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Unformatted text preview: Stat 512 2 Solutions to Homework #10 Dr. Simonsen Due Wednesday, November 9, by 4:30 pm Problems 1 3 continue the analysis begun on Homework #9. 1. Refer to the Hay Fever Relief dataset from problem 19.14. The table below gives the exact quantities of ingredients corresponding to the three levels (low, medium, and high) of the two factors. Treating the quantities of each ingredient as quantitative variables, analyze these data using linear regression. Include linear and centered quadratic terms for each predictor and the product of the centered linear terms. Summarize the results of this analysis. Quantity (in milligrams) Factor Level X 1 (Ingredient 1) X 2 (Ingredient 2) Low 5.0 7.5 Medium 10.0 10.0 High 15.0 12.5 The levels for factor A are 5, 10, and 15, and the levels for factor B are 7.5, 10, and 12.5. With regression we find that the linear, quadratic, and interaction terms are all significant in the model. For this model, R 2 = 0.9886, indicating an excellent fit. The regression coefficients are positive for the linear terms, and negative for the quadratic terms. This indicates that there is an increase in relief with increasing amounts of the ingredients, but that the relief increase levels off with the higher amounts. The coefficient of the interaction term is positive, suggesting that the relief increases with increased levels of both A and B. The REG Procedure Dependent Variable: relief Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 370.46063 74.09213 520.63 <.0001 Error 30 4.26937 0.14231 Corrected Total 35 374.73000 Root MSE 0.37724 RSquare 0.9886 Dependent Mean 7.18333 Adj RSq 0.9867 Coeff Var 5.25165 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > t Intercept 1 6.06667 0.37197 16.31 <.0001 amt1 1 0.59500 0.01540 38.63 <.0001 amt2 1 0.87000 0.03080 28.25 <.0001 amt1sq 1 0.03900 0.00534 7.31 <.0001 amt2sq 1 0.18000 0.02134 8.43 <.0001 amt12 1 0.10350 0.00754 13.72 <.0001 [Note to grader:...
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 Spring '11
 libo
 Linear Regression

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