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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 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.

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 ...

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