9. 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

We are asked to find the regression line from the various summations given. A regression line has the following equation:

y = ax + b

The coefficient 'a' is equal to the gradient which is required to solve this problem and can be solved with the following formulae.

a = Sxy/Sxx

Sxy = ∑xy - (∑x∑y) / N

Sxy = 26570 - (3920) (2650) / 460

Sxy = 3987.4

Sxx = ∑x² - (∑x) ²/N

Sxx = 48530 - (3920) ²/460

Sxx = 15124.8

a = Sxy/Sxx

a = 3987.4/15124.8

a = 0.264

Now that we have solved for the gradient, we can solve or the constant 'b'.

b = (∑y/N) - a (∑x/N)

b = (2650/460) - 0.264 (3920/460)

b = 5.86 - 2.25

b = 3.61

The population regression line is therefore:

y = 0.264x + 3.61