Skip to content

CA Foundation · Quantitative Aptitude · Correlation and Regression

For 10 pairs of observations, the sums were recorded as Σx = 98, Σy = 65, Σx² = 1062, Σy² = 475 and Σxy = 656. It was later found that one pair was wrongly entered as (6, 10) when the correct pair is (8, 5). What is the correct coefficient of correlation?

The correct coefficient is 0.60. After replacing the wrong pair, the sums become Σx = 100, Σy = 60, Σx² = 1090, Σy² = 400 and Σxy = 636. Then r = 360 divided by the square root of (900 × 400), which is 360/600. Using uncorrected sums gives about 0.26.

  1. A0.60Correct
  2. B0.26
  3. C0.40
  4. D0.80

Explanation

Corrected sums: Σx = 98 − 6 + 8 = 100; Σy = 65 − 10 + 5 = 60; Σx² = 1062 − 36 + 64 = 1090; Σy² = 475 − 100 + 25 = 400; Σxy = 656 − 60 + 40 = 636. Then nΣxy − ΣxΣy = 6360 − 6000 = 360; nΣx² − (Σx)² = 10900 − 10000 = 900; nΣy² − (Σy)² = 4000 − 3600 = 400. r = 360/√(900×400) = 360/600 = 0.60. Using the uncorrected sums gives about 0.26, which is wrong.

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