Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Textbook Question
Chapter 13.3, Problem 36E
An investigation of the relationship between x = Traffic flow (thousands of cars per 24 hours) and y = Lead content of bark on trees near the highway (mg/g dry weight) yielded the accompanying data. A simple linear regression model was fit, and the resulting estimated regression line was ŷ = 28.7 + 33.3x. Both residuals and standardized residuals are also given.
- a. Plot the (x, residual) pairs. Does the resulting plot suggest that a simple linear regression model is an appropriate choice? Explain.
- b. Construct a standardized residual plot. Does the plot differ significantly in general appearance from the plot in Part (a)?
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Chapter 13 Solutions
Introduction To Statistics And Data Analysis
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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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