sta108_handout14

sta108_handout14 - Handout 14 Model selection: all possible...

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Unformatted text preview: Handout 14 Model selection: all possible regression models Electric Bill data: Y =annual electricity bill, X 1 =monthly income, X 2 = number of persons, X 3 = area. . Largest model under consideration: Y = + 1 X 1 + 2 X 2 + 3 X 3 + , k = 3. Models to be considered: i) no predictor variable: Y = + ii) regression with one predictor variable: Y = + 1 X 1 + , Y = + 2 X 2 + , Y = + 3 X 3 + , iii) regression with two predictor variables: Y = + 1 X 1 + 2 X 2 + , Y = + 1 X 1 + 3 X 3 + , Y = + 2 X 2 + 3 X 3 + . iv) regression with three predictor variables: Y = + 1 X 1 + 2 X 2 + 3 X 3 + . The goal is to select the most appropriate of these 2 3 = 8 models. For any model with p- 1 predictor variables, the number of beta parameters estimated is equal to p and we will denote the residual sum of squares by SSE p . Note that df ( SSE p ) = n- p, MSE p = SSE p / ( n- p ) , R 2 p = SSR p /SSTO = 1- SSE p /SSTO,...
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sta108_handout14 - Handout 14 Model selection: all possible...

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