Question

Corvette Prices. Use the age and price data for Corvettes from Exercise 14.23.

a. compute the standard error of the estimate and interpret your answer

b. interpret your result from part (a) if the assumptions for regression inferences hold.

c. obtain a residual plot and a normal probability plot of the residuals.

d. decide whether you can reasonably consider Assumptions $1-3$ for regression inferences to be met by the variables under consideration. (The answer here is subjective, especially in view of the extremely small sample sizes.)

Short answer

a). The required solution is $16.89$.

b). The predicted value will differ by $16.89$from the actual value.

c). The residual plot and probability plot are shown below.

d). The residual plot shows no pattern, and the normal probability plot is linear, so it appears appropriate.

Step-by-step solution

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

Using the relation, calculate the standard deviation of the supplied data.

$\sigma =\sqrt{\frac{\sum {\left(x_i-\mu \right)}^2}{N}}$

We will obtain after solving

$\sigma =53.42$

Then calculate the standard error

Standard error $\left({\sigma }_e\right)=\frac{\sigma }{\sqrt{n}}$

${\sigma }_e=\frac{53.42}{\sqrt{10}}$

$=16.89$

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

As may be seen in portion (a), the standard error is about.

$\text{Standard error}\left({\sigma }_e\right)=\frac{\sigma }{\sqrt{n}}$

${\sigma }_e=\frac{53.42}{\sqrt{10}}$

As a result, the predicted value will differ $16.89$ from the actual value.

Part (c) Step 1: Given Information

Given data:

Part (c) Step 2: Given Information

Determine the residual.

$\text{residual}=y-\hat{y}$

Here $\hat{y}$is the linear fit value.

Using MATLAB sketch a residual plot and normal probability plot.

A residual plot:

The normal probability:

Part (c) Step 1: Given Information

Given data:

Part (d) Step 2: Explanation

The residual plot shows no pattern, and the normal probability plot is linear, so it appears appropriate.