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Chapter 14: Q 4 (page 588)

Regarding analysis of residuals, decide in each case which assumption for regression inferences may be violated.

a. A residual plot - that is, a plot of the residuals against the observed values of the predictor variable-shows curvature.

b. A residual plot becomes wider with increasing values of the predictor variable.

c. A normal probability plot of the residuals shows extreme curvature.

d. A normal probability plot of the residuals shows outliers but is otherwise roughly linear.

Short Answer

Expert verified

Part (a) The case of plot of the residuals against the observed value of the predictor variable shows curvature.

Part (b) the case of a residual plot becomes wider with increasing values of the predictor variabie.

Part (c) the case of a normal probability plot of the residuals shows extreme curvature.

Part (d)When a normal probability plot of the residuals shows cutlers

Step by step solution

01

Given information

Assumption for regression inferences

02

Step 2:Explaination Part (a)

Assumption 1 is vialated in the case of plot of the residuals against the observed value of the predictor variable shows curvature.

03

Step 2:Explaination Part (b)

Assumption 2 is vialated in the case of a residual plot becomes wider with increasing values of the predictor variabie.

04

Step 2:Explaination Part (c)

Assumption 3 is volated in the case of a normal probability plot of the residuals shows extreme curvature.

05

Step 2:Explaination Part (d)

When a normal probability plot of the residuals shows cutlers but is otherwise roughly linear, we say that the assumption 3 is viclated.

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Most popular questions from this chapter

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.)

In Exercises 14.70-14.80, use the technology of your choice to do the following tasks.

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.

14.70 Birdies and Score. The data from Exercise 14.34 for number of birdies during a tournament and final score for 63 women golfer are on the WeissStats site.

To find and interpret a confidence interval, at the specified confidence level 95%for the slope of the population regression line that relates the response variables to the predictor variable.


Find a95%prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

a. Obtain a point estimate for the mean tax efficiency of all mutual fund portfolios with6%of their investments in energy securities.

b. Determine a95%confidence interval for the mean tax efficiency of all mutual fund portfolios with6%of their investments in energy securities.

c. Find the predicted tax efficiency of a mutual fund portfolio with 6%of its investments in energy securities.

d. Determine a 95%prediction interval for the tax efficiency of a mutual fund portfolio with 6%of its investments in energy securities.
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