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Chapter 12: Q. 23 (page 764)

The slope β of the population regression line describes

(a) the exact increase in the selling price of an individual unit when its appraised value increases by \(1000

(b) the average increase in the appraised value in a population of units when the selling price increases by \)51000.

(c) the average increase in selling price in a population of units when the appraised value increases by \( 1000.

(d) the average selling price in a population of units when a unit's appraised value is 0.

(e) the average increase in appraised value in a sample of 16 units when the selling price increases by \) 1000.

Short Answer

Expert verified

(c) the average increase in selling price in a population of units when the appraised value increases by $ 1000.

Step by step solution

01

Given Information

Need to find the slope of the population regression.

02

Explanation

In general: The slope of the population regression line is the average increase of y as x increases by 1.

Since y is the actual selling price in thousands of dollars and x is the appraised market value in thousands of dollars, the correct answer then has to be (c).

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Most popular questions from this chapter

A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

(a) The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

(b) The sum of the residuals is not 0. Obviously, there is a major error present.

(c) Using the regression line to predict a player’s total winnings from his average number of putts almost always results in errors of less than \(200,000.

(d) For two players, the regression line under predicts their total winnings by more than\)800,000.

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.

Random assignment is part of a well-designed comparative experiment because

(a) It is more fair to the subjects.

(b) It helps create roughly equivalent groups before treatments are imposed on the subjects.

(c) It allows researchers to generalize the results of their experiment to a larger population.

(d) It helps eliminate any possibility of bias in the experiment.

(e) It prevents the placebo effect from occurring

Following the debut of the new SAT Writing test in March 2005, Dr. Les Perelman from the Massachusetts Institute of Technology collected data from a set of sample essays provided by the College Board. A least-squares regression analysis was performed on these data. The two graphs below display the results of that analysis. Explain why the conditions for performing inference are not met in this setting.

Paired tires Exercise 69 in Chapter 8 (page 519 ) compared two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The scatterplot below displays the two estimates (in thousands of miles) for each tire.

Computer output from a least-squares regression analysis of these data is shown below. Assume that the conditions for regression inference are met.

(a) Verify that the 99% confidence interval for the slope of the population regression line is (0.5785,1.001).

(b) Researchers want to test whether there is a difference between the two methods of estimating tire wear.

Explain why an appropriate pair of hypotheses for this test isH0:β=1versusHa:β≠1

(c) What conclusion would you draw for this significance test based on your interval in part (a)? Justify your answer.

Determining tree biomass It is easy to measure the “diameter at breast height” of a tree. It’s hard to measure the total “aboveground biomass” of a tree, because to do this you must cut and weigh the tree. The biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. Combining data on 378trees in tropical rain forests gives this relationship between biomass y measured in kilograms and diameter x measured in centimeters:

lny^=-2.00+2.42lnx
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