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Chapter 12: Q. 53 (page 818)

Students in Mr. Handford鈥檚 class dropped a kickball beneath a motion detector. The detector recorded the height of the ball (in feet) as it bounced up and down several times. Here is a computer output from a linear regression analysis of the transformed data of log(height) versus bounce number. Predict the highest point the ball reaches on its seventh bounce.

a. 0.35feet

b. 2.26feet

c. 0.37feet

d. 2.32feet

e. 0.43feet

Short Answer

Expert verified

The correct option is (e).

Step by step solution

01

Given information

The given data is

02

Explanation

The general equation is y^=b0+b1x

The computation of the constant b0is noted in the computer output's row "Constant" and column "Coef":

b0=0.45374

The computation of the slope b1is mentioned in the computer output's row "Bounce" and column "Coef":

b1=-0.117160

Substitute the values in the equation

role="math" localid="1654189474140" =0.45374-0.117160x

logy=0.45374-0.117160x

Put the value of x

logy=0.45374-0.117160(7)

=-0.36638

Then take the exponential

y^=10logyy^=10-0.36638y^=0.43

The option is (e).

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Most popular questions from this chapter

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.

Section I: Multiple ChoiceChoose the best answer for Questions AP4.1鈥揂P4.40.
AP4.1 A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than the current wheat variety. The proportion of a current wheat crop lost to insects is 0.04. Thus, the company wishes to test the following hypotheses:
H0:p=0.04

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Which of the following significance levels and sample sizes would lead to the highest power for this test?
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Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (the distance around the neck in inches) for 10 randomly selected bears. Here is some regression output for these data

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