tutorial 7 - Tutorial 7 1. A student stated: ”Adding...

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Unformatted text preview: Tutorial 7 1. A student stated: ”Adding predictor variables to a regression model can never reduce R 2 , so we should include all available predictor variables in the model.” Comment. 2. For a model with X 1 , X 2 , X 3 , X 4 predictors, we have n = 30 and SSE ( X 1 ) = 161 . 081 , SSE ( X 2 ) = 195 . 846 , SSE ( X 3 ) = 56 . 432 , SSE ( X 4 ) = 225 . 584 SSE ( X 1 , X 2 ) = 146 . 635 , SSE ( X 1 , X 3 ) = 16 . 579 , SSE ( X 1 , X 4 ) = 161 . 044 , SSE ( X 2 , X 3 ) = 45 . 660 , SSE ( X 2 , X 4 ) = 195 . 403 , SSE ( X 3 , X 4 ) = 56 . 431 SSE ( X 1 , X 2 , X 3 ) = 12 . 436 , SSE ( X 1 , X 2 , X 4 ) = 146 . 604 , SSE ( X 1 , X 3 , X 4 ) = 16 . 383 , SSE ( X 2 , X 3 , X 4 ) = 45 . 656 , SSE ( X 1 , X 2 , X 3 , X 4 ) = 12 . 246 , SST = 226 . 189 (a) find SSR ( X 1 , X 2 | X 3 , X 4 ) (b) In model Y = β + β 1 X 1 + β 2 X 2 + β 3 X 3 + ε , test H : β 1 = β 2 = 0 with α = 0 . 05. (c) Find the largest model in which every predictor variable is not significant at α = 0 . 05....
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