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Chapter 14: Q 14.10 (page 560)

The figure shows three residual plots and a normal probability plot of residuals. For each part, decide whether the graph suggests a violation of one or more of the assumptions for regression inferences. Explain your answers.

Short Answer

Expert verified

a) Assumptions I and 2 appear to be met.

b)Assumption2 is violated.

c)Assumption 2 may have been violated in this case.

d)Assumption 3 may not have been violated in this case. It also appears to be reasonable.

Step by step solution

01

Given Information

02

Explanation

The residuals in part (a) are scattered about thex-axis (residuals= 0) and fall roughly in a horizontal band, indicating that Assumptions I and 2 appear to be met.

Part (b) of the plot indicates that the assumption of equal standard deviations (Assumption2) is violated.

The plot in part (c) suggests that the constant standard deviation is violated. As a result, Assumption 2 may have been violated in this case.

The plot in pad (d) indicates that there is no violation of the assumption of normal populations.

As a result, assumption 3 may not have been violated in this case. It also appears to be reasonable.

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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.)

we repeat the data and provide the sample regression equations for Exercises a.Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

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)-(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% Te 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 a95% 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).
14.100 Movie Grosses. The data from Exercise 14.36 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. Specified value of the predictor variable: S 100 million.

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.

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

b. Determine a 95%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 with6% of its investments in energy securities.

d. Determine a95%prediction interval for the tax efficiency of a mutual fund portfolio with 6%of its investments in energy securities.
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