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From the equation 5x 6y 90 0 5 90 y x 6 6 5 byx 6 from

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Unformatted text preview: (Y-67) = 65 + 0.57Y – 38.19 = 26.81 + 0.57Y Note: Suppose, we are given two regression equations and we have not been mentioned the regression equations of Y on X and X on Y. To identify, always assume that the first equation is Y on X then calculate the regression co-efficient byx = b1 and bxy = b2. If these two are satisfied the properties of regression co-efficient, our assumption is correct, otherwise interchange these two equations. = 0.8 × Example 7: Given 8X – 10Y + 66 = 0 and 40X – 18Y = 214. Find the correlation coefficient, r. Solution: Assume that the regression equation of 8X- 10Y + 66 = 0. -10Y = -66-8X 10Y = 66 + 8X 66 8 X Y= + 10 10 Now the coefficient attached with X is byx 8 4 i.e., byx = = 10 5 231 Y on X is The regression equation of X on Y is 40X-18Y=214 In this keeping X left side and write other things right side i.e., 40X = 214 + 18Y 214 18 i.e., X = +Y 40 40 Now, the coefficient attached with Y is bxy 18 9 = 40 20 Here byx and bxy are satisfied the properties of regression coefficients, so our assumption is correct. b yx b xy Correlation Coefficient, r = i.e., bxy = = 49 × 5 20 = 36 100 6 10 = 0.6 = Example 8: Regression equations of two correlated variables X and Y are 5X-6Y+90 = 0 and 15X-8Y-130 = 0. Find correlation coefficient. Solution: Let 5X-6Y+90 =0 represents the regression equation of X on Y and other for Y on X 6 90 Now X= Y – 5 5 232 bxy = b2 = 6 5 For 15X-8Y-130 = 0 15 130 Y= X– 8 8 byx = b1 15 = 8 r = ± b1 b2 15 6 × 85 = 2.25 = 1.5 >1 It is not possible. So our assumption is wrong. So let us take the first equation as Y on X and second equation as X on Y. From the equation 5x – 6y + 90 = 0, 5 90 Y= X– 6 6 5 byx = 6 From the equation 15x - 8y – 130 = 0, 8 130 X= Y+ 15 15 8 bxy = 15 Correlation coefficient, r = ± b1 b2 = = 58 × 6 15 40 90 2 = 3 = 233 = 0.67 Example 9: The lines of regression of Y on X and X on Y are respectively, y = x + 5 and 16X = 9Y – 94. Find the variance of X if the variance of Y is 19. Also find the covariance of X and Y. Solution: From regression line Y on X, Y =...
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