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Chapter 12: Q. 18 (page 792)

The professor swims Here are data on the time (in minutes) Professor Moore takes to swim 2000yards and his pulse rate (beats per minute) after swimming on a random sample of 23days:

Is there convincing evidence of a negative linear relationship between Professor Moore鈥檚 swim time and his pulse rate in the population of days on which he swims2000yards?

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Most popular questions from this chapter

A distribution that represents the number of cars X parked in a randomly selected residential driveway on any night is given by

Given that there is at least 1 car parked on a randomly selected residential driveway on a particular night, which of the following is closest to the probability that exactly 4cars are parked on that driveway?

a. 0.10

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A scatterplot of yversus xshows a positive, nonlinear association. Two different transformations are attempted to try to linearize the association: using the logarithm of the y-values and using the square root of the y-values. Two least-squares regression lines are calculated, one that uses x to predict log(y) and the other that uses x to predict y. Which of the following would be the best reason to prefer the least-squares regression line that uses x to predict log(y)?

a. The value of r2is smaller.

b. The standard deviation of the residuals is smaller.

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e. The distribution of residuals is more Normal.

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.
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T12.11 Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, 3 chickens were randomly assigned to each of 5 different doses of growth hormone (0, 0.2, 0.4, 0.8, and 1.0 milligrams). The subsequent weight gain (in ounces) was recorded for each chicken. A researcher plots the data and finds that a linear relationship appears to hold. Here is computer output from a least-squares
regression analysis of these data. Assume that the conditions for performing inference about the slope 尾1of the true regression line are met.

a. Interpret each of the following in context:
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Do beavers benefit beetles? Researchers laid out 23circular plots, each 4meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth so beetles prefer them. If so, more stumps should produce more beetle larvae

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role="math" localid="1654159204144" PredictorCoefSECoefTPConstant鈭�1.2862.853鈭�0.450.657Stumps11.8941.13610.470.000S=6.41939R-Sq=83.9%R-Sq(adj)=83.1%
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