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Chapter 14: Q.14.29 (page 562)

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

Expert verified

a). The required solution is 16.89.

b). The predicted value will differ by 16.89from 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

01

Part (a) Step 1: Given Information

Given data:

02

Part (a) Step 2: Explanation

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

蟽=鈭�xi-渭2N

We will obtain after solving

蟽=53.42

Then calculate the standard error

Standard error 蟽e=蟽n

蟽e=53.4210

=16.89

03

Part (b) Step 1: Given Information

Given data:

04

Part (b) Step 2: Explanation

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

Standard error蟽e=蟽n

蟽e=53.4210

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

05

Part (c) Step 1: Given Information

Given data:

06

Part (c) Step 2: Given Information

Determine the residual.

residual=y-y^

Here y^is the linear fit value.

Using MATLAB sketch a residual plot and normal probability plot.

A residual plot:

The normal probability:

07

Part (c) Step 1: Given Information

Given data:

08

Part (d) Step 2: Explanation

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

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Most popular questions from this chapter

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b) - (h).
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%Te 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).

14.10 PCBs and Pelicans. The data from Exercise 14.40for shell thickness and concentration of PCBs of 60Anacapa pelican eggs are on the WeissStats site. Specified value of the predictor variable: 220ppm.

Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks, use伪=0.01presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

14.95 Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise 14.25.

x
57
85
57
65
52
67
62
80
77
53
68
y
8.0
22.0
10.5
22.5
12.0
11.5
7.5
13.0
16.5
21.0
12.0

a. Obtain a point estimate for the mean quantity of volatile emissions of all (Solanum tuberosum) plants that weigh 60g.
b. Find a 95%confidence interval for the mean quantity of volatile emissions of all plants that weigh 60g.
c. Find the predicted quantity of volatile emissions for a plant that weighs 60g.
d. Determine a 95%prediction interval for the quantity of volatile emissions for a plant that weighs 60g.

In this Exercise 14.51, we repeat the information from Exercise 14.15.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y:

b. Find a 90%confidence interval for the slope of the population regression line.

role="math" localid="1652333468446" x3412y450-1 role="math" localid="1652333507650" y^=-3+x

Following are the age and price data for custom homes, use 伪=0.01

presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.
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