The editors of a national automotive magazine recently studied 30 different auto

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) The standard error of the estimate is a negative value due to the multicollinearity problems in the model.

C) 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.

D) None of the above is true.

Regression Statistics Multiple R 0.906876 R Square Adjusted R Square Standard Error 30 Observations ANOVA SS MS Regression 89.88341785 Residual Total 506.1666667 Coefficients Standard Enor t Stat P-value Lower 95%Upper 95% 41.77425 5.612843566 Intercept Curb Weight -0.00608 0.00145286 0.959134 0.887531206 cylinders Horse Power 0.052399 0.023938405 Torque -0.01747 0.024737052 0 to 60 mph 0.492998 0.486960357 Price as Tested -0.00015 4.31238E-05 Displacement 2.11223 0.88675014

Explanation / Answer

The correct answer is (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.

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