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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) - Mathematics

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Sum

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.

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Solution

x y xy
1 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 
Σx= 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

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
  Is there an error in this question or solution?
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