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Chapter 14: Q. 14.65 (page 571)

In each of Exercises 14.64-14.69, apply Procedure 14.2 on page 567 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the predictor variable.
14.65 Corvette Prices. Refer to Exercise 14.59;90%

Short Answer

Expert verified

The Confidence interval at90% is [71.0382,85.8079].

Step by step solution

01

Given information

To determine 90%confidence interval that refer to Exercise 14.59.

02

Explanation

The provided sample data as follows:

x
12
24
10
9
15
17
9
18
16
22
y
84
79
81
90
81
85
82
84
83
75

Determine the degree of freedom as follows:
df=n-2

=10-2

=8
The value of t0.1is 1.860, as determined by the student t-test.

Determine the confidence interval as follows:

x炉-t0.1脳sn=82.4-1.860脳3.949710

=71.0382

x炉-t0.1脳sn=82.4+1.860脳3.949710

=85.8079

Finally,

Confidence interval=[71.0382,85.8079].

03

Explanation

Plot a graph as follows:

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Most popular questions from this chapter

Following are the data on the percentage of investments in energy securities and tax efficiency95%,伪=0.05 . find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the predictor variable.

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.

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).

14.101 Acreage and Value. The data from Exercise 14.37for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Specified value of the predictor variable: 2.5 acres.

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.

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.
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