to follow the F(df1,df2) distribution with df1 equal to the number of linear restrictions and df2 = n - k - 1. The value of the test statistic for the partial F test is computed as Use F table to get the critical value Fα(df1,df2). Using the critical value approach, the decision rule is to reject the null hypothesis if the test statistic F(df1,df2) is greater than the critical value Fα(df1,df2); otherwise, do not reject the null hypothesis

Consider the following regression results based on 30 observations. Notes: Parameter estimates... a. Formulate the hypotheses to determine whether x2 and x3 are jointly significant in explaining y. b. Define the restricted and the unrestricted models needed to conduct the test. c. Calculate the value of the test statistic. d. At the 5% significance level, find the critical value(s). e. What is your conclusion to the test?

The numerical measure that gauges dispersion from the sample regression equation is the sample _______ of the residual.

Variance

A correlation coefficient r = −0.85 could indicate a _______________________________.

Very strong NEGATIVE linear relationship

Consider the following simple linear regression model: y = β0 + β1x +ε.The EXPLANATORY variable is ____.

Consider the following simple linear regression model: y = β0 + β1x +ε.The RESPONSE variable is ____.

A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β0 + β1 Double Faults + β2Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. Is the relationship between Win and Aces significant at the 5% significance level?

Yes, because the relevant p-value is less than 0.05.

When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = -2.95 with a corresponding p-value of [ 0.0061 ] At the 5% significance level, can you conclude that the correlation coefficient differs from zero?

Yes, since the p-value is less than 0.05.

^^^ At the 1% significance level, which of the following is the correct confidence interval of the regression coefficient β1?

[0.0390, 0.5300]

^^ According to the modified model, which of the following is a 95% prediction interval for Attendance when Price and Rides equal $85 and 30, respectively? (Note that t0.025,27 = 2.052.)

[12,740, 56,080]

^^^ According to the modified model, which of the following is a 95% prediction interval for y when x equals 2? (Note that t0,025,10 = 2.228.)

[14.21, 35.35]

^^^ According to the modified model, which of the following is a 95% confidence interval for E(y) when x equals 2? (Note that t0,025,10 = 2.228.)

[18.63, 30.93]

^^ According to the modified model, which of the following is a 95% confidence interval for expected Attendance when Price andRides equal $85 and 30, respectively? (Note that t0,025,27 = 2.052.)

[26,080, 42,740]

Which of the following is the 95% confidence interval for the regression coefficient β1, if df = 30, b1= −2 and

[−8.13, 4.13]

When estimating a multiple regression model, the following portion of output is obtained: a. What is the sample regression equation? b. Interpret the slope coefficient for x1. c. Find the predicted value for y if x1 equals 22 and x2 equals 41.

a. y = b0+b1X1+b2X2 For each explanatory variable, the corresponding slope coefficient measures the change in the predicted variable of the response variable given a unit increase in the associated explanatory variable, holding all other explanatory variables constant. Use given coefficients, x1 andx2, to compute the value of .

The following portion of regression results was obtained when estimating a multiple regression model.

a: y= b0 + b1X For each explanatory variable, the corresponding slope coefficient measures the change in the predicted variable of the response variable given a unit increase in the associated explanatory variable, holding all other explanatory variables constant constant. Use given coefficients andx to compute the value of . SST = SSR + SSE. . The standard error of the estimate is a point estimate of the standard deviation of a random error, and it is computed as . The coefficient of determination is the proportion of the variation in the response variable that is explained by the sample regression equation, and it is computed as 1 - SSE / SST .

The following portion of regression results was obtained when estimating a simple linear regression model. What is the sample regression equation? b. Interpret the slope coefficient for x1. c. Find the predicted value for y if x1 equals 200. d. Fill in the missing values A and B in the ANOVA table. e. Calculate the standard error of the estimate. f. Calculate R2.

