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Chapter 14: Q. 14.23 (page 561)

14.23 Corvette Prices. The Kelley Blue Book provides information on wholesale and retail prices of cars. Following are age and price data for 10 randomly selected Corvettes between 1 and 6 years old.

Here, xdenotes age, in years, and ydenotes price, in hundreds of dollars.

Short Answer

Expert verified
The residuals are fairly centered and symmetric about the x-axis, and they fall in a horizontal band.
Although the deviation from linearity is considerable for some worries, we can also state that the normal probability plot for the residuals is (very) roughly linear.

Step by step solution

01

Given Information

Given table:

x=age

y=price

The table shows the age and pricing of ten Corvettes aged one to six years.

02

Explanation

Regression-inference assumptions 1-3 require that the constants 尾0,尾1and 蟽be constants such that, for every age x, the prices of all Corvettes within that age have a normal distribution with means 尾0+尾1xand a standard deviation of 蟽.

There is a band of roughly horizontal residuals that is symmetric about the x-axis and centered on it. It is also important to note that the normal probability plot for the residuals is (roughly) linear, but the deviation is enough to cause concern.

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Most popular questions from this chapter

In Exercises 14.48, we repeat the information from Exercises 14.12.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y:

b. Find a 90%confidence interval for the slope of the population regression line.

x243y357 role="math" localid="1652276835214" y^=2+x

Following are the data on age of fetuses and length of crown-rump.use伪=0.10presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

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 standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

y=14-3x

Gas Guzzlers. The data from Exercise 14.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site. Specified value of the predictor variable: 3.0L.

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)-(f).

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).

14.97 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.
See all solutions

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