Skip to content

CA Foundation · Quantitative Aptitude · Correlation and Regression

If every value of X is multiplied by 4 and increased by 7, while Y is left unchanged, how does the regression coefficient of Y on X change?

The regression coefficient of Y on X becomes one quarter of its original value. A change of origin, adding 7, has no effect, while a scale change of 4 in X multiplies the covariance by 4 and the variance of X by 16, so the ratio is divided by 4.

  1. AIt is multiplied by 4
  2. BIt is divided by 4Correct
  3. CIt is divided by 4 and then reduced by 7
  4. DIt remains unchanged

Explanation

Regression coefficient is independent of change of origin but not of scale. With u = 4x + 7 and Y unchanged, b(y on u) = Cov(u,y)/Var(u) = 4Cov(x,y)/(16Var(x)) = byx/4. Adding 7 has no effect. Multiplying by 4 would wrongly treat the scale change as acting on the numerator only.

Did you get it right without looking?

One question tells you little. A timed set on Correlation and Regression shows your real accuracy, how long you take and where you lose marks.

Practise Correlation and RegressionFree diagnostic mock

More Correlation and Regression questions