Q21. With respect to testing the validity of the model’s results, Williams may wish to perform:

A)   a Durbin-Watson test, but not a Breusch-Pagan test.

B)   both a Durbin-Watson test and a Breusch-Pagan test.

C)   a Breusch-Pagan test, but not a Durbin-Watson test.

Q22. Williams decides to use two-tailed tests on the individual variables, at a 5% level of significance, to determine whether electric generator sales are explained by each of them individually. Williams concludes that:

A)   all of the variables explain sales.

B)   all of the variables except snowfall explain sales.

C)   all of the variables except snowfall and housing starts explain sales.

Q23. When Williams ran the model, the computer said the R² is 0.233. She examines the other output and concludes that this is the:

A)   adjusted R² value.

B)   neither the unadjusted nor adjusted R² value, nor the coefficient of correlation.

C)   unadjusted R² value.

Q24. In preparing and using this model, Williams has least likely relied on which of the following assumptions?

A)   A linear relationship exists between the dependent and independent variables.

B)   There is a linear relationship between the independent variables.

C)   The disturbance or error term is normally distributed.

Q25. Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i

where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5.

The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero?

A)     R&D, COMP, and CAP only.

B)     R&D, ADV, COMP, and CAP.

C)     ADV and CAP only.

答案和详解如下：

Q21. With respect to testing the validity of the model’s results, Williams may wish to perform:

A)   a Durbin-Watson test, but not a Breusch-Pagan test.

B)   both a Durbin-Watson test and a Breusch-Pagan test.

C)   a Breusch-Pagan test, but not a Durbin-Watson test.

Correct answer is B)

Since this is not an autoregression, a test for serial correlation is appropriate so the Durbin-Watson test would be used. The Breusch-Pagan test for heteroskedasticity would be a good idea.

Q22. Williams decides to use two-tailed tests on the individual variables, at a 5% level of significance, to determine whether electric generator sales are explained by each of them individually. Williams concludes that:

A)   all of the variables explain sales.

B)   all of the variables except snowfall explain sales.

C)   all of the variables except snowfall and housing starts explain sales.

Correct answer is B)

The calculated t–statistics are:

·  Heating Oil: (2.00 / 0.827) = 2.4184

·  Low Temperature: (3.00 / 1.200) = 2.5000

·  Snowfall: (10.00 / 4.833) = 2.0691

·  Housing Starts: (5.00 / 2.333) = 2.1432

All of these values are outside the t–critical value (at (26 − 4 − 1) = 21 degrees of freedom) of 2.080, except the change in snowfall. So Williams should reject the null hypothesis for the other variables and conclude that they explain sales, but fail to reject the null hypothesis with respect to snowfall and conclude that increases or decreases in snowfall do not explain sales.

Q23. When Williams ran the model, the computer said the R² is 0.233. She examines the other output and concludes that this is the:

A)   adjusted R² value.

B)   neither the unadjusted nor adjusted R² value, nor the coefficient of correlation.

C)   unadjusted R² value.

Correct answer is A)

This can be answered by recognizing that the unadjusted R-square is (335.2 / 941.6) = 0.356. Thus, the reported value must be the adjusted R². To verify this we see that the adjusted R-squared is: 1− ((26 − 1) / (26 − 4 − 1)) × (1 − 0.356) = 0.233. Note that whenever there is more than one independent variable, the adjusted R² will always be less than R².

Q24. In preparing and using this model, Williams has least likely relied on which of the following assumptions?

A)   A linear relationship exists between the dependent and independent variables.

B)   There is a linear relationship between the independent variables.

C)   The disturbance or error term is normally distributed.

Correct answer is B)         

Multiple regression models assume that there is no linear relationship between two or more of the independent variables. The other answer choices are both assumptions of multiple regression.

Q25. Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i – 2.0 COMP_i + 8.0 CAP_i

where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5.

The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero?

A)     R&D, COMP, and CAP only.

B)     R&D, ADV, COMP, and CAP.

C)     ADV and CAP only.

Correct answer is A)

The critical t-values for 40-4-1 = 35 degrees of freedom and a 5% level of significance are ± 2.03.

The calculated t-values are:
t for R&D = 1.25 / 0.45 = 2.777
t for ADV = 1.0/ 2.2 = 0.455
t for COMP = -2.0 / 0.63 = -3.175
t for CAP = 8.0 / 2.5 = 3.2
Therefore, R&D, COMP, and CAP are statistically significant.

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