The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon.A number of different independent variables were collected.The following regression output is the result of using a forward selection stepwise regression approach. Based on the regression output,which of the following statements is true?
A)There is a multicollinearity problem since the standard error of the estimate actually increased when the second variable,"Price as Tested," entered the model.
B)The R-square value increased when the second variable entered the model.
C)Neither variable in the model is statistically significant at the alpha = 0.05 level.
D)The reason that only two variables entered the model is due to the small sample size used in this study.

Question

The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon.A number of different independent variables were collected.The following regression output is the result of using a forward selection stepwise regression approach.  Based on the regression output,which of the following statements is true?
A)There is a multicollinearity problem since the standard error of the estimate actually increased when the second variable,"Price as Tested," entered the model. 
B)The R-square value increased when the second variable entered the model. 
C)Neither variable in the model is statistically significant at the alpha = 0.05 level. 
D)The reason that only two variables entered the model is due to the small sample size used in this study.

Quizplus · Accepted Answer

The R-square value increased from 0.383 to 0.626 when the "Price as Tested" variable entered the model, indicating that this variable has added significant explanatory power to the model. There does not appear to be a multicollinearity problem since the VIF values are all below 5. Both variables in the model, "Weight" and "Price as Tested," are statistically significant at the alpha = 0.05 level, as indicated by their respective p-values. The size of the sample is not necessarily related to the number of variables that enter the model, so D is not a valid explanation for why only two variables were included.

The Editors of a National Automotive Magazine Recently Studied 30