Suppose x1,...,xn and y1,...,yn have means x, y; the standard deviations are sx > 0, sy > 0; and the correlation is r. Let cov(x, y) = 1 n

n i=1 (xi − x)(yi − y).

(“cov” is shorthand for covariance.) Show that—

(a) cov(x, y) = rsx sy .

(b) The slope of the regression line for predicting y from x is cov(x, y)/var(x).

(c) var(x) = cov(x, x).

(d) cov(x, y) = xy − x y.

(e) var(x) = x2 − x2.