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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

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

a. Determine the standand error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

In each of Exercises 14.64-14.69, apply Procedure 14.2 an page 567 to find and interpret a confidence interval, at the specified confidence level for the slope of the population regression line that relates rite response variable to the predicter variable.

Crown-Rump Length. Refer to Exercise 14.62;90%.

Based on a sample of data points, what is the best estimate of the population regression line?

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.
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