The grade point average (GPA) against IQ test score for 78 seventh-grade student

Question

The grade point average (GPA) against IQ test score for 78 seventh-grade students show a roughly straight-line pattern with quite a bit of scatter. the correlation between these variables is r = 0.634. Fill in the blank: percent of the observed variation among the GPAs of these 78 students is explained by the straight-line relationship between GPA and IQ score. (Give your answer to one decimal place.) Fill in the blank: percent of variation in GPA is explained by differences in GPA among students with similar IQ scores. (Give your answer to one decimal place.)

Explanation / Answer

Step - 1:

Percent of variation in y values that can be explained by x values

= Coefficient of determination

= r2

Here,

r = 0.634

So,

Percent of observed variation among the GPAs of these 78 students is explained by the straight - line relationship between GPA and IQ score

= (0.634)2

= 0.402

= 40.2 percent

Step - 2:

Percent of variation in GPA that is explained by differences in GPA among students with similar IQ scores

= (100 - 40.2)%

= 59.8 percent

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