# Regression

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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 to ) and her grade point average (from to ) 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 labeled " ," may aid in calculations.)

Standardized test Grade point average, y xy

Score, x

800 2.33 1864

890 2.72 2420.8

1220 2.88 3513.6

830 2.34 1942.2

1070 2.85 3049.5

1240 3.21 3980.4

1120 2.26 2531.2

1000 2.97 2970

1500 3.10 4650

1480 3.50 5180

1300 3.13 4069

1340 3.78 5065.2

1400 2.88 4032

1000 2.37 2370

940 2.24 2105.6

Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below

1. 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.

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###### Education

- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

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