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    building ANOVA from sums of squares and testing a hypothesis

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    Given the information below calculate SST, SSR, and SSE, determine the coefficient of determination then use ANOVA and the 0.05 level in testing whether r2 is significantly different from zero.

    x: 4 1 4 6 least squares equation

    y: 381 403 394 385 y = 404.94 - 3.78x

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    Solution Preview

    First let's signify data in upper case and deviations from mean in lower case so

    X = data
    x = (X - Xbar)
    Xbar =

    Y = data
    y = (Y - Ybar)

    lets define SST, SSR, and SSE

    SST = total sum of squares = Sum (yi^2)
    SSR = residual sum of squares = Sum (ei^2)
    SSE = explained sum of squares = Sum ...

    Solution Summary

    I begin by defining the sums of squares.
    SST = total sum of squares
    SSR = residual sum of squares
    SSE = explained sum of squares
    Next, I construct the ANOVA table and compute r2.
    Finally I test the hypothesis that r2 is different from 0.