Given the augmented Phillips model: y = β0 + β1x1+β2x2 +ε, where y = actual rate of inflation (%), x1 = unemployment rate (%), and x2 = anticipated inflation rate (%). The response variable or variables(s) in this model is (are) the ___________________.

actual inflation rate

An real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model as Rent = β0 + β1 Bedroom + β2 Bath + β3 Sqft + ε. The following ANOVA table shows a portion of the regression results. The slope coefficient attached to Bedroom indicates that, holding other explanatory variables constant, ____________.

an additional bedroom increases rent, on average, by $226

We use ______ to derive the coefficient of determination.

analysis of variance (ANOVA)

Excel and virtually all other statistical packages report the p-value ____________________________________.

for a two-tailed test that assesses whether the regression coefficient differs from zero

If the variance of the error term is not the same for all observations, we ___________________________.

cannot conduct tests of significance

In regression, the two types of interval estimates concerning y are called _________________________________.

confidence interval and prediction interval

Serial correlation occurs when the error term is ______________________.

correlated across observations

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ______________.

decrease by 60,000

The relationship between the response variable and the explanatory variables is _________ if the value of the response variable is uniquely determined by the explanatory variables.

deterministic

When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________.

df1 = r and df2 = n - k - 1

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β0 + β1 Price + β2 Temperature + β3 Rides + ε, whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $), Temperature is the average daily temperature (in oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether Temperature is significant at the 5% significance level, she ________________________________________________________________.

does not reject H0:β2 = 0, and concludes that Temperature is not significant

^^^ When testing whether Bath is significant at the 5% significance level, she ___________________________________________________________________.

does not reject H0:β2 = 0, and concludes that the number of bathrooms does not significantly influence rent.

When confronted with multicollinearity, a good remedy is to _______________________ if we can justify its redundancy.

drop one of the collinear variables

Consider the following simple linear regression model: y = β0 + β1x +ε. The random error term is ____.

If _____ is substantially greater than zero and the number of explanatory variables is large compared with sample size, then the adjusted R2 will differ substantially from R2.

error sum of squares (SSE)

One of the required assumptions of regression analysis states that the error term has a(an) ________ value of zero.

expected Conditional on x1, x2, ..., xk, the error term has an expected value of zero, or E(ε) = 0.

If the confidence interval does not contain the value zero, then the ________ variable associated with the regression coefficient is significant.

explanatory

c. At the 5% significance level, what is the conclusion to the test using the critical-value approach? Explain. d. At the 5% significance level, what is the conclusion to the test using the p-value approach? Explain.

for the test statistic tdf can be found in the t table. Using critical value approach, the decision rule is reject the null hypothesis if the test statistic greater than or less than ; otherwise, do not reject the nul. Using p-value , the decision rule is reject the null hypothesis if the p-value is less than the significance level α; do not reject the null hypothesis if the p-value is greater than the significance level α.

In regression, multicollinearity is considered problematic when two or more explanatory variables are ___________.

highly correlated

x 3 13 9 .. 20 y 50 83 20 ..160 a) construct and interpret a scatterplot

if observations are close to line with positive slope, relationship between x and y is STRONG and POSITIVE

increase by 30,000.

Unlike the coefficient of determination, the coefficient of correlation in a simple linear regression ___________.

indicates whether the slope of the regression line is positive or negative

When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a __________.

lower standard error of the estimate and a higher adjusted coefficient of determination

Test statistic for the test of linear restrictions is using all of the following, except ______________________.

mean error sum of squares

The _______ regression model allows us to study how the response variable is influenced by two or more explanatory variables.

multiple

Conditional on x1, x2, ..., xk, the error term ε is ________ distributed.

normally

When testing the overall significance of the regression model at the 5% level given a critical value of F0.05,(2,20) = 3.49, the decision is to

not reject H0 and conclude that the explanatory variables are not jointly significant

^^^ When testing whether there are abnormal returns, the conclusion to the test is at the 5% significance level is to ___________________________________________________.

