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Chapter 14: Q 14.8 (page 560)

Identify two graphs used in a residual analysis to check the Assumptions 1-3 for regression inferences, and explain the reasoning behind their use:

Short Answer

Expert verified

Their use is justified because failure to meet these two conditions calls into question the validity of one or more of the assumptions for regression inferences for the variables under consideration.

Step by step solution

01

Given Information

The given assumption for regression inferences is 1-3

02

Explanation

- The residuals' normal probability plot should be roughly linear.

- A plot of the residuals against the predictor variable values should be symmetric about thex axis and fall roughly in a horizontal band.

Their use is justified because failure to meet these two conditions calls into question the validity of one or more of the assumptions for regression inferences for the variables under consideration.

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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 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).

14.98 Birdies and Score. The data from Exercise 14.34 for number of birdies during a tournament and final score of 63 women golfers are on the WeissStats site. Specified value of the predictor variable:12birdies.

14.97 Study Time and Score. Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks from Exercise 14.27.

x
10
15
12
20
8
16
14
22
y
91
81
84
74
85
80
84
80


a. Determine a point estimate for the mean test score of all beginning calculus students who study for 15hours.
b. Find a 99% confidence interval for the mean test score of all beginning calculus students who study for 15 hours.
c. Find the predicted test score of a beginning calculus student who studies for 15 hours.
d. Determine a 99% prediction interval for the test score of a beginning calculus student who studies for 15hours.

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 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.

a. Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

y=14-3x

In Exexcises 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% 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 obfained in part (e).
14.102 Home Size and Value. The data from Exercise 14.38 for home size (in square feet) and assessed value (in thousands of dollars) for the same homes as in Exercise 14.101 are on the WeissStats site. Specified value of the predictor variable: 3000 sq. ft.
See all solutions

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