Question

Currently, a manager is using a regression model that predicts gas mileage​ (in miles per​ gallon) based on the horsepower of a car and the​ car's weight​ (in pounds). She believes that the effect of HP on gas milage is affected by the weight and vice versa. Develop a regression model that includes​ horsepower, weight, and this new interaction effect to predict gas mileage. Complete parts​ (a) and​ (b).

MPG- 15.3,19.5,20.8,18.9,17.2,27.5,44.4,27.2,28.3,21.1

Horsepower-187,101,143,171,166,72,70,89,87,134

Weight-4757,3537,3227,4448,4296,3191,2106,2490,2605,3871

a. At the 0.01level 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?

A.H0​:β3=0

H1​:β3>0

B.H0​:β3≥0

H1​:β3<0

C.H0​:β3≠0

H1​:β3=0

D.H0​:β3≤0

H1​:β3>0

E.H0​:β3=0

H1​:β3≠0

F.H0​:β3=0

H1​:β3<0

What is the​ p-value for this​ test?

​p-value=

​(Round to three decimal places as​ needed.)

What is the conclusion for this​ test?

Since the​ p-value for the interaction term is ___than α​,____H0.

There____ enough evidence to conclude that the interaction term makes a significant contribution to the model.

b. Which regression model is more​appropriate, the original given model or the new model with the interaction​ term? Explain.

A.The new model is more appropriate because the interaction is not significant.

B.The new model is more appropriate because the interaction is significant.

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

D.The old model is more appropriate because the interaction is significant.

E.The new model is more appropriate because the coefficient of the interaction term is not equal to 0.

3)The data provided give the gasoline mileage​ (in miles per​ gallon) based on the horsepower of a​ car's engine and the weight of the car​ (in pounds). Using the data​ provided, determine the VIF for each independent variable in the model. Is there reason to suspect the existence of​ collinearity?

MPG- 15.3,19.9,20.5,18.4,17.5,27.2,44.8,27.9,28.4,21.2

Horsepower- 191,108,140,173,164,68,60,85,85,135

weight- 4724,3531,3223,4494,4297,3192,2111,2487,2606,3874

Determine the VIF for each independent variable in the model.

VIF 1=___

VIF 2=___

​(Round to three decimal places as​ needed.)

Is there reason to suspect the existence of ​collinearity?

A.Yes. The VIF for each independent variable is less than 5.

B.No. The VIF for each independent variable is greater than 5.

C.Yes. The VIF for each independent variable is greater than 5.

D.No. The VIF for each independent variable is less than 5.

Answer 1

Using Minitab software, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

The correct hypotheses are - H₀​:β₃ =0 against H₁​:β₃ ≠0

The p-value for this​ test = 0.038

Since the​ p-value for the interaction term is greater than α​ = 0.01, fail to reject H₀

There is not enough evidence to conclude that the interaction term makes a significant contribution to the model.

b) ans-> C.The old model is more appropriate because the interaction is not significant.

3. VIF 1 = 40.09 and VIF 2 = 16.8

C.Yes. The VIF for each independent variable is greater than 5.