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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.
Solution
| 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
Σxy = 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
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