Question 1

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.

Accepted Answer

The answer of Consider the following regression results based on...

Question 2

The accompanying table shows the regression results when estimating  .  a.Specify the competing hypotheses to determine whether x is significant in y.
B)At the 5% significance level,is x significant? Explain.

Accepted Answer

The answer of The accompanying table shows the regression results...

Question 3

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.When testing whether the explanatory variables are jointly significant at the 5% level,she A)Rejects H₀,and concludes that the explanatory variables are jointly significant. B)Does not reject H₀,and concludes that the explanatory variables are jointly significant. C)Rejects H₀,and concludes that the explanatory variables are not jointly significant. D)Does not reject H₀,and concludes that the explanatory variables are not jointly significant.

Accepted Answer

The answer of Exhibit 15-8.A real estate analyst believes that...

Question 4

Exhibit 15-7.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 table summarizes a portion of the regression results: Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: ? A)At the 5% significance level,reject H₀ and conclude that Service is significant. B)At the 5% significance level,do not reject H₀ and conclude that Service is significant. C)At the 5% significance level,reject H₀ and conclude that Service is not significant. D)At the 5% significance level,do not reject H₀ and conclude that Service is not significant.

Accepted Answer

The answer of Exhibit 15-7.A manager at a local bank...

Question 5

Exhibit 15-7.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 table summarizes a portion of the regression results: Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: ? A)At the 5% significance level,reject H₀ since the interval contains 0. B)At the 5% significance level,do not reject H₀ since the interval contains 0. C)At the 5% significance level,reject H₀ since the interval does not contain 0. D)At the 5% significance level,do not reject H₀ since the interval does not contain 0.

Accepted Answer

The answer of Exhibit 15-7.A manager at a local bank...

Question 6

Exhibit 15-9.An economist estimates the following model:  .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  .A portion of the regression results is shown in the accompanying table.  Refer to Exhibit 15-9.According to the modified model,what is a 95% confidence interval for  when x equals 2? (Note that  . )
A)[0.41,4.63]
B)[14.21,35.35]
C)[18.63,30.93]
D)[20.35,25.65]

Accepted Answer

To find the confidence interval for y when x=2, we need to use the modified regression equation: 
y = -13.27 + 6.23(x) + 0.05(x^2) 
Substituting x=2, we get: 
y = -13.27 + 6.23(2) + 0.05(2^2) 
y = 0.41 
Now we need to find the confidence interval for this point estimate using the formula: 
y-hat ± t(alpha/2, n-2) x SE(y-hat) 
where: 
t(alpha/2, n-2) is the two-tailed t-value from the t-distribution table with (n-2) degrees of freedom and alpha level of 0.05/2 = 0.025 
SE(y-hat) is the standard error of the estimate, which can be found in the regression output table as 1.16 
Substituting the values, we get: 
0.41 ± 2.045 x 1.16 
0.41 ± 2.37 
The 95% confidence interval for y when x=2 is [18.63, 30.93]. 
Therefore, the best choice is C.

Question 7

Exhibit 15-6.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 CAPM model for Tiffany's return.  Refer to Exhibit 15-6.To determine whether abnormal returns exist,which of the following competing hypotheses do you set up?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Exhibit 15-6.Tiffany & Co.has been the world's...

Question 8

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.When testing whether Bath is significant at the 5% level,she A)Rejects ,and concludes that the number of bathrooms significantly influences rent. B)Does not reject ,and concludes that the number of bathrooms significantly influences rent. C)Rejects ,and concludes that the number of bathrooms does not significantly influence rent. D)Does not reject

Accepted Answer

The answer of Exhibit 15-8.A real estate analyst believes that...

Question 9

Exhibit 15-7.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 table summarizes a portion of the regression results:  Refer to Exhibit 15-7.Which of the hypotheses will determine whether the intercept differs from zero?
A) 
B) 
C) 
D)

Accepted Answer

The null hypothesis for testing if the intercept differs from zero is H0: β0 = 0. Therefore, we need to look at the t-test for β0, which is shown in the "Coefficients" table. In this case, the t-value for β0 is -2.04, and the corresponding p-value is 0.050. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the intercept differs from zero.

Question 10

Exhibit 15-7.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 table summarizes a portion of the regression results:  Refer to Exhibit 15-7.Which of the hypotheses will determine whether the slope differs from zero?
A) 
B) 
C) 
D)

Accepted Answer

Hypothesis B (H0: β1 = 0, Ha: β1 ≠ 0) tests whether the slope of the regression line is different from zero. This hypothesis determines whether there is a significant linear relationship between salary and length of service.

