Suppose the correlation between two variables is positive, but the regression slope for predicting Y from X is negative. Which conclusion is correct?
Correct answer: B. This is impossible when both standard deviations are positive
- A. This is possible in ordinary least-squares regression
- B. This is impossible when both standard deviations are positive
- C. It proves that Y has zero variance
- D. It means the intercept must be negative
Explanation
The slope for predicting Y from X equals the correlation multiplied by the ratio of the standard deviations. With positive standard deviations, its sign must match the sign of the correlation.
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About Correlation and Regression
Correlation describes the direction and strength of association between two variables using scatter diagrams and correlation coefficients. Regression covers fitted lines, regression equations, prediction and least squares, with a clear distinction between association and causation and between estimating a response value and reversing the roles of the variables.
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