# building ANOVA from sums of squares and testing a hypothesis

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.