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5 November, 14:26

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

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  1. 5 November, 15:57
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    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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