II. Data on income and Expenditure of some families are given: Income 20 35 34 18 40 (X) Expenditure 30 28 54 16 35 (Y) A. Find the Karl Person's coefficient of correlation B. Find an estimate of income when expenditure is 15 C. Find an estimate of expenditure when income is 25 D. Estimate the simple linear regression model

II. Data on income and Expenditure of some families are given: Income 20 35 34 18 40 (X) Expenditure 30 28 54 16 35 (Y) A. Find the Karl Person's coefficient of correlation B. Find an estimate of income when expenditure is 15 C. Find an estimate of expenditure when income is 25 D. Estimate the simple linear regression model

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section: Chapter Questions

Problem 18T

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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?