Stat 351 Homework #4 Due date: Monday, July 13, 2020 at 12.00 Noon CDT. Submit your homework via one of the following methods. 1. Type your answers in a word document and submit as a word document...

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Stat 351 Homework #4 Due date: Monday, July 13, 2020 at 12.00 Noon CDT. Submit your homework via one of the following methods. 1. Type your answers in a word document and submit as a word document file or pdf file. 2. Write down your answers in a piece of paper and submit the scan copy of the answer. 3. Write down your answers in a piece of paper and submit a snapshot of the answer. Make sure to show your work if you did any calculation. This question is based on Section 16.1 General Linear Models. 1. Below is the plot of standardized residual vs ŷ after fitting a predictor ? to predict ?. a. What problem is presented in the above plot? How to correct this problem? b. The plot blow is a scatter plot of a data set (6 observations) with ? being the response and ? the only predictor. Since there is a curvilinear pattern, a quadratic model with x and 2x as the predictors is fitted. y 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 y x y Complete the following ANOVA table based on the above description. df SS MS F Regression (i)? (iv)? 270.9236 (vi)? Residual (ii)? 31.65271 10.5509 Total (iii)? 573.5 (v)? c. Discuss two different approaches to correct when the constant variance assumption is violated. d. Define the term interaction in general linear model. This question is based on Section of Multicollinearity. 2. a. Define the term multicollinearity in multiple linear regression. b. How to detect multicollinearity by considering the pairwise correlation among the independent variables. c. What difficulty caused by multicollinearity This question is based on Section 16.2 Determining when to Add or Delete variables. 3. In a regression analysis involving 30 observations, the following estimated regression equation was obtained: �̂� = 11.1 − 3.6?1 + 8.1?2 For this estimated regression equation, ??? = 1805, ??? = 1705. Suppose that variables ?3 ??? ?4 are added to the model and the following regression equation is obtained. �̂� = 17.6 − 3.8?1 − 2.3?2 + 7.6?3 + 2.7?4 For this estimated regression equation, ??? = 1805, ??? = 1760. a. Find the SSE for reduced model. b. Find the SSE for Full model. c. Use partial F test to determine whether ?3 ??? ?4 contribute significantly to the model. Use ? = 0.05. This question is based on Section 16.4 Variable Section procedures. 4. The following output is taken from applying Backward elimination variable selection procedure to fit a regression model to predict Y (Earnings) using Scoring Avg., Greens in Reg., Putting Avg. and Sand Saves. (consider α to remove = 0.05) Regression Analysis: Earnings Scoring Avg., Greens in Reg., Putting Avg. and Sand Saves Candidate terms: Scoring Avg., Greens in Reg., Putting Avg., Sand Saves ----Step 1---- -----Step 2---- -----Step 3---- Coef P Coef P Coef P Constant 19835 22252 31737 Scoring Avg. -248 0.050 -344.9 0.001 -440.3 0.000 Greens in Reg. 4326 0.056 3726 0.092 Putting Avg. -2795 0.211 Sand Saves 1767 0.007 1622 0.012 1507 0.022 S 250.178 253.259 262.749 R-sq 70.26% 68.30% 64.57% R-sq(adj) 65.50% 64.64% 61.94% R-sq(pred) 40.91% 44.93% 39.06% Mallows’ Cp 5.00 4.64 5.78 a) What variables should be included in the model from the above variable selection procedure? b) According to this output, write down the estimated regression equation to predict Earnings. The following output is taken from applying Best Subsets Regression to fit a regression model to predict RPG (runs/game) statistic. Best Subsets Regression: Earnings vs Scoring Avg., Greens in Reg., Putting Avg. and Sand Saves Response is Earnings ($1000) G r S e P c e u o n t S r s t a i i n n i n d g n g S A R A a v e v v R-Sq R-Sq Mallows g g g e Vars R-Sq (adj) (pred) Cp S . . . s 1 56.8 55.3 28.1 10.3 284.75 X 1 32.0 29.6 0.4 31.1 357.41 X 2 64.6 61.9 39.1 5.8 262.75 X X 2 59.5 56.5 29.8 10.1 281.05 X X 3 68.3 64.6 44.9 4.6 253.26 X X X 3 65.5 61.5 32.6 7.0 264.35 X X X 4 70.3