Question 1

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 ________.

Accepted Answer

A)  reject the null hypothesis; we can conclude that leverage significantly explains returns 
B)  reject the null hypothesis; we cannot conclude that leverage significantly explains returns 
C)  not reject the null hypothesis; we cannot conclude that leverage significantly explains returns 
D)  not reject the null hypothesis; we can conclude that leverage significantly explains returns

Question 2

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?

Accepted Answer

A)  0.66 
B)  1.42 
C)  1.96 
D)  2.25

Question 3

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

Accepted Answer

A)  Yes, because the p-value of 0.0745 is greater than 0.05. 
B)  No, because the p-value of 0.0745 is greater than 0.05. 
C)  Yes, because the slope coefficient of 1.417 is less than the test statistic of 2.25. 
D)  No, because the slope coefficient of 1.417 is less than the test statistic of 2.25.

Question 4

A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β0 + β1Price + β2Rides + 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
Price* = Price - 85 and Rides* = Rides - 30. A portion of the regression results is shown in the accompanying table.  According to the modified model, which of the following is a 95% confidence interval for expected Attendance when Price and Rides equal $85 and 30, respectively? (Note that t0,025,27 = 2.052.)

Accepted Answer

A)  [12,740, 56,780] 
B)  [16,330, 53,450] 
C)  [26,080, 42,740] 
D)  [28,900, 41,500]

Question 5

In a multiple regression based on 30 observations, the following information is provided: = 469 - 2x₁+ 6x₂ - 0.5x₃and s_e= 16. Also, when x₁ = 30, x₂ = 10, and x₃ = 65 se( ₀) = 37. 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.

Accepted Answer

The answer of In a multiple regression based on 30...

Question 6

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 ________.

Accepted Answer

A)  reject H0, and conclude that the explanatory variables are jointly significant 
B)  not reject H0, and conclude that the explanatory variables are jointly significant 
C)  reject H0, and cannot conclude that the explanatory variables are jointly significant 
D)  not reject H0, and cannot conclude that the explanatory variables are jointly significant

Question 7

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 Capital Asset Pricing Model (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.

Accepted Answer

The answer of Pfizer Inc. is the world's largest research-based...

Question 8

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?

Accepted Answer

A)  Only x1  
B)  Only x3  
C)  x1 and x2  
D)  x2 and x3

Question 9

Test statistic for the test of linear restrictions uses all of the following, except ________.

Accepted Answer

A)  total sum of squares of the restricted model 
B)  error sum of squares of the restricted model 
C)  number of linear restrictions 
D)  number of explanatory variables in the unrestricted model

Question 10

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε.  When testing whether or not x1 and x2 are jointly significant, the null hypothesis is ________.

Accepted Answer

A)  H0: β1 = β2  
B)  H0: β1 ≠ β2  
C)  H0: β1 + β2 = 0 
D)  H0: β1 = β2 = 0

Question 11

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 ________.

Accepted Answer

A)  H0: β1 = 0 
B)  H0: β1 = 1 
C)  H0: b1 = 0 
D)  H0: b1 = 1

Question 12

Which of the following violates the assumptions of regression analysis?

Accepted Answer

A)  The error term is normally distributed. 
B)  The error term has a zero mean. 
C)  The error term is correlated with an explanatory variable. 
D)  The error term has a constant variance.

Question 13

In a simple linear regression based on 30 observations, the following information is provided: = 32.3 + 1.45x and s_e= 3.2. Also, se( ₀) evaluated at x = 20 is 1.3. A) Construct a 95% confidence interval for E(y) if x = 20. B) Construct a 95% prediction interval for y if x = 20.

Accepted Answer

The answer of In a simple linear regression based on...

Question 14

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

Accepted Answer

A)  1.96 
B)  3.49 
C)  8.04 
D)  10

Question 15

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 ________.

Accepted Answer

A)  rejects H0: β1 = 0, and concludes that DoubleFaults is significant 
B)  does not reject H0: β1 = 0, and concludes that DoubleFaults is significant 
C)  rejects H0: β1 = 0, and cannot conclude that DoubleFaults is significant 
D)  does not reject H0: β1 = 0, and cannot concludes DoubleFaults is significant

Question 16

The term multicollinearity refers to the condition when the variance of the error term, conditional on x1, x2, …, xn, is the same for all observations.

Accepted Answer

A) True 
 B)False

Question 17

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  . The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return.  When testing whether there are abnormal returns, or whether the alpha coefficient is significantly different from zero, the value of the test statistic is ________.

Accepted Answer

A)  −1.98 
B)  1.98 
C)  4.33 
D)  9.58

Question 18

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.

Accepted Answer

The answer of A simple linear regression, Sales = β₀...

Question 19

Refer to below regression results.  When testing the overall significance of the regression model at the 5%, the decision is to ________.

Accepted Answer

A)  reject H0; we can conclude that the explanatory variables are jointly significant. 
B)  not reject H0; we can conclude that the explanatory variables are jointly significant. 
C)  reject H0; we cannot conclude that the explanatory variables are jointly significant. 
D)  not reject H0; we cannot conclude the explanatory variables are jointly significant.

Question 20

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

Accepted Answer

A)  −1.98 
B)  1.98 
C)  4.33 
D)  9.58

Exam 15: Inference With Regression Models

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?

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

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 ________.

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?

Test statistic for the test of linear restrictions uses all of the following, except ________.

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. When testing whether or not x₁ and x₂ are jointly significant, the null hypothesis is ________.

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 ________.

Which of the following violates the assumptions of regression analysis?

In a simple linear regression based on 30 observations, the following information is provided: = 32.3 + 1.45x and s_e= 3.2. Also, se( ₀) evaluated at x = 20 is 1.3. A) Construct a 95% confidence interval for E(y) if x = 20. B) Construct a 95% prediction interval for y if x = 20.

Given the following portion of regression results, which of the following is the value of the F_2,20 test statistic?

The term multicollinearity refers to the condition when the variance of the error term, conditional on x₁, x₂, …, x_n, is the same for all observations.

Refer to below regression results. When testing the overall significance of the regression model at the 5%, the decision is to ________.

Exam 15: Inference With Regression Models

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?

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

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 ________.

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?

Test statistic for the test of linear restrictions uses all of the following, except ________.

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. When testing whether or not x1 and x2 are jointly significant, the null hypothesis is ________.

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 ________.

Which of the following violates the assumptions of regression analysis?

In a simple linear regression based on 30 observations, the following information is provided: = 32.3 + 1.45x and se = 3.2. Also, se( 0) evaluated at x = 20 is 1.3. A) Construct a 95% confidence interval for E(y) if x = 20. B) Construct a 95% prediction interval for y if x = 20.

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

The term multicollinearity refers to the condition when the variance of the error term, conditional on x1, x2, …, xn, is the same for all observations.

Refer to below regression results. When testing the overall significance of the regression model at the 5%, the decision is to ________.

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?

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

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 ________.

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?

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. When testing whether or not x₁ and x₂ are jointly significant, the null hypothesis is ________.

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 ________.

In a simple linear regression based on 30 observations, the following information is provided: = 32.3 + 1.45x and s_e= 3.2. Also, se( ₀) evaluated at x = 20 is 1.3. A) Construct a 95% confidence interval for E(y) if x = 20. B) Construct a 95% prediction interval for y if x = 20.

Given the following portion of regression results, which of the following is the value of the F_2,20 test statistic?

The term multicollinearity refers to the condition when the variance of the error term, conditional on x₁, x₂, …, x_n, is the same for all observations.