CA Foundation · Quantitative Aptitude · Correlation and Regression
For a bivariate data set, the mean of X is 40, the mean of Y is 60, and the regression coefficient of Y on X is 0.5. Using the regression line of Y on X, what is the estimated value of Y when X = 50?
The estimated Y is 65. The regression line of Y on X passes through the means (40, 60), and moving X up by 10 raises Y by 0.5 × 10 = 5, giving 60 + 5 = 65.
- A55
- B65Correct
- C70
- D80
Explanation
The regression line of Y on X is Y − Ȳ = b_yx(X − X̄). So Y − 60 = 0.5(50 − 40) = 5, which gives Y = 65. The value 55 comes from subtracting the increment instead of adding it.
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 bivariate data set, the regression coefficient of Y on X is 1.6. Which of the following values CANNOT be the regression coefficient of…
- 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)?