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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

Respuesta :

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

Working out 'b'

[tex]b = \frac{S_{xy}}{S_{xx}} [/tex]
[tex]S_{xy} = [/tex]Σxy - [ΣxΣy]/N
[tex]S_{xx}=[/tex] Σx² - [Σx]²/N

[tex]S_{xy} = 26570 - \frac{(3920)(2650)}{460}= \frac{91710}{23} =3987.39[/tex]
[tex]S_{xx}=48530- \frac{(3920)^2}{460}=15124.78 [/tex]
[tex]b= \frac{3987.39}{15124.78}=0.264 [/tex]

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

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