# 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

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.

#### 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
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
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