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 (with some values missing)was recently presented to the editors by the magazine's analysts: Based on this output and your understanding of multiple regression analysis,which of the following statements is true?
A)The overall multiple regression model explains a significant portion of the variation in highway mileage when tested at a significance level of 0.05.
B)Only the two independent variables are statistically significant in the presence of the others when a significance level of 0.05 is used to test.
C)The standard error of the estimate is a negative value due to the multicollinearity problems in the model.
D)None of the above is true.

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 (with some values missing)was recently presented to the editors by the magazine's analysts:  Based on this output and your understanding of multiple regression analysis,which of the following statements is true?
A)The overall multiple regression model explains a significant portion of the variation in highway mileage when tested at a significance level of 0.05. 
B)Only the two independent variables are statistically significant in the presence of the others when a significance level of 0.05 is used to test. 
C)The standard error of the estimate is a negative value due to the multicollinearity problems in the model. 
D)None of the above is true.

Quizplus · Accepted Answer

From the given output, we can see that the p-value for F-statistic is less than 0.05 (0.000), indicating that the overall multiple regression model is statistically significant at a significance level of 0.05. Therefore, option A is true.

Option B is false because all the independent variables are statistically significant at a significance level of 0.05 except for the variable "Cylinders".

Option C is false because the standard error of the estimate cannot be negative due to multicollinearity problems. It is an estimate of the standard deviation of the errors in the regression model, and it is always a positive value.

The Editors of a National Automotive Magazine Recently Studied 30