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# week5 - Decomposition of Sum of Squares The total sum of...

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STA302/1001 - week 5 1 Decomposition of Sum of Squares The total sum of squares (SS) in the response variable is The total SS can be decompose into two main sources; error SS and regression SS… The error SS is The regression SS is It is the amount of variation in Y ’s that is explained by the linear relationship of Y with X . ( 29 - = 2 Y Y SSTO i . 2 = i e SSE ( 29 - = . 2 2 1 X X b SSR i

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STA302/1001 - week 5 2 Claims First, SSTO = SSR +SSE, that is Proof:…. Alternative decomposition is Proof: Exercises. ( 29 ( 29 + - = - = 2 2 2 1 2 i i i e X X b Y Y SSTO ( 29 ( 29 ( 29 - + - = - = 2 2 2 ˆ ˆ i i i i Y Y Y Y Y Y SSTO
STA302/1001 - week 5 3 Analysis of Variance Table The decomposition of SS discussed above is usually summarized in analysis of variance table (ANOVA) as follow: Note that the MSE is s 2 our estimate of σ 2 .

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STA302/1001 - week 5 4 Coefficient of Determination The coefficient of determination is It must satisfy 0 ≤ R 2 ≤ 1.
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