Question

Find the regression line of best fit from the following data.

Σx = 24, Σy = 44, Σxy = 306, Σx² = 164, Σy² = 576, n = 4

Answer 1

Given,

Σx = 24, Σy = 44, Σxy = 306

Σx² = 164, Σy² = 576, n = 4

Slope b:

`b = (n(sumxy) - (sumx)(sumy))/(n(sumx^2) - (sumx)^2)`

`b = (4 xx 306 - 24 xx 44)/(4 xx 164 - (24)^2)`

= `(1224 - 1056)/(656 - 576)`

= `168/80`

= 2.1

Now y-intercept (a):

`a = (sumy - b(sumx))/n`

`a = (44 - 2.1 xx 24)/4`

= `(44 - 50.4)/4`

`a = (-6.4)/4`

= –1.6

The regression line equation is

y = a + bx

y = –1.6 + 2.1

The regression line of best fit is

y = –1.6 + 2.1x.