Homework SourseThe pearson correlation between two variables X and Y is r
The pearson correlation between two variables X and Y is r = -0.16. Their sample means and standard deviations are:
Consider the least-squares regression line Y\' = ay + byX. The slope of this regression line is _______, and the intercept is ______. The variation in the variable X explains ____% of the variation in the variable Y.
| sample mean | X = 8.07 | Y = 48.17 |
| sample standard deviation | SX = 1.95 | Sy = 23.04 |
Solution
Given,
X-mean = 8.07
Y-mean = 48.17
SD Sx = 1.95
SD Sy = 23.04
r = -0.16
Therefore,
Slope of the regression line (by) = r *(Sy / Sx)
= -0.16 * (23.04/1.95)
= -1.89 Answer
Intercept (ay) = Y-mean - by * X-mean
= 48.17 - (-1.89 * 8.07)
= 63.42 Answer
The variation in Y over the variation in X = Sy/Sx
= 23.04 / 1.95
= 11.82 Answer
