488 CHAPTER 9 Correlation and Regression Duration, x Time, y Duration, x Time, y 1.80 56 3.78 79 1.82 58 3.83 85 1.90 62 3.88 80 1.93 56 4.10 89 1.98 57 4.27 90 2.05 57 4.30 89 2.13 60 4.43 89 2.30 57 4.47 86 2.37 61 4.53 89 2.82 73 4.55 86 3.13 76 4.60 92 3.27 77 4.63 91 3.65 77 TRY IT YOURSELF 1 Find the equation of the regression line for the number of years out of school and annual contribution data used in Try It Yourself 4 in Section 9.1. Answer: Page A42 Using Technology to Find a Regression Equation Use technology to find the equation of the regression line for the Old Faithful data used in Section 9.1. (See table at the left.) SOLUTION Recall from Example 6 of Section 9.1 that there is a significant linear correlation between the duration of Old Faithful’s eruptions and the time between eruptions. Minitab, Excel, and the TI-84 Plus each have features that calculate a regression equation. Use such technology to find the regression equation. You should obtain results similar to the displays shown below. MINITAB Regression Analysis: Time versus Duration Regression Equation Time = 33.68 + 12.481 Duration Coefficients Term Coef SE Coef T-Value P-Value Constant 33.68 1.89 17.79 0.000 Duration 12.481 0.546 22.84 0.000 EXCEL 12.48094 A 26 27 28 29 Slope: =SLOPE(B1:B25, A1:A25) 33.6829 Y-intercept: =INTERCEPT(B1:B25, A1:A25) List the eruption durations in cells A1 through A25 and the times until the next eruption in cells B1 through B25. TI-84 PLUS LinReg y=ax+b a=12.48094391 b=33.68290034 r2=.9577738551 r=.9786592129 From the displays, you can see that the regression equation is ny = 12.481x + 33.683. The TI-84 Plus display at the right shows the regression line and a scatter plot of the data in the same viewing window. To do this, use the Stat Plot feature to construct the scatter plot and enter the regression equation as y1. TRY IT YOURSELF 2 Use technology to find the equation of the regression line for the salaries and average home game attendances for the teams in Major League Baseball listed on page 469. Answer: Page A42 EXAMPLE 2 To explore this topic further, see Activity 9.2 on page 496. 9.2 TI-84 PLUS
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