h1.pdf - Group 6 \u2013 Ben Gildersleeve Ruoru Feng Molly Easley Math 739\/839 Fall 2018 Homework 4 \u2013 Model Adequacy MATH 739\/839-01 Fall 2018 1(17 total

h1.pdf - Group 6 – Ben Gildersleeve Ruoru Feng Molly...

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1 Group 6 Ben Gildersleeve, Ruoru Feng, Molly Easley Math 739/839 Fall 2018 November 11, 2018 Homework 4 Model Adequacy MATH 739/839-01 Fall 2018 1. (17 total pts) The data set NCAAFootball2005.JMP contains the statistics for 117 Division I college football teams from 2005. There are 18 potential regressors in the data set and the response is winning percentage, Win Pct. The regressor column titles will provide some clues as to the nature of the regressor for the football aficionados. The column School is not of value for modeling and is not be used in a model. It may be of interest for identifying interesting points, but otherwise it can be disregarded. However, an understanding of American football is not required to complete this assignment successfully. (a) (3 pts.) Fit and state a full MLR model using the Fit Model platform. Discuss the Actual by Predicted plot and your conclusions about the adequacy of the model based upon that plot. Using all of the 18 available regressors, we fit a whole model to predict Win Percentage. The null hypothesis being tested is that the regressors have no effect on the response. The alternate hypothesis is that at least one regressor has a significant effect on the response. H o : β 1 = β 2 = … β j = 0; for j = 1, 2, …, 18 H a : β j ≠ 0 for at least one j Overall the model appears to be significant in at least one regressor. For an Analysis Of Variance test on the regressors, the resulting F Ratio is 30.1 with p-value < .0001. With a p-value less than our significance value of 0.05, we reject our null hypothesis. On the Actual by Predicted plot, there are several values outside of the 95% CI. This indicates some concern about the adequacy of this model for accurate predictions. The Summary of Fit table shows a moderate fit with R 2 = 85%, or that the model describes only 85% of variation between predicted and actual observations. There is a bit of overfit due to the large quantity of regressors. This is shown by R 2 adjusted of 81.8% compared to R 2 84.7%. One aspect of the model we found surprising were the positive slopes on the Rush Rank and Pass Rank regressors. We would expect that a lower numbered rank (like 1st or 2nd) would result in a higher win percentage, but instead, the model suggests that a higher numbered rank (like 50th or 100th) would result in a higher win percentage. The only other two regressors who have a positive coefficient are KO Ret Rank and Def 4th Down Rank. The data set NCAA Football 2005 resulted in the following full MLR model for Win Percentage: 𝑊𝑖? ???????𝑎?? = 106.62 + (0.066 ∗ ???ℎ?𝑎??) + (0.053 ∗ ?𝑎???𝑎??) − (0.249 ∗ ???????𝑎??)
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2 − (0.051 ∗ ???ℎ𝐷???𝑎??) − (0.009 ∗ ?𝑎??𝐷???𝑎??) − (0.149 ∗ ?????𝐷???𝑎??) − (0.061 ∗ ????????𝑎??) + (0.011 ∗ ??????𝑎??) − (0.157 ∗ ???𝑎??𝑖??𝑎??) − (0.011 ∗ ???𝑎???𝑌???𝑎??) − (0.032 ∗ 𝐷??????????𝑎??) − (0.004 ∗ 𝐷????????𝑎??) − (0.061 ∗ 𝐷???𝑎????𝑎??) − (0.047 ∗ 𝐷???????????𝑎??) − (0.12 ∗ ???3??𝐷???𝑎??) − (0.108 ∗ 𝐷??3??𝐷???𝑎??) − (0.064 ∗ ???4?ℎ𝐷???𝑎??) + (0.051 ∗ 𝐷??4?ℎ𝐷???𝑎??) (b) (3 pts.) For the full model, generate the residual versus predicted plot and comment on any nonrandom
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3 patterns that might appear.
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