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Reading 12: Multiple Regression and Issues in Regression A

Q14. Using data from the past 20 quarters, Brent calculates the t-statistic for marketing expenditures to be 3.68 and the t-statistic for salespeople at 2.19. At a 5% significance level, the two-tailed critical values are tc = +/- 2.127. This most likely indicates that:

A)   the t-statistic has 18 degrees of freedom.

B)   both independent variables are statistically significant.

C)   the null hypothesis should not be rejected.

Q15. Brent calculated that the sum of squared errors (SSE) for the variables is 267. The mean squared error (MSE) would be:

A)   14.831.

B)   14.055.

C)   15.706.

Q16. Brent is trying to explain the concept of the standard error of estimate (SEE) to Johnson. In his explanation, Brent makes three points about the SEE:

  • Point 1: The SEE is the standard deviation of the differences between the estimated values for the independent variables and the actual observations for the independent variable.

  • Point 2: Any violation of the basic assumptions of a multiple regression model is going to affect the SEE.

  • Point 3: If there is a strong relationship between the variables and the SSE is small, the individual estimation errors will also be small.

How many of Brent’s points are most accurate?

A)   1 of Brent’s points are correct.

B)   All 3 of Brent’s points are correct.

C)   2 of Brent’s points are correct.

Q17. Assuming that next year’s marketing expenditures are $3,500,000 and there are five salespeople, predicted sales for Mega Flowers will be:

A)   $11,600,000.

B)   $24,200,000.

C)   $2,400,000.

Q18. Brent would like to further investigate whether at least one of the independent variables can explain a significant portion of the variation of the dependent variable. Which of the following methods would be best for Brent to use?

A)   The F-statistic.

B)   The multiple coefficient of determination.

C)   An ANOVA table.

答案和详解如下:

Q14. Using data from the past 20 quarters, Brent calculates the t-statistic for marketing expenditures to be 3.68 and the t-statistic for salespeople at 2.19. At a 5% significance level, the two-tailed critical values are tc = +/- 2.127. This most likely indicates that:

A)   the t-statistic has 18 degrees of freedom.

B)   both independent variables are statistically significant.

C)   the null hypothesis should not be rejected.

Correct answer is B)

Using a 5% significance level with degrees of freedom (df) of 17 (20-2-1), both independent variables are significant and contribute to the level of expected sales.

Q15. Brent calculated that the sum of squared errors (SSE) for the variables is 267. The mean squared error (MSE) would be:

A)   14.831.

B)   14.055.

C)   15.706.

Correct answer is C)

The MSE is calculated as SSE / (n – k – 1). Recall that there are twenty observations and two independent variables. Therefore, the MSE in this instance [267 / (20 – 2 - 1)] = 15.706.

Q16. Brent is trying to explain the concept of the standard error of estimate (SEE) to Johnson. In his explanation, Brent makes three points about the SEE:

  • Point 1: The SEE is the standard deviation of the differences between the estimated values for the independent variables and the actual observations for the independent variable.

  • Point 2: Any violation of the basic assumptions of a multiple regression model is going to affect the SEE.

  • Point 3: If there is a strong relationship between the variables and the SSE is small, the individual estimation errors will also be small.

How many of Brent’s points are most accurate?

A)   1 of Brent’s points are correct.

B)   All 3 of Brent’s points are correct.

C)   2 of Brent’s points are correct.

Correct answer is C)

The statements that if there is a strong relationship between the variables and the SSE is small, the individual estimation errors will also be small, and also that any violation of the basic assumptions of a multiple regression model is going to affect the SEE are both correct.

The SEE is the standard deviation of the differences between the estimated values for the dependent variables (not independent) and the actual observations for the dependent variable. Brent’s Point 1 is incorrect.

Therefore, 2 of Brent’s points are correct.

Q17. Assuming that next year’s marketing expenditures are $3,500,000 and there are five salespeople, predicted sales for Mega Flowers will be:

A)   $11,600,000.

B)   $24,200,000.

C)   $2,400,000.

Correct answer is B)

Using the regression equation from above, expected sales equals 12.6 + (1.6 x 3.5) + (1.2 x 5) = $24.2 million. Remember to check the details – i.e. this equation is denominated in millions of dollars.

Q18. Brent would like to further investigate whether at least one of the independent variables can explain a significant portion of the variation of the dependent variable. Which of the following methods would be best for Brent to use?

A)   The F-statistic.

B)   The multiple coefficient of determination.

C)   An ANOVA table.

Correct answer is A)

To determine whether at least one of the coefficients is statistically significant, the calculated F-statistic is compared with the critical F-value at the appropriate level of significance.

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