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As part of the study described in exercise 10, the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state. (Again, D.C. counts as a state.) The corre- lation between these 51 pairs of averages was 0.97. Would the correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests-be larger than 0.97, about 0.97, or less than 0.97? Explain briefly.

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Answer:

The correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests would be  less than 0.97.

Step-by-step explanation:

Averaging data into blocks (in this scenario, by State) tends to a reduction in variation and an increase in correlation between the studied variables. Therefore, when applying regression to the original individual data, a reduced correlation would be expected:

Therefore,  the correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests would be  less than 0.97.

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