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# Computing Sample Correlation Coefficients

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A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on this test and performance in college.

We have chosen a random sample of fifteen students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 1600 ) and her grade point average (from 0 to 4) for her first year in college. The data are shown below, with denoting the score on the standardized test and denoting the first-year college grade point average. A scatter plot of the data is shown in Figure 1. Also given are the products of the standardized test scores and grade point averages for each of the fifteen students. (These products, written in the column labelled "," may aid in calculations.)

Standardized Test score x Grade Point average y Xy
1010 2.42 2444.2
1250 3.30 4125
1070 3.10 3317
1100 2.16 2376
890 2.75 2447.5
1350 3.48 4698
780 2.40 1872
1500 3.03 4545
1500 3.45 5175
990 3.15 3118.5
1290 2.98 3844.2
940 2.16 2030.4
1190 2.83 3367.7
1410 3.27 4610.7
860 2.23 1917.8

What is the value of the slope of the least squares regression line for these data? Round your answer to at least four decimal places.