Derive equation (12.14) from equation (12.12).

(a) Transform the numerator of the term in equation (12.13) so that it equals the sample covariance of x1i and x2i.

(b) Transform the denominator of the term in equation (12.13) so that it equals the product of the sample variances for x1i and x2i.

(c) If we perform both of the transformations of parts a and

b, does the value of the term in equation (12.13) change or remain the same? If it changes, what further transformations are necessary to maintain its original value?

(d) Perform the transformations of parts

a, b, and, if necessary, c in order to derive equation (12.14).