Skip to content

CA Foundation · Quantitative Aptitude · Correlation and Regression

Two variables x and y are transformed into u = (x − 50)/10 and v = (100 − y)/5. If the correlation coefficient between u and v is 0.6, what is the correlation coefficient between x and y?

The correlation between x and y is −0.6. Correlation is unaffected by shifting the origin or dividing by a positive constant, but v uses 100 minus y, which reverses the direction of y. The sign of r therefore flips while its magnitude remains 0.6.

  1. A0.6
  2. B−0.6Correct
  3. C0.3
  4. D−0.3

Explanation

Correlation is independent of change of origin and of scale when the scale factors are positive. Here u moves in the same direction as x, but v = (100 − y)/5 moves opposite to y because of the negative sign on y. So the sign of r reverses and the magnitude stays 0.6, giving r(x, y) = −0.6. Option 0.6 ignores the sign reversal.

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