not reject H0, and do not conclude there are abnormal returns

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: When testing whether the slope coefficient differs from 3, the critical values at the 5% significance level are −2.069 and 2.069. The conclusion to the test is to

not reject H0; the slope coefficient does not differ from 3

A sample of 200 monthly observations is used to run a simple linear regression: Returns = β0 + β1 Leverage + ε. A 5% level of significance is used to study if leverage has a significant influence on returns. The value of the test statistic for the regression coefficient of Leverage is calculated as t198 = -1.09, with an associated p-value of 0.2770. The correct decision is to

not reject the null hypothesis and conclude that leverage does not significantly explain returns

When estimating y = β0 + β1x1 + β2x2 + β3x3 + ε, you wish to test H0: β1 = β2 = 0 versus HA: At least one βi = 0. The value of the test statistic is F(2,20) = 2.50 and its associated p-value is 0.1073. At the 5% significance level, the conclusion is to

not reject the null hypothesis and conclude that x1 and x2 are not jointly significant

The F test can be applied for any number of linear restrictions; the resulting test is often referred to as the _____ F test.

partial

The R2 of a multiple regression of y on x1 and x2 measures the __________.

percent variability of y that is explained by the variability of x1 and x2

It is common to refer to the interval estimate for an individual value of y as the _________ interval.

prediction It is common to refer to the interval estimate for an individual value of y as the prediction interval. The interval estimate for the mean of y is referred to as the confidence interval.

The actual value y may differ from the expected value E(y). Therefore, we add a ______ ____ term ε to develop a simple linear regression model.

random error

When testing the overall significance of the regression model at the 5% level given a critical value of F0.05,(2.20) = 3.49, the decision is to

