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

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