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

(a) For the variables Mpg and disp, assumption 1 for regression conclusions is violated.

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, Gas Guzzlers. Use the data on the WeissStats site for gas mileage and engine displacement for 121 vehicles referred to in Exercise 14.41.We need to decide that whether we can reasonably apply the regression t-lest. If so, then also do part (b).

Part (a) Step 2: Explanation

Given:

Calculation: Using MINITAB, create the residual plot.

Procedure with Minitab:

First, select Start > Regression > Regression.

Step 2: In the Response field, type MPG.

Step 3: Select Column Disp in Predictors.

Step 4: In Graphs, under Residuals vs the variables, enter the columns Disp.

Step 5: Click the OK button.

OUTPUT FROM MINITAB:

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

Part (a) Step 3: MINITAB procedure

Procedure with Minitab:

Step 1: Select Start >Regression > from the menu. Regression

Step 2: In the Response field, type MPG.

Step 3: Select Column Disp in Predictors.

Step 4: Select Normal probability plot of residuals from the Graphs menu.

Step 5: Click the OK button.

OUTPUT FROM MINITAB:

The following is the assumption for regression inferences:

Line of population regression:

For each value $X$of the predictor variable, the conditional mean of the response variable $\left(Y\right)$is ${\beta }_0+{\beta }_{1}X$.

Standard deviation equal:

The response variable's $\left(Y\right)$standard deviation is the same as the explanatory variable's $\left(X\right)$standard deviation. The standard deviation is represented by the symbol $\sigma$.

Populations that are typical:

The response variable follows a normal distribution.

Independent Observations: The responses variable observations are unrelated to one another.

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.