Question

A population data set produced the following information. N=460, ∑x=3920, ∑y=2650, ∑xy=26,570, ∑x2=48,530 Find the population regression line. Round to three decimal places. Use the format as an example when submitting your equation 456.123 + 789.123x

Answer 1

Regression line is given in the form of: y = a + bx
Where b is the gradient

Working out 'b'


`b = (S_(xy))/(S_(xx))`

`S_(xy) =`Σxy - [ΣxΣy]/N

`S_(xx)=` Σx² - [Σx]²/N


`S_(xy) = 26570 - ((3920)(2650))/(460)= (91710)/(23) =3987.39`

`S_(xx)=48530- ((3920)^2)/(460)=15124.78`

`b= (3987.39)/(15124.78)=0.264`

Working out 'a'

a = [∑y/N] - b[∑x/N]
a = [2650/460] - 0.264[3920/460]
a = 5.86 - 2.25
a = 3.61

Regression line equation is
y = 3.61 + 0.264x