Based on the data shown below, calculate the regression line (each value to two decimal places) y = ____________ x + ____________ x y 4 12.84 5 14.72 6 11.7 7 10.78 8 8.96 9 5.94 10 5.72 11 1.4
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Based on the data shown below, calculate the regression line (each value to two decimal places)
y = ____________ x + ____________
x | y |
---|---|
4 | 12.84 |
5 | 14.72 |
6 | 11.7 |
7 | 10.78 |
8 | 8.96 |
9 | 5.94 |
10 | 5.72 |
11 | 1.4 |
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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?XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.
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