CA Foundation · Quantitative Aptitude · Correlation and Regression
For 10 pairs of ranks with no ties, Spearman's rank correlation coefficient is 0.4. What is the value of Σd²?
Σd² is 99. From R = 1 - 6Σd²/[n(n²-1)], 0.4 = 1 - 6Σd²/990, so 6Σd²/990 = 0.6, giving 6Σd² = 594 and Σd² = 99.
- A99Correct
- B66
- C396
- D594
Explanation
0.4 = 1 - 6Σd²/(10 × 99), so 6Σd²/990 = 0.6. Hence 6Σd² = 594 and Σd² = 99. The value 594 is 6Σd², which is not Σd² itself, while 396 uses 0.4 × 990 and forgets the 1 - R step.
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.
More Correlation and Regression questions
- For a set of paired data, the sum of products of deviations Σ(x - x̄)(y - ȳ) = 180, Σ(x - x̄)² = 400 and Σ(y - ȳ)² = 144. What is the coeffi…
- For the data x: 1, 2, 3, 4, 5 and y: 1, 4, 9, 16, 25 (y = x²), the Pearson correlation coefficient is approximately 0.98. Which conclusion i…
- Two variables X and Y have standard deviations 3 and 4 respectively, and the correlation coefficient between them is 0.5. What is the varian…
- A study finds that the number of ice creams sold in a city and the number of drowning incidents are strongly positively correlated across th…
- Which of the following statements about Karl Pearson's coefficient of correlation (r) is correct?
- Let u = (x - 10)/5 and v = (30 - y)/2. For the data, r(u, v) = 0.6, σu = 2 and σv = 3. What is the regression coefficient of y on x (b_yx)?