If the standard deviation of X is doubled while the standard deviation of Y and the correlation remain unchanged, the regression coefficient of Y on X will:
Correct answer: B. Become half its former value
- A. Double in value
- B. Become half its former value
- C. Remain exactly unchanged
- D. Change its sign
Explanation
The coefficient is b_yx = r(s_y/s_x). Doubling s_x while keeping r and s_y fixed divides the coefficient by two, without changing its sign.
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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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