A popular, nationwide standardized test taken by high-school juniors and seniors

Question

A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless attempt to predict performance in college fronm performance on this test. 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 y denoting the first-year college grade point average. The least- squares regression line for these data is y = 1.0120+0.0016 x . This line is shown in the scatter plot in Figure 1. Standardized test score, x Grade point average, y 2.08 3.19 3.00 284 2.81 2.78 2.41 2.41 2.14 3,65 2.51 3.05 2.92 3.41 3.50 3.8 3.6 3.4 3.2 960 1480 1020 1070 1210 900 810 870 1110 1330 1010 1380 1270 1260 1490 25 2.6- 24 13 800 900 1000 1100 1200 1300 1400 1500 Figure 1

Explanation / Answer

1) Less than

b) y = 1.0120 + 0.0016 * x

Increase of 0.0016 points in GPA.

c) when x = 1270

y = 1.0120 + 0.0016 * 1270

y = 3.044

d) Observed = 2.92

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