[2008] Topic 9: Multiple Regression: Estimation and Hypothesis Testing 相关习

aianjie

 

AIM 2: Define and interpret the partial slope coefficient.

1、Which of the following statements regarding the results of a regression analysis is FALSE? The:

A) slope coefficient in a multiple regression is the value of the dependent variable for a given value of the independent variable.

B) slope coefficient in a multiple regression is the change in the dependent variable for a one-unit change in the independent variable, holding all other variables constant.

C) intercept is the value that the dependent variable takes on if all the independent variables had a value of zero.

D) slope coefficients in the multiple regression are referred to as partial betas.

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gita

 

The correct answer is A

The slope coefficient is the change in the dependent variable for a one-unit change in the independent variable.

gita

 

4、An analyst is estimating a regression equation with three independent variables, and calculates the R2, the adjusted R2, and the F-statistic. The analyst then decides to add a fourth variable to the equation. Which of the following is most accurate?

A) The R2 and F-statistic will be higher, but the adjusted R2 could be higher or lower.

B) The adjusted R2 will be higher, but the R2 and F-statistic could be higher or lower.

C) The R2 will be higher, but the adjusted R2 and F-statistic could be higher or lower.

D) The adjusted R2 and F-statistic will be higher, but the R2 could be higher or lower.

gita

 

The correct answer is C

The R2 will always increase as the number of variables increase. The adjusted R2 specifically adjusts for the number of variables, and might not increase as the number of variables rise. As the number of variables increases, the regression sum of squares will rise and the residual T sum of squares will fall—this will tend to make the F-statistic larger. However, the number degrees of freedom will also rise, and the denominator degrees of freedom will fall, which will tend to make the F-statistic smaller. Consequently, like the adjusted R2, the F-statistic could be higher or lower.