In a multiple linear regression model is equal to:

Question

Options

• AThe total SS- MSE
• Bthe sum of Type I SS of all model terms
• Cthe sum of Type II SS of all model terms
• Dthe sum of SSE and MSE

• A
  14% (5)
• B
  78% (29)
• C
  5% (2)
• D
  3% (1)

Explanation

In multiple linear regression, the Model SS (Regression SS) equals the sum of Type I (sequential) SS because Type I SS are computed by adding each predictor to the model one at a time in order - each term's contribution is conditional only on terms entered before it. Summing all of these sequential contributions exactly accounts for the total explained variation, making their sum equal to Model SS.

Why the distractors are wrong:

• A is wrong because subtracting MSE (a mean square, not a sum of squares) from Total SS is dimensionally inconsistent - the correct identity is Total SS − SSE = Model SS.
• C is wrong because Type II SS (partial SS) adjust each term for all other terms simultaneously; in models with correlated predictors, these partials overlap and do not sum cleanly to Model SS.
• D is wrong because adding SSE (unexplained variation) to MSE mixes incompatible quantities and moves in the wrong direction - you'd be adding back error, not isolating the model fit.

Memory tip: Think of Type I SS as building blocks stacked in order - each block adds only new height, so all blocks stacked together equal the total model height (Model SS). Type II SS, by contrast, are each measured as if they were the only block, so they can't simply be summed.

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