11.61 Instead of using the computing formula on page 367, we can obtain the correlation coefficient r with the formula r = ± 1 −  (y −y)2  (y − y)2 which is analogous to the formula used to define ρ. Although the computations required by the use of this formula are tedious, the formula has the advantage that it can be used also to measure the strength of nonlinear relationships or relationships in several variables. For instance, in the multiple linear regression in Example 12, one could calculate the predicted values by means of the equation y = 46.4 + 7.78 x1 − 1.65 x2

(c) Substitute the results obtained in

(a) and

(b) into the above formula for r. The result is called the multiple correlation coefficient. 11.62 With reference to Exercise 11.39, use the theory of the preceding exercise to calculate the multiple correlation coefficient (which measures how strongly the current gain is related to the two independent variables).