Answer to Question #204908 in Statistics and Probability for kapil kumar

Question

co-efficients of correlation, and The two regression equations from the following informationN= 10, ∑X= 350, ∑Y= 310, ∑(X-35)2 = 162, ∑(Y-31)2 = 222, ∑(X-35)(Y-31)= 92

Answer 1

$∑(x−35)^2=162=∑dx^2=162$

$∑(y−31)^2=222=∑dy^2=222$

$∑(x−35(y−31)=92=∑dxdy=92$

 Regression equation $X- X¯ = b_{xy} Y-Y¯$

$​$

$b_{xy} =\frac {N∑XY - ∑X∑Y}{N∑Y^2 -(∑Y)^2}$

= $=\frac{ 10 (108500) -108500}{10(96100) -96100}$

$=\frac{ 976500}{864900}$

$b_{xy}= 1.13$

$x¯= √162$

$= 12.73$

$Y¯=√222$

$= 14.9$

Regression equation of X on Y

$X - 12.73 = 1.13(Y -14.9)$

$X =1.13Y -2.17$

Regression equation of Y on X

$Y - Y¯= b_{xy} (X-X¯)$

$= Y - 14.9 = 1.13(X -12.73)$$Y = 1.13X + 2.17$