stat512prob10 - CH19PR14.DAT The two active ingredients...

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Statistics 512: Problem Set No. 10 Due November 20, 2009 Problems 1 - 3 refer to the coin-operated terminals dataset of Problem 20.2 ( ch20pr02.dat ). 1. Perform the two-way ANOVA without interaction for this model. Use the results of hypothesis tests to determine whether main effects are present (significant). 2. Plot the data vs. the location factor using two different lines for the two levels of week. Based on your graph, do you think that interaction is important for this problem? 3. Use the Tukey comparison to determine all significant differences in means in the main effect for location. For Problem 4, use the marketing research contractors data described in Problem 24.9 on page 1023 of the text ( CH24PR09.DAT ). 4. Run the full three-way analysis of variance for these data, and check the assumptions. Sum- marize the results of the hypothesis tests for main and interaction effects, and your conclusions regarding the assumptions. Problems 5 - 7 refer to the hay fever relief problem 19.14 on page 868 (
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Unformatted text preview: CH19PR14.DAT ). The two active ingredients occur in the following quantities in the study: Quantity (in milligrams) Factor X 1 X 2 Level (ingredient 1) (ingredient 2) Low 5.0 7.5 Medium 10.0 10.0 High 15.0 12.5 5. 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: Y i,j,k = β + β 1 x i,j,k, 1 + β 2 x i,j,k, 2 + β 3 x 2 i,j,k, 1 + β 4 x 2 i,j,k, 2 + β 5 x i,j,k, 1 x i,j,k, 2 + ± i,j,k . Summarize the results of this analysis. 6. Check the assumptions of the regression model used in Problem 5. 7. Give a discussion comparing the two-way ANOVA model and the regression (Problem 5) approaches to this analysis. Include a comparison of the values of R 2 for the two analyses and the conclusions drawn concerning interactions. 1...
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