SECTION 9.1 Correlation 475 Number of years out of school, x Annual contribution (in thousands of dollars), y 1 12.5 10 8.7 5 14.6 15 5.2 3 9.9 24 3.1 30 2.7 TRY IT YOURSELF 4 Calculate the correlation coefficient for the number of years out of school and annual contribution data in Try It Yourself 1. Interpret the result in the context of the data. Answer: Page A42 Using Technology to Calculate a Correlation Coefficient Use technology to calculate the correlation coefficient for the Old Faithful data in Example 3. Interpret the result in the context of the data. SOLUTION Minitab, Excel, the TI-84 Plus, and StatCrunch each have features that allow you to calculate a correlation coefficient for paired data sets. Use such technology to find r. You should obtain results similar to the displays shown. Rounded to three decimal places, the correlation coefficient is r ≈ 0.979. Round to three decimal places. This value of r suggests a strong positive linear correlation. Interpretation As the duration of the eruptions increases, the time until the next eruption tends to increase. TRY IT YOURSELF 5 Use technology to calculate the correlation coefficient for the data on page 469 on the salaries and average home game attendances for the teams in Major League Baseball. Interpret the result in the context of the data. Answer: Page A42 To explore this topic further, see Activity 9.1 on page 485. 9.1 Tech Tip Before using the TI-84 Plus to calculate r, make sure the diagnostics feature is on. To turn on this feature, from the home screen, press 2nd CATALOG and cursor to DiagnosticOn. Then press ENTER twice. EXAMPLE 5 MINITAB Method Correlations Correlation type Pearson Duration Number of rows used 25 Time 0.979 EXCEL 0.978659213 =CORREL(A1:A25,B1:B25) List the eruption durations in cells A1 through A25 and the times until the next eruption in cells B1 through B25. A 26 TI-84 PLUS LinReg y=ax+b a=12.48094391 b=33.68290034 r2=.9577738551 r=.9786592129 STATCRUNCH Correlation between Duration and Time is: 0.97865921
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