tutorial 7 - Tutorial 7 1 A student stated Adding predictor...

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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 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + ε , test H 0 : 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. 3. State the number of degrees of freedom that are associated with each of the following extra sums of squares: (1) SSR ( X 1 | X 2 ); (2) SSR ( X 2 | X 1 , X 3 ) (3) SSR ( X 1 , X 2 | X 3 , X 4 ); (4) SSR ( X 1 , X 2 , X 3 | X 4 , X 5 ) 4. Refer to Patient satisfaction date (see the Example of Chapter 2) a. Obtain the analysis of variance table that decomposes the regression sum of squares into extra sums of squares associated with X 2 ; with X 1 , given X 2 ; and with X 3 , given X 2 and X 1 . b. Test whether X
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