(17) While calculating the coefficient of correlation between two variables r and y, the following results were obtained: n = 25, = 125, y = 100, 22 = 650, y - 460, ry 508. It was however later discovered at the time of checking that two pairs of observations (x, y) were copied (6, 14) and (8,6), while the correct values were (8,12) and (6,8) respectively. Determine the correct value of the coefficient of correlation. (18) Let X and Y be two random variables with variances o2 and 2 respectively and r is the correlation coefficient between them. If U = X + KY and V = X+Y, find the value of k such that U and V are uncorrelated. (19) If X and Y are random variables each with variance 1 and 1+2ab r(ax+by,bX+aY). a+62 then find r(X,Y), the correlation between X and Y. (20) Obtain the equations of two lines of regression for the following data: Also, obtain the X 65 66 67 67 68 69 70 72 Y 67 68 65 68| 72 | 72 |69|71 estimate of X for Y-70.