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Chapter 12: Q. 3 (page 787)

Oil and residuals Researchers examined data on the depth of small defects in the Trans-Alaska Oil Pipeline. The researchers compared the results of measurements on 100defects made in the field with measurements of the same defects made in the laboratory. The figure shows a residual plot for the least-squares regression line based on these data. Explain why the conditions for performing inference about the slope 尾1 of the population regression line are not met.

Short Answer

Expert verified

Equal variance requirement has not been met.

Step by step solution

01

Given information:

We have been given that:

A residual plot for the least-squares regression line based on the data.

02

Explanation:

Conditions for performing inference:

1.Linearity

2.Independence

3.Equal Variance

4.Normality

5.Random

According to the residual plot for the least-squares regression line equal variance condition has not been met.

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Most popular questions from this chapter

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for inference about the slope are met. Here is computer output from the regression analysis:

T12.7 Which of the following is the 95% confidence interval for the slope 尾1 of the population regression line?
a. 7,897,179卤3,023,782
b. 7,897,179卤2.000(3,023,782)
c. 鈭�4,139,198卤1,698,371
d. 鈭�4,139,198卤1.960(1,698,371)
e. 鈭�4,139,198卤2.000(1,698,371)

Insurance adjusters are always concerned about being overcharged for accident repairs. The adjusters suspect that Repair Shop1quotes higher estimates than Repair Shop2. To check their suspicion, the adjusters randomly select 12cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to fix the vehicle. The estimates are given in hundreds of dollars.

Assuming that the conditions for inference are met, which of the following significance tests should be used to determine whether the adjusters鈥� suspicion is correct?

a. A pairedt test

b. A two-sample ttest

c. A t test to see if the slope of the population regression line is0

d. A chi-square test for homogeneity

e. A chi-square test for goodness of fit

After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be us

where

渭G=true mean reduction in blood pressureusing the generic drug 渭G=true mean reduction in blood pressureusing the name@brand drug

渭G=true mean reduction in blood pressure

using the generic drug

渭G=true mean reduction in blood pressure

using the name@brand drug

In the context of this situation, which of the following describes a Type I error?

a. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is less effective.

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

c. The FDA finds convincing evidence that the generic drug is equally effective, when in reality it is less effective.

d. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is less effective.

e. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is equally effective.

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers aged 21or older with an initial BAC of 0took part in a study to find out. Each volunteer drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. A least-squares regression analysis was performed on the data using x=number of beers and y=BAC. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

a. Find the critical value for a 99%confidence interval for the slope of the true regression line. Then calculate the confidence interval.

b. Interpret the interval from part (a).

c. Explain the meaning of 鈥渓ocalid="1654184305701" 99%confident鈥� in this context

Here is computer output from the least-squares regression analysis of the beer and blood alcohol dat

T12.12 Foresters are interested in predicting the amount of usable lumber they can harvest from various tree species. They collect data on the diameter at breast height (DBH) in inches and the yield in board feet of a random sample of 20 Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber 12 inches by 12 inches by 1 inch.) Here is a scatterplot of the data.

a. Here is some computer output and a residual plot from a least-squares regression on these data. Explain why a linear model may not be appropriate in this case.

The foresters are considering two possible transformations of the original data: (1) cubing the diameter values or (2) taking the natural logarithm of the yield measurements. After transforming the data, a least-squares regression analysis is performed. Here is some computer output and a residual plot for each of the two possible regression models:

b. Use both models to predict the amount of usable lumber from a Ponderosa pine with diameter 30 inches.
c. Which of the predictions in part (b) seems more reliable? Give appropriate evidence to support your choice.
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