Print For the data below, the regression model Y 51.39003 0.02779x 0.00698X2i pr

Question

Print For the data below, the regression model Y 51.39003 0.02779x 0.00698X2i predicts gas mileage (in miles per gallon) based on the horsepower of a car, X cars weight, X2, (in pounds) Develop a regression model that includes horsepower, weight, and their interaction to predict gas mileage. Complete parts (a)and (b) 3 Click the icon to view the data. a. At the 0.01 level of significance, is there evidence that the interaction term makes a significant contribution to the model? Let the interaction variable be X3. What are the null and alternative hypotheses for this test? O A. Ho: A320 O B. Ho: 83 30 H1: A3

Explanation / Answer

a) option E) is correct

as we want to check if there is significant contribution .

p-value = 0.0344821951

since the p-value is greater than alpha , we fail to reject Ho. There is not enough evidence.

b) A) is correct

the old model is more appropriate because the interaction is not significant .

Below is the result of new model .

X Variable 3 is the interaction term.

SUMMARY OUTPUT Regression Statistics Multiple R 0.941193 R Square 0.885844 Adjusted R Square 0.828766 Standard Error 3.524602 Observations 10 ANOVA df SS MS F Significance F Regression 3 578.4040808 192.80136 15.51993528 0.003112 Residual 6 74.53691917 12.42282 Total 9 652.941 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 93.64331 16.34831609 5.7280097 0.001228609 53.64043 133.6462 53.64043 133.6462 X Variable 1 -0.45593 0.169948855 -2.6827427 0.036402866 -0.87178 -0.04008 -0.87178 -0.04008 X Variable 2 -0.01832 0.00524685 -3.4908674 0.012969654 -0.03115 -0.00548 -0.03115 -0.00548 X Variable 3 0.000108 3.97847E-05 2.7234995 0.034482195 1.1E-05 0.000206 1.1E-05 0.000206

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