Question

Gas Guzzlers. Use the data on the WeissStats site for gas mileage and engine displacement for 121 vehicles referred to in Exercise 14.41.

Short answer

The regression t-test is not appropriate for this situation.

Step-by-step solution

Step 1:

Using MINITAB, create a residual plot.

Procedure with MINITAB:

Step 1: Select Stat > Regression > Regression.

Step 2: Fill the column MPG in Response.

Step 3: In Predictors, fill in the Disp columns.

Step 4: Under Residuals vs the variables in Graphs, enter the columns Disp.

Step 5: Press OK button.

Step 2:

output MINITAB:

Step 3:

MINITAB is used to create a normal probability plot of residuals.

Procedure for MINITAB:

Step 1: Select Stat > Regression > Regression .

Step 2: Enter the column MPG In Response.

Step 3: In Predictors, fill in the Disp.

Step 4: From the Graphs , choose Normal probability plot of residuals.

Step 5: Press OK button.

Step 4:

output MINITAB:

Step 5:

The following is the assumption for regression inferences:

Regression line of the population:

For each value $\chi$of the predicator variable, the conditional mean of the response variable $\gamma$is

${\beta }_0+{\beta }_{1}X$

Equal standard deviation:

The response variable's $\gamma$standard deviation is the same as the explanatory variable's $\chi$standard deviation. The standard deviation is represented by the symbol $\sigma$.

Normal populations:

The response variable's distribution is normal.

Independent observations:

The response of variable observations are unrelated to one another.

Step 6:

Examine whether the graph shows a violation of one or more of the regression inference assumptions.

- There is a concave upward curve in the residual plot versus engine displacement.

- The presence of outliers in the data is evident from the normal probability plot of residuals and the residual plot. As a result, the linear model is ineffective.

As a result, for the variables Mpg and Disp, assumption $1$for regression inferences is broken.

Step 7:

Part (a) ,it is obvious that shows the regression inference assumptions have been violated. As a result, it is impossible to determine whether the data are sufficient to establish that the predictor variable is effective for predicting the responder variable. That is, the regression t-test is not appropriate for this situation.