Question

Find the equation of the regression line of y on x, if the observations (x, y) are as follows : 
(1,4),(2,8),(3,2),(4,12),(5,10),(6,14),(7,16),(8,6),(9,18)
Also, find the estimated value of y when x = 14.

Answer 1

x	y	xy
1	4	4
2	8	16
3	2	6
4	12	48
5	12	50
6	14	84
7	16	112
8	6	48
9	18	162

n = 9
Σx = 45 

Σy = 90

x = 5 , y = 10 
Σx² = 285

Σ_xy = 530
`b = b_xy = (Sigma_Xy - n bar x  bary )/(Σx^2 n(bar x)`2)'

`= (530 - 9xx5xx10)/(285- 9 xx 25) = 80/60 = 4/3`

`= bary - barx`
`a = 10-4/3 xx 5`
`a =10/3`
 Therefore  the regression equation of y on x is y= a + bx

y = `10/3 + 4/3 x`

3y = 4x × 14 + 10
    3y = 4 × 14 + 10
3y = 66

y = 22