CMA Intermediate · Financial Management and Business Data Analytics · Data Analysis and Modelling
A regression of Y on X gives a slope of 2 and a regression of X on Y gives a slope of 0.32. What is the correlation coefficient between X and Y?
The correlation coefficient is the geometric mean of the two regression coefficients. The product 2 x 0.32 equals 0.64, whose square root is 0.8. Because both slopes are positive, the correlation is +0.8.
- A0.8Correct
- B0.64
- C0.32
- D1.6
Explanation
r squared = byx x bxy = 2 x 0.32 = 0.64, so r = 0.8. The sign is positive because both slopes are positive. 0.64 is r squared, not r. 1.6 is an incorrect value because r cannot exceed 1.
Did you get it right without looking?
One question tells you little. A timed set on Data Analysis and Modelling shows your real accuracy, how long you take and where you lose marks.
More Data Analysis and Modelling questions
- For five observations, the sums are: n = 5, ΣX = 20, ΣY = 50, ΣXY = 230, ΣX² = 90. Using least squares, what is the regression coefficient o…
- The marks of seven analysts' reports scores, arranged in ascending order, are 4, 6, 8, 10, 12, 14 and 40. Which measure best represents a ty…
- A retailer in Pune fits a simple linear regression of monthly sales (Y, in ₹ lakh) on advertising spend (X, in ₹ lakh) and obtains Y = 40 + …
- A dataset of 5,000 invoices of a Pune manufacturer has values with mean ₹80,000 and standard deviation ₹10,000. Using the z-score rule that …
- Daily returns (in %) of a stock over four days are 2, 4, 6 and 8. Treating these four days as the entire population, what is the standard de…
- A firm estimates the regression line Y = 40 + 5X, where Y is monthly maintenance cost (Rs thousand) and X is machine hours (hundreds). What …