reject H0 and conclude that the explanatory variables are jointly significant.

`````The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. When testing whether the explanatory variables are jointly significant at the 5% significance level, the conclusion is to ____________________________________________________________________.

reject H0, and conclude that the explanatory variables are jointly significant

In regression, the predicted values concerning y are subject to _____________.

sampling variation

^^^ When testing whether the beta coefficient is significantly greater than one, the relevant critical value at the 5% significance level is t0.05,58 = 1.672. The conclusion to the test is to

reject H0, and conclude that the return on Tiffany stock is riskier than the return on the market

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. When testing whether Advertising is significant at the 10% significance level, the conclusion is to _______________________________.

reject H0; advertising is significant

When testing linear restrictions, the test statistic is assumed to follow the y = β0 + β1x1 + β2x2 + β3x3 + ε, you wish to test H0: β1 = β2 versus HA: β1 ≠ β2 The value of the test statistic is F(1,30) = 7.75 and its associated p-value is 0.0092. At the 1% significance level, the conclusion is to

reject the null hypothesis and conclude that the influence of x1 and x2 on y is not the same

^^^ When testing whether the explanatory variables Bath and Sq ft are jointly significant, the p-value associated with the test is 0.0039. At the 5% significance level, she.

rejects H0, and concludes that at least one of the explanatory variables, Bath and/or Sq ft, is significant in explaining Rent

^^ When testing whether the explanatory variables Temperature and Rides are jointly significant, the p-value associated with the test is 0.0000. At the 1% significance level, the researcher.

rejects H0, and concludes that at least one of the explanatory variables, Temperature and Rides, is significant in explaining Attendance

63 A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model:Attendance = β0 + β1 Price + β2 Temperature + β3 Rides + ε, whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $), Temperature is the average daily temperature (in oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether the explanatory variables are jointly significant at the 5% significance level, the researcher.

rejects H0, and concludes that the explanatory variables are jointly significant

^^^ When testing whether the explanatory variables are jointly significant at the 5% level, she

rejects H0, and concludes that the explanatory variables are jointly significant

A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β0 + β1 Double Faults + β2Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. Excel shows that the 95% confidence interval for β1 is [−0.12, −0.002]. When determining whether or not Double Faults is significant at the 5% significance level, he

rejects H0: β1 = 0, and concludes that Double Faults is significant

^^^ When testing whether Bedroom is significant at the 5% significance level, she.

rejects H0:β1 = 0, and concludes that the number of bedrooms significantly influences rent

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β0 + β1 Price + β2 Temperature + β3 Rides + ε, whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $), Temperature is the average daily temperature (in oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether Rides is significant at the 1% significance level, she

rejects H0:β3 = 0, and concludes that Rides is significant

With regression analysis, we explicitly assume that one variable, called the _______ variable, is influenced by other variable, called the explanatory variable.

response

Which of the following is the relationship between the slope and correlation coefficient?

rxy = b1 sx/sy

Simple linear regression analysis differs from multiple regression analysis in that ___________________________________________________________.

simple linear regression uses only one explanatory variable

Which of the following is the correct expression for computing a 100(1 - α)% prediction interval for an individual value of y?

sqrt[ + s2e]

The following scatterplot indicates that the relationship between the two variables x and y is ______________. (going up right) ----> /

strong and positive

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: When testing whether the slope coefficient differs from 3, the value of the test statistic is ____.

t23 = -0.079

In the sample regression equation = b0 + b1x, What is ?

the predicted value of y, given specific x value

For a given confidence level, the prediction interval is always wider than the confidence interval because

the prediction interval is for a particular value of y rather than for the expected value E(y)

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if ______________.

the price of Product A increases by $1, then on average, demand decreases by 20,000

Consider the following sample regression equation = 200 + 10x, where y is the supply for Product A (in 1000s)(in 1,000s) and x is the price of Product A (in $). The slope coefficient indicates that if ___________.

the price of Product A increases by $1, then on average, supply increases by 10,000

The standard error of the estimate measures ______________.

the standard deviation of the residuals.

Consider the following simple linear regression model: y = β0 + β1x +ε. β0 and β1 are __________________.

the unknown parameters

The standard error of the estimate measures ____________.

the variability of the observed y-values around the predicted y-values.

Multicollinearity is suspected when ________________________________________________.

there is a high R2 coupled with insignificant explanatory variables

One of the assumptions of regression analysis is

there is no perfect multicollinearity among any explanatory variables

Serial correlation is typically observed in __________________.

time series data

Over the past 30 years, the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. When testing whether the correlation coefficient differs from zero, the value of the test statistic is t28 = 2.31. At the 5% significance level, the critical value is t0.025,28 = 2.048. The conclusion to the hypothesis test is to ___________.

to reject H0; we can conclude that the correlation coefficient differs from zero.

Given the augmented Phillips model: Given the augmented Phillips model: y = β0 + β1x1+β2x2 +ε, where y = actual rate of inflation (%), x1 = unemployment rate (%), and x2 = anticipated inflation rate (%). The response variable or variables(s) in this model is (are) the ___________________.

unemployment rate and anticipated inflation rate

The _________ model is a complete model that imposes no restrictions on the coefficients.

unrestricted

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

x1 and x2

^^^ At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

x1 and x2

Consider the following data: = 20, sx = 2, = -5, sy = 4, and b1 = 0.40. Which of the following is the sample regression equation?

y = -13 + 0.40x

Consider the following data: = 20, sx = 2, = -5, sy = 4, and b1 = -0.8. Which of the following is the sample regression equation?

y = 11 - 0.80x

A statistics student is asked to estimate y = β0 + β1x + ε. She calculates the following values: = 440, , = 1,120, n = 11. Which of the following is the sample regression equation?

y = 60.80 - 1.29x

Consider the sample regression equation = 10 - 5x, with an R2 value of 0.65. Which of the following is the value of the sample correlation between y and ?

−0.81

A statistics student is asked to estimate y = β0 + β1x + ε. She calculates the following values: = 440, , = 1,120, n = 11. The value of the slope b1 is ____.

−1.29

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β0 + β1 Price + β2 Temperature + β3 Rides + ε, whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $), Temperature is the average daily temperature (in oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether Price is significant in explaining Attendance, the value of the test statistic is _____.

data Final Exam

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