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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.

σ=∑xi-μ2N

We will obtain after solving

σ=53.42

Then calculate the standard error

Standard error σe=σn

σe=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 errorσe=σn

σe=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

14.24 Custom Homes. Hanna Properties specializes in custom home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, xdenotes the size, in hundreds of square feet, rounded to the nearest hundred, and ydenotes price, in thousands of dollars, rounded to the nearest thousand.

In this Exercise 14.49, we repeat the information from Exercises 14.13.

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.

x312y-40-5 y^=1-2x

14.22 Tax Efficiency. Tax efficiency is a measure ranging from 0 to 100 - of how much tax due to capital gains stock or mutual funds investors pay on their investments each year, the higher the tax efficiency, the lower the tax. The paper "At the Mercy of the Manager" (Financial Planning, Vol. 30(5), pp. 54-56 ) by C. Israelsen examined the relationship between investments in mutual fund portfolios and their associated tax efficiencies. The following table shows the percentage of investments in energy securities (x)and tax efficiency (y)for 10 mutual fund portfolios.

In Exercises 14.48-14.57, we repeat the information from Exercises 14.12-14.21.

a. Deride, at the lore significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y.

b. Find a localid="1653240248143" 90%confidence interval for the slope of the population regression line.

y=1+2x

In this Exercise 14.5, we repeat the information from Exercise 14.14.

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.

x04312y19843 y^=1+2x
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