Question

Complete the following activity to find, the equation of line of regression of Y on X and X on Y for the following data:

Given:`n=8,sum(x_i-barx)^2=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

Solution:

Given:`n=8,sum(x_i-barx)=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

∴ `b_(yx)=(sum(x_i-barx)(y_i-bary))/(sum(x_i-barx)^2)=square`

∴ `b_(xy)=(sum(x_i-barx)(y_i-bary))/(sum(y_i-bary)^2)=square`

∴ regression equation of Y on :

`y-bary=b_(yx)(x-barx)` `y-bary=square(x-barx)`

`x-barx=b_(xy)(y-bary)`  `x-barx=square(y-bary)`

Answer 1

Given:`n=8,sum(x_i-barx)=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

∴ `b_(yx)=(sum(x_i-barx)(y_i-bary))/(sum(x_i-barx)^2)=24/36=bb(2/3)`

∴ `b_(xy)=(sum(x_i-barx)(y_i-bary))/(sum(y_i-bary)^2)=24/40=bb(3/5)`

∴ regression equation of Y on :

`y-bary=b_(yx)(x-barx)` `y-bary=bb(2/3)(x-barx)`

`x-barx=b_(xy)(y-bary)`  `x-barx=bb(3/5)(y-bary)`