question archive A university admissions committee must analyze the relationship between a student's score in the SAT and ACT

A university admissions committee must analyze the relationship between a student's score in the SAT and ACT

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A university admissions committee must analyze the relationship between a student's score in the SAT and ACT. They believe that the a student's score in the SAT is related to their ACT score. They would like to develop a linear regression equation to help see this relation. From their records, the committee obtains the score on the SAT, X, and the score on the ACT, Y, for 9 different students. These data are below.

Student 1 2 3 4 5 6 7 8 9

SAT 1440 1550 1590 1320 1120 1400 1510 1580 1320

ACT 33 32 35 33 29 30 34 32 28

Find the correlation and linear regression for the data.

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Answer:

The linear correlation coefficient between ACT and SAT score is \approx 0.6817

The regression line is

ACT score(y) = 17.065 + 0.01*SAT score(x)

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