Anonymous

Can You Find The Equation Of The Regression Line. X Is 12,14,10,9,15,8 And Y Is 29,35,28,23,36,18?

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Anonymous Profile
Anonymous answered
6. Find the equation of regression line of x on y from the following data
x 0 1 2 3 4
y 21 8 27 34 35
Anonymous Profile
Anonymous answered
Find the equation of regression line of xon y from the following data:
X   0   1   2    3  4
y  21  8  27 34 35
Oddman Profile
Oddman answered
The slope of the regression line is given by
m = (∑xy - (∑x)(∑y)/n) / (∑x^2 - (∑x)^2/n)
And the intercept of the regression line is given by
b = (∑y - m(∑x))/n

Your n=6 numbers give
∑xy = 12*29 + 14*35 + 10*28 + 9*23 + 15*36 + 8*18
= 348 + 490 + 280 + 207 + 540 + 144 = 2009
∑x = 12 + 14 + 10 + 9 + 15 + 8 = 68
∑y = 29 + 35 + 28 + 23 + 36 + 18 = 169
∑x^2 = 144 + 196 + 100 + 81 + 225 + 64 = 810
So we can compute
m = (2009 - 68*169/6) / (810 - 68^2/6)
= (2009 - 1915 1/3) / (810 - 770 2/3) = (93 2/3)/(39 1/3) = (281/3)/(118/3) = 2 45/118
b = (169 - 281/118*68)/6 = 1 21/118
The equation of the regression line is y = (2 45/118)x + (1 21/118) ≈ 2.381x + 1.178

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