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Assignment 8 Chapter 10 I would like you to complete 3 of the following problems. You may select any 3 that you think would be interesting to you. I have separated them into categories so that you can get an idea of what the problems may be like since they cover different concepts. The textbook does not cover neural nets or non-linear function fitting, so you may choose all 3 of your problems from the Multiple Logistic Regression category. That is, there is no need to use neural nets or try a non-linear function fit. On the other hand, there is much to be learned by watching those videos, even if you do not want to attempt to complete a problem using neural nets or a non-linear function fit. Multiple Logistic Regression This recording covers the concepts and techniques in R that you should use: Multiple Logistic Regression Note: In the video I split the data in order to use cross-validation, but you do not need to do so in the assignment problems. This recording is a sports related one that may be interesting if you wanted to try Problem 10.48, or if you wanted to see once again how glm() can also be used for a probability or a proportion, not just for a binary response variable: Multiple Logistic Regression for a Proportion Problem 10.25 (p.490) File: Election08.csv. This is similar to problem 10.26 (below), which is an extension of problem 9.36 you did in Assignment 7. Read the description of the fields in this file in 9.36 on p.449. You may ignore part c. In part d, you can use backward elimination, as suggested, or you could use the step() command if you wish. Problem 10.26 (p.490) File: Election16.csv. This builds from problem 9.36 you did in Assignment 7. Read the description of the fields in this file in 9.36 on p.449. You may ignore part c. In part d, you can use backward elimination, as suggested, or you could use the step() command if you wish. Problem 10.28 (p.491) File: Leukemia.csv This builds from problem 9.41 you did in Assignment 7. Read the description of the fields in this file in 9.41 on p.450. You may ignore part c and part d. In part e you should calculate and discuss confidence intervals for the ̂ ’ and for the odds ratios when comparing with the work in 9.41. Problem 10.29 (p.491) File: ICU.csv Follow the instructions in the textbook for this problem. Problem 10.48 (p.495/496) File: Hoops.csv On this one, you don’t need to follow the instructions. Simply choose some variables that you consider might be important to predict a win. Use step() to reduce to a significant model, and discuss how the model seems to work. You should also look for errors – the difference between what the data has for the variable WinLoss and what your model predicts (use fitted()). Artificial Neural Nets Re-do any of the problems above that you may have done that used multiple logistic regression, but now using an artificial neural net. You will need to install and then load the package neuralnet, and this is illustrated in the following recording, which also shows how to use the functions in the package: Recording on using an artificial neural net in R: Artificial Neural Net using neuralnet You should split the data in order to use cross-validation as is done in the video. You may want to experiment with different hidden layers as I do in the video. You should provide a plot() of your “best” neural net model. Discuss anything of interest, especially any comparisons with the multiple regression process. Non-linear Function Fitting Quite often theory or experience indicates what functional form a model should take, and yet the function cannot easily be transformed to a regression form. Recording on non-linear function fitting (and smoothing – generalized additive models): Non-linear Function Fitting: gam() and nls() MN COVID Deaths and Logistic Model File: MN COVID Deaths.csv See the separate document with a similar title for instructions for completing this question. One aspect that I hope you get from this exercise is that the near future is not always wellpredicted by the near past. No matter how good the model is. There also is a document describing some details about the logistic function. Cosmic microwave background radiation File: COBE.csv See the separate document with a similar title for instructions. This example illustrates a couple of points: the fit of actual data to theory is remarkably good, showing that the data is consistent with quantum theory and with the Big Bang Theory.

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