In a high school, all of the 11th graders take both math and physics. After the

Question

In a high school, all of the 11th graders take both math and physics. After the students have taken the midyear exam in both subjects, the physics teachers are considering the results, and have found the value of r^2, the square of the correlation coefficient between the math scores and the physics scores. Which of the following is best answered by consideration of the value of r^2? (A) Whether high physics scores are associated with high math scores (B) Whether the relationship between physics scores and math scores would be better represented by a curve or a straight line (C) To what extent the variation in physics scores can be explained by a linear relationship between physics scores and math scores (D) Whether there is an outlier in the scatterplot of physics scores and math scores (I) Whether the physics scores are on the whole higher than the math scores

Explanation / Answer

The correlation coefficient r2 between two variables X and Y is defined as the degree of linear relationship between the two variables X and Y. X and Y are said to be positively associated, if on one hand X increases and on the other hand Y increases. X and Y are said to be negatively associated, if on one hand X increases but on the other hand Y decreases. X and Y are said to have zero correlation if X changes but Y remains constant or vice versa.

Hence, when the correlation between maths and physics scores is calculated, it means that we are finding the degree of linear relationship between the two scores, i.e whether they are positively associated, or negatively associated or have no association between them. Thus, the most appropriate answer to the stated question is,

(A) Whether high physics scores are associated with high maths scores.

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