1. Ideally you should analyze a data set collected by you that is important for your own interests and passions. If such a set is not available, see if you can borrow a data set from your friends, advisers, web pages, or research papers, etc. (but not from our textbook). If you borrow a data set, you should clearly specify its origin. Do not use any data sets used in the class. But do not make up your own data set.

2. The data set must have at least 30 observations and at least three predictor variables.

If you can have more predictors, it is better.

3. Write a short description of the data and how it is collected. Also write down any

background information that may be important for analysis.

4. While analyzing the data, look at all aspects of the model building (or selection) and

do hypothesis testing regarding what will make sense for that data set. Approach the

problem in a step-by-step way.

5. At every step clearly state what you are going to do and interpret the result properly.

6. Grading will not depend on the final result, but on your approach to the problem. If it turns out that none of the predictors is important for explanation of the response, do not worry. If you have looked at the problem carefully, have done all that you are able to do but are unable to get a good result, you can still get an excellent grade.

7. Bonus: You can earn a bonus of up to 5% on your final course grade for performing non-linear regression analