Question

Gas Guzzlers. The data from Exercise 14.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site. Specified value of the predictor variable: $3.0L.$

a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(f).

b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

c. Find and interpret a $95\%$confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.

e. Find and interpret a $95\%$prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

Short answer

It is not applying the conditional mean and predicted value t-interval procedure to the given data in a reasonable manner. As a result, the remaining parts (b) -(f) are omitted.

Step-by-step solution

Given Information 

Given in the question that to consider the data's from exercise 14.41. Then we have to decide whether you can reasonably apply the conditional mean and predicted value $t$-interval procedures to the data. If so, then also do parts (b)-(f).

Explanation

Using the data from Exercise 14.41, determine whether it is possible to implement the conditional mean and preceded value 4 -interval procedure to data

.$\begin{array}{|cccc|}\hline \text{DISP}& \text{MPG}& 4& 16\\ 1.8& 31& 4& 15\\ 3.5& 20& 1.8& 26\\ 3.2& 22& 3& 22\\ 1.8& 22& 3& 23\\ 2.8& 20& 3& 19\\ 2.5& 24& 4.6& 18\\ 2.8& 20& 4.6& 19\\ 2.8& 24& 2& 24\\ 3.1& 22& 4& 18\\ 3.8& 20& 1.8& 27\\ 3.8& 21& 1.8& 27\\ 3.8& 21& 2.8& 24\\ \hline\end{array}$

$\begin{array}{|rrrr|}\hline 3& 20& 3.2& 22\\ 4.6& 20& 3.2& 19\\ 4.3& 15& 2.5& 24\\ 4.3& 15& 4.6& 19\\ 2.2& 26& 4& 16\\ 5.7& 20& 2.5& 22\\ 3.1& 22& 3& 22\\ 2.4& 24& 2& 28\\ 1.8& 31& 2.4& 24\\ 4.3& 17& 1.8& 27\\ 5.7& 13& 3& 18\\ 3.4& 19& 2.4& 25\\ 2.5& 22& 3& 23\\ \hline\end{array}$

$\begin{array}{|cccc|}\hline 3.2& 21& 3.3& 15\\ 2.5& 21& 2.4& 23\\ 3.3& 18& 4& 19\\ 2.2& 24& 3.1& 24\\ 2& 24& 3.8& 20\\ 3.3& 19& 3.4& 19\\ 3.9& 16& 2& 23\\ 5.2& 13& 3.3& 18\\ 3.3& 18& 3.3& 19\\ 2.7& 22& 2.4& 23\\ 5.2& 13& 3.8& 21\\ 2.5& 22& 3.4& 18\\ 2& 24& 2.4& 25\\ \hline\end{array}$

$\begin{array}{|rrrr|}\hline 4.6& 19& 2.5& 24\\ 2& 28& 2& 22\\ 4.6& 13& 2.3& 23\\ 4& 16& 1.9& 29\\ 4.6& 16& 1.9& 28\\ 4& 18& 2.5& 22\\ 3& 21& 2.2& 23\\ 4.3& 15& 2.2& 24\\ 4.3& 15& 1.6& 29\\ 4.3& 17& 3.4& 18\\ 5.7& 13& 3& 23\\ 2.3& 25& 2.2& 25\\ 3& 23& 3& 23\\ \hline\end{array}$

$\begin{array}{|rrrr|}\hline 2& 24& 3& 22\\ 1.6& 31& 1.8& 30\\ 3.2& 18& 2& 22\\ 2& 25& 3& 19\\ 2& 27& 3.4& 19\\ 2& 25& 2& 24\\ 3& 23& 2& 29\\ 3.3& 16& 1.8& 24\\ 3.2& 18& 2.4& 21\\ \hline\end{array}$

Explanation

As determined by the residual plot versus engine displacement. There is an upward concave curve pattern. The residual plot and the probability value of residuals show that there are outliers. As a result, the linear model is inapplicable.

As a result, for the variables Mpg and disp, assumption $1$for regression inferences is violated. Furthermore, the interpretation for standard error obtained in part (a) is invalid.

As a result, able to apply the mean and predicted value t-interval procedure to the given data is not reasonable. As a result, the remaining parts (b) -(f) are omitted.