CFA Level 1: Regression Analysis | Variables X and Y | Perfect Negative Correlation

Regression Analysis of Y against X

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Question

Variables X and Y are perfectly negatively correlated. Given only this information, if you run a regression of Y against X, which of the following is/are true?

I. The intercept term is zero.

II. The slope equals 1.

III. R-square equals 1.

IV. The percentage of unexplained variance equals 100%.

Answers

Explanations

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A. B. C. D. E. F. G.

E

If Y = aX + b, then X and Y are perfectly negatively correlated for any value of b and any negative value of a. Hence, given the information in the question, the slope must be negative but not necessarily equal to 1 and the intercept term cannot be determined. Since the correlation coefficient is 1, R-square is also 1, as expected, since all the variation in Y can be explained by variation in X. Note that the percentage of unexplained variance equals zero.

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