lianai

 

Hays is aware that part, but not all, of the total variation in expected sales can be explained by the regression equation. Which of the following statements correctly reflects this relationship?

A) SST = RSS + SSE. 

B) SST = RSS + SSE + MSE. 

C) MSE = RSS + SSE. 

D) SSE = RSS = SST. 

lianai

 

The correct answer is A

RSS (Regression sum of squares) is the portion of the total variation in Y that is explained by the regression equation. The SSE (Sum of squared errors), is the portion of the total variation in Y that is not explained by the regression. The SST is the total variation of Y around its average value. Therefore, SST = RSS + SSE. These sums of squares will always be calculated for you on the exam, so focus on understanding the interpretation of each.

lianai

 

Hays decides to test the overall effectiveness of the both independent variables in explaining sales for Milky Way. Assuming that the total sum of squares is 389.14, the sum of squared errors is 146.85 and the mean squared error is 2.576, calculate and interpret the R2.

A) The R2 equals 0.623, indicating that the two independent variables account for 62.3% of the variation in monthly sales.

B) The R2 equals 0.623, indicating that the two independent variables account for 37.7% of the variation in monthly sales.

C) The R2 equals 0.242, indicating that the two independent variables account for 24.2% of the variation in monthly sales.

D) The R2 equals 0.242, indicating that the two independent variables account for 75.8% of the variation in monthly sales.

lianai

 

The correct answer is A

The R2 is calculated as (SST – SSE) / SST. In this example, R2 equals (389.14–146.85) / 389.14 = .623 or 62.3%. This indicates that the two independent variables together explain 62.3% of the variation in monthly sales. The value for mean squared error is not used in this calculation.

lianai

 

Stepp is concerned about the validity of Hays’ regression analysis and asks Hays if he can test for the presence of heteroskedasticity. Hays complies with Stepp’s request, and detects the presence of unconditional heteroskedasticity. Which of the following statements regarding heteroskedasticity is most correct?

A) Unconditional heteroskedasticity does create significant problems for statistical inference.

B) Heteroskedasticity occurs when the variance of the residuals in the same across all observations in the sample.

C) Unconditional heteroskedasticity usually causes no major problems with the regression.

D) Heteroskedasticity can be detected either by examining scatter plots of the residual or by using the Durbin-Watson test.

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The correct answer is C

Unconditional heteroskedasticity occurs when the heteroskedasticity is not related to the level of the independent variables. This means that it does not systematically increase or decrease with changes in the independent variable(s). Note that heteroskedasticity occurs when the variance of the residuals is different across all observations in the sample and can be detected either by examining scatter plots or using a Breusch-Pagen test.

 

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23、Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated:

AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt

with a PI calculated t-statstic of 0.45, a TEEN calculated t-statstic of 2.2, and an INS calculated t-statstic of 0.63.

The equation was estimated over 40 companies. Using a 5 percent level of significance, which of the independent variables significantly different from zero?

A) PI and INS only.

B) PI, TEEN, and INS.

C) PI only.

D) TEEN only.

lianai

 

The correct answer is D

The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant.

 

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AIM 9: Define, calculate and interpret hypothesis testing for individual partial regression coefficients, joint hypothesis testing, and ANOVA.

1、Consider the following analysis of variance (ANOVA) table:

Source	Sum of squares	Degrees of freedom	Mean square
Regression	550	1	550.000
Error	750	38	19.834
Total	1,300	39

The F-statistic for the test of the fit of the model is closest to:

A)    0.965.

B)    27.730.

C)   0.423.

D)   0.733.

lianai

 

The correct answer is B

F = Mean Square of Regression / Mean Square of Error = 550 / 19.834 = 27.730.