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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

Fill in the blanks.

a. The line y=β0+β1xis called the ____

b. The common conditional standard deviation of the response variable is denoted _____

c. For x=6, the conditional distribution of the response variable is a____ distribution having mean___ and standard deviation____.

Movie Grosses. Box Office Mojo collects and posts data on movie grosses. For a random sample of 50 movies, we obtained both the domestic (U.S.) and overseas grosses, in millions of dollars. The data are presented on the WeissStats site.

PCBs and Pelicans. Use the data points given on the WeissStats site for shell thickness and concentration of PCBs for 60Anacapa pelican eggs referred to in Exercise 14.40.

a. Decide whether you can reasonably apply the regression t-test. If so, then also do part (b).

b. Decide, at the 5%significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

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% 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).

14.103 High and Low Temperature. The data from Exercise 14.31for average high and low temperatures in January of a random sample, of 50cities are on the WeissStats site. Specified value of the predictor variable: 55°F.

Which graph used in a residual analysis provides roughly the same information as a scatterplot? What advantages does it have over a scatterplot?
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