CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
For a data set, the regression line of Y on X is y = 2 + 0.5x. If the mean of X is 10, and each X value is changed to X' = X + 4 while Y is unchanged, what is the new regression coefficient of Y on X'?
The new regression coefficient remains 0.5. Regression coefficients are independent of a change of origin, so adding 4 to every X value only alters the intercept, which becomes 0, and leaves the slope of Y on X unchanged.
- A0.5Correct
- B2.5
- C0.9
- D4.5
Explanation
Regression coefficients are independent of change of origin. Shifting X by 4 changes only the intercept, not the slope. The slope stays 0.5, and the new intercept becomes 2 - 0.5 x 4 = 0. Option 2.5 wrongly adds the shift to the slope.
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