Skip to content

CA Foundation · Quantitative Aptitude · Correlation and Regression

In a regression study of household income (X, in ₹ thousands per annum) and household savings (Y, in ₹ thousands per annum) across 50 families, the following statistics are computed: mean of X = 150, mean of Y = 30, standard deviation of X = 40, standard deviation of Y = 12, and correlation coefficient r = 0.80. Calculate the slope of the regression line of Y on X.

The regression slope is calculated using b = r × (SD_Y / SD_X). Substituting: b = 0.80 × (12/40) = 0.24. This indicates each ₹1000 income increase is associated with ₹240 additional savings.

  1. A0.24Correct
  2. B0.20
  3. C0.75
  4. D1.33

Explanation

The slope b = r × (SD_Y / SD_X) = 0.80 × (12 / 40) = 0.80 × 0.30 = 0.24. This means for every ₹1000 increase in annual income, savings increase by ₹240 on average. Option B results from dividing correlation by the ratio; option C confuses correlation with slope; option D reverses the ratio of standard deviations.

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