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Math Help - How to calculate X in a series based on 2 correlated arrays

  1. #1
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    How to calculate X in a series based on 2 correlated arrays

    Hi -

    I have two arrays of numbers that have a -0.99 correlation. Since they are correlated, I assume I can determine what an unknown number is in array 1 if I have the corresponding number in array 2. But I don't know how. Can someone show me how to solve for X in the series of numbers below?

    Many thanks!
    Derrick

    90.3 4.55
    90.31 4.56
    89.99 4.6
    90.21 4.58
    90.23 4.57
    90.95 4.51
    90.8 4.53
    91.42 4.48
    91.19 4.51
    91.05 4.52
    90.9 4.55
    91.35 4.51
    119.43 2.98
    118.01 3.03
    117.8 3.06
    118.73 3.02
    118.52 3.02
    118.32 3.04
    119.86 2.96
    119.69 2.97
    120.88 2.91
    121.44 2.89
    119.97 2.96
    118.32 3.05
    116.98 3.1
    116.24 3.15
    116.45 3.15
    X 3.13
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  2. #2
    MHF Contributor
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    Re: How to calculate X in a series based on 2 correlated arrays

    Hey dmbeas12.

    Is the correlation a linear correlation or a non-linear one?
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  3. #3
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    Re: How to calculate X in a series based on 2 correlated arrays

    Hi -

    The correlation is linear. I was able to figure out X by getting the trendline equation in Excel. I plugged the numbers into Excel and plotted a scatter diagram. Then, I selected one of the dots on the chart, right clicked and selected Add Trendline. In the trendline window, there is an option to "Display Equation on chart." The equation is exactly what I needed to solve for X, which was y = -0.0543x + 9.4645.

    Dr. Math also helped show me how to do it the manual way:

    Since the correlation is so high (and the graph is
    clearly linear), you could manually find the equation of the line
    through two of the given points, say (90.3, 4.55) and (116.45, 3.15),
    using the slope and the point-slope form:

    3.15 - 4.55
    m = ------------- = -0.053537
    116.45 - 90.3

    y - y1 = m(x - x1)

    y - 4.55 = -0.053537(x - 90.3)

    y = -0.053537x + 9.3843911
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