Question

The following results were obtained with respect to two variables x and y. 
∑ x = 15 , ∑y = 25, ∑xy = 83, ∑xy = 55, ∑y² =135 and n =5
(i) Find the regression coefficient xy b . 
(ii) Find the regression equation of x on y. 

Answer 1

 (a) Given that,
∑x = 15, ∑y = 25, ∑xy = 83,
∑ x²  = 55 , ∑y² = 135 and n = 5

(i) regression coefficient bxy = `(cov(x,y))/(V(y))`
`{bar x = 3, bar y = 5 }=(∑xy - n  barx  bary)/(∑y^2 - n(bary)^2)`

                                 ` = (83 - 5 xx3xx5)/(135-5(25))`

                                   `= (83 - 5xx3xx5)/(135 - 5(25))`
                                    = 0.8 
(ii)  Regression equation of x on y 
 x - x  = b_xy (y - y)
x = 0.8y + 3 - 0.8 × 5
x = 0.8y + 3 - 4

x = 0.8 y = 1