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Chapter 14: Q 3 (page 587)

What two plots did we use in this chapter to decide whether we can reasonably presume that the assumptions for regression inferences are met by two variables of a population? What properties should those plots have?

Short Answer

Expert verified

Residual plot and Normal Probability_plot

Step by step solution

01

Step 1:Given information

Given two plots

02

Step 2:Explaination

Residual plot: A plot of the residuals against the observed values of the predictor variable. It represents a plot of the residuals against the observed values of the predictor variable should roughly in a horizontal band and it is centered and symmetric about the x-axis.

Normal Probability_plot: A normal probability plot of the residuals should be roughly linear.

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Most popular questions from this chapter

Suppose that xand yare two variables of a population with xa predictor variable and ya response variable.

a. The distribution of all possible values of the response variable ycorresponding to a particular value of the predictor variable xis called a distribution of the response variable.

b. State the four assumptions for regression inferences.

14.96 Crown-Rump Length. Following are the data on age of fetuses and length of crown-rump from Exercise 14.26.

x
10
10
13
13
18
19
19
23
25
28
y
66
66
108
106
161
166
177
288
235
280

a. Determine a point estimate for the mean crown-rump length of all 19-week-old fetuses.
b. Find a 90% confidence interval for the mean crown-rump length of all 19-week-old fetuses.
c. Find the predicted crown-rump length of a 19-week-old fetus.

d. Determine a 90%prediction interval for the crown-rump length of a 19 -week-old fetus.

14.75 High and Low Temperature. The data from Exercise 14.39for average high and low temperatures in January for a random sample of 50cities are on the WeissStats site.

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.

Gas Guzzelrs. Use the data on the WeissStats site for gas mileage and engine displacement for 121vehicles referred to in Exercise 14.41

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.

14.95 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.
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