Question

The slope of the least squares regression line is given by

where r is the correlation coefficient, sx is the standard deviation of the X‑values, and sy is the standard deviation of the Y‑values. If r = 0.25, sx = 2, and sy = 5, then how much should we expect Y to decrease for every one unit of increase in X?

A) 0.625 units

B) 0.25 units

C) 1.5 units

D) 2.5 units

E) 0.1 units

Answer 1

The slope of the least squares regression line is 0.625 units.

Step-by-step explanation:

The slope of the least squares regression line is given by the formula:

slope = r * (sy / sx)

Given that r = 0.25, sx = 2, and sy = 5, we can substitute these values into the formula:

slope = 0.25 * (5 / 2) = 0.25 * 2.5 = 0.625 units.

Therefore, for every one unit increase in X, we should expect Y to decrease by 0.625 units.