ms-08 mba assignment july dec 2010 Question 5

5.Compute the two regression equations on the basis of the following data:

	X	Y
Mean	40	45
Standard Deviation	10	9

Given that the coefficient of correlation between X & Y is

 0.50. Also estimate the value of Y for X=48?

Solution:

 _             _

 X = 40 ; Y = 45 ;  s   = 10 ;  s    = 9;  r = 0.50

                                 X                   Y

Regression equation of X on Y

      _                         _

X – X = r   s    (Y – Y)

                      X

                              ----

                             s

                            Y

(X-40)= 0.5(10/9) (Y-45)

X-40= 0.56(Y-45)

X-40=0.56Y-25.2

X=0.56Y+ 14.8

Regression equation of Y on X

      _                        _

Y – Y = r   s       (X-X)

             Y     

         ---

         s

           X           

Y-45 = 0.5 (9/10) ( X- 40)

Y-45 = 0.45X – 18

Y = 0.45X + 23

When X = 48 , Y = 0.45(48) + 23

                             =  44.6