Correlation and Simple Linear Regression

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 x denoting the score on the standardized test and y denoting the first-year college grade point average. A scatter plot of the data is shown in Figure 1. Also given is the product of the standardized test score and the grade point average for each of the fifteen students. (These products, written in the column labelled "xy", may aid in calculations.) Standardized Grade point test score, x average, y xy 830 2.40 1992 1510 3.06 4620.6 1070 2.98 3188.6 3.8- 3.6+ 940 2.19 2058.6 X 3.4- 1280 3.10 3968 3.2- X X 1490 3.54 5274.6 3- X X X X 2.8- 900 2.65 2385 Grade point average X 2.6+ 990 2.21 2187.9 2.4- X 1190 2.87 3415.3 2.2- X X 2.32 2 - 800 1856 1.8 - 1270 3.24 4114.8 800 900 1000 1100 1200 1300 1400 1500 1090 2.34 2550.6 1400 Standardized test score 2.94 4116 Figure 1 1020 3.00 3060 1350 3.66 4941 Send data to calculator v Send data to ExcelWhat is the slope of the leastsquares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least four decimal places. (If necessary, consult a list of formulas.) m x s