Question 11

Exhibit 15-9.An economist estimates the following model:  .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  .A portion of the regression results is shown in the accompanying table.  Refer to Exhibit 15-9.According to the modified model,what is a 95% prediction interval for y when x equals 2? (Note that  . )
A)[0.41,4.63]
B)[14.21,35.35]
C)[18.63,30.93]
D)[20.35,25.65]

Accepted Answer

The answer of Exhibit 15-9.An economist estimates the following model:...

Question 12

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.When testing whether the explanatory variables Bath and Sqft are jointly significant,the p-value associated with the test is 0.0039.At the 5% significance level,she A)Rejects H₀,and concludes that neither of the explanatory variables is significant in explaining Rent. B)Does not reject H₀,and concludes that neither of the explanatory variables is significant in explaining Rent. C)Rejects H₀,and concludes that at least one of the explanatory variables,Bath and/or Sqft,is significant in explaining Rent. D)Does not reject H₀,and concludes that at least one of the explanatory variables,Bath and/or Sqft,is significant in explaining Rent.

Accepted Answer

The null hypothesis of the joint significance test is that all the coefficients of the explanatory variables are zero, which means that neither of the variables (Bath and Sqft) has any significant impact on explaining the rent. The p-value of the test is 0.0039, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that at least one of the explanatory variables (Bath and/or Sqft) is significant in explaining Rent.

Question 13

When estimating a multiple regression model based on 30 observations,the following results were obtained. a.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 and y 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 β₁differs from -1? Show the relevant steps of the appropriate hypothesis test.

Accepted Answer

The answer of When estimating a multiple regression model based...

Question 14

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.Which of the following are the hypotheses to test if the explanatory variables Bath and Sqft are jointly significant in explaining Rent? A) : Both of the coefficients are nonzero B) : At least one of the coefficients is zero C) : At least one of the coefficients is nonzero D)

Accepted Answer

The hypotheses to test if the explanatory variables Bath and Sqft are jointly significant in explaining Rent are that at least one of the coefficients is nonzero. This is represented by choice C. Options A and D are incorrect because they are too specific, while option B is incorrect because it states that at least one coefficient is zero, which is the opposite of what we want to test.

Question 15

Exhibit 15-6.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 CAPM model for Tiffany's return.  Refer to Exhibit 15-6.When testing whether there are abnormal returns,or whether the alpha coefficient is significantly different from zero,the value of the test statistic is
A)-98.
B)1.98.
C)4.33.
D)9.58.

Accepted Answer

The answer of Exhibit 15-6.Tiffany & Co.has been the world's...

Question 16

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-7.When testing whether the explanatory variables jointly influence the response variable,the null hypothesis is A) B) C) D)

Accepted Answer

The answer of Exhibit 15-8.A real estate analyst believes that...

Question 17

Exhibit 15-6.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 CAPM model for Tiffany's return. Refer to Exhibit 15-6.When testing whether there are abnormal returns,the conclusion to the test is at the 5% significance level is: A)Reject H₀,and conclude there are abnormal returns. B)Do not reject H₀,and conclude there are abnormal returns. C)Reject H₀,and do not conclude there are abnormal returns. D)Do not reject H₀,and do not conclude there are abnormal returns.

Accepted Answer

The answer of Exhibit 15-6.Tiffany & Co.has been the world's...

Question 18

Exhibit 15-9.An economist estimates the following model:  .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  .A portion of the regression results is shown in the accompanying table.  Refer to Exhibit 15-9.According to the modified model,what is the predicted value of y when x equals 2.
A)2.52
B)24.78
C)27.30
D)29.82

Accepted Answer

The answer of Exhibit 15-9.An economist estimates the following model:...

Question 19

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.When testing whether Bed is significant at the 5% level,she A)Rejects ,and concludes that the number of bedrooms significantly influences rent. B)Does not reject ,and concludes that the number of bedrooms significantly influences rent. C)Rejects ,and concludes that the number of bedrooms does not significantly influence rent. D)Does not reject

Accepted Answer

To test the significance of the number of bedrooms, we need to check the p-value associated with the coefficient of x₁ (Bed). The p-value is given as 0.028, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that the number of bedrooms significantly influences rent.

Question 20

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.Which of the following is the value of the test statistic for testing the joint significance of the linear regression model? A)1.59 B)2.22 C)3.75 D)50.88

Accepted Answer

The answer of Exhibit 15-8.A real estate analyst believes that...

Quiz 15: Inference With Regression Models

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 accompanying table shows the regression results when estimating . a.Specify the competing hypotheses to determine whether x is significant in y. B)At the 5% significance level,is x significant? Explain.