7. Scores on the Math SAT average 600 with a SD of 100. An SAT prep school enrol

Question

7. Scores on the Math SAT average 600 with a SD of 100. An SAT prep school enrolls a group of students who scored 300 their first time tested. On their second test, their average was 400. The prep course administrators claim this 100-point gain was due to their course. (the correlation between scores on the first test and scores on the second was found to be 0.67). Is the 100-point gain evidenceThat the prep-coursehelpsoris_- the improvement simply due to the regression effect. Show calculation to justify your answer.

Explanation / Answer

Answer to the question)

the question states that the correlation coefficient is 0.67

this implies the coefficient of determination (R2) = (0.67)^2

R2 = 0.4479

This implies that the first test score is able to explain only 44.79% of the variation in the score

this implies that out of the 100 increase in the second test score , only 44.79 increase attributes to the first test score

Thus the claim of the prep course that the entire 100 point gain is due to the prep couse alone is incorrect!

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