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

x 0 1 2 3 4

y 21 8 27 34 35

x 0 1 2 3 4

y 21 8 27 34 35

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

X 0 1 2 3 4

y 21 8 27 34 35

Y = - 1.2 + 2.4x

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

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

Didn't find the answer you were looking for?