Correct option is C
The correct answer is (c).
Introduction
The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. In this problem, it is calculated using the geometric mean of the two regression coefficients derived from the given lines of regression.
Since both regression coefficients are positive, the correlation coefficient must also be positive.
Information Booster
- The line of regression of Y on X allows us to find the regression coefficient
- From the equation 10y = 8x + 66, we get y = 0.8x + 6.6, making
- The line of regression of X on Y provides the regression coefficient
- From 40x = 18y + 214, we get x = 0.45y + 5.35, making
- The correlation coefficient r is given by the formula
- Substituting the values: .
- The sign of $r$ is always the same as the signs of the regression coefficients, which are both positive here.
- Option A (0.5): This is mathematically incorrect and represents a miscalculation of the geometric mean of the regression coefficients.
- Option B (-0.5): Incorrect because both regression coefficients are positive, so the correlation coefficient cannot be negative.
- Option D (-0.6): This has the correct magnitude but the wrong sign. The correlation coefficient shares the sign of the regression slopes.
English
10 Questions
20 Marks
12 Mins
