handout_week 14

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University of Illinois, Urbana Champaign *

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440

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Statistics

Date

Jan 9, 2024

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docx

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6

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Lab 14: Lack of Fit Tests and Correlation REVIEW QUESTIONS Writing complete factorial models and drawing interactions 1) a.) How do you write a two-factor complete factorial in a CRD? b.) How about a three factor? c.) What if I changed the design to complete factorial in a RCBD? d.) What are the assumptions for a RCBD? 2.) Draw a significant three-factor interaction if A = 2 levels, B = 2 levels, and C = 3 levels. Marginal means and model selection 3) What are the kinds of marginal means we have discussed in the course thus far? How do we calculate them? 1
4) If I am reading a word problem, what clues am I looking for to know if I should be using a CRD, RCBD, or Latin square design? 4b) What are some ways we have discussed to quantify if a RCBD is better than a CRD? How do calculate it and what does it mean? Understanding differences in designs and fixed versus random effects 5) Compare and contrast between a fixed effect and a random effect. Give an example of an RCBD where the blocks should be fixed, and one example of an RCBD where the blocks should be random. 2
6) Suppose that an RCBD has been implemented, and that the block effect was significant in the corresponding statistical model. Moreover, suppose that the MSE from this RCBD statistical model was compared to the MSE of a CRD model. Which model would you expect to have a smaller MSE? MORE ON LINEAR REGRESSION Lack of Fit Tests 7.) We have a dataset that takes a sample of 10 Pittsburgh Penguins players and their penalty infraction minutes (x variable) and their points scored (Y variable) during the 2017 Stanley Cup Playoffs. The data are presented below. Xi Yij Ybar i (Yij - Ybar i)^2 70 33 19 196 70 5 19 196 35 9 10.5 2.25 35 12 10.5 2.25 25 21 32.5 132.25 25 44 32.5 132.25 21 23 23 0 21 23 23 0 10 16 15.5 0.25 10 15 15.5 0.25 SUM: 661.5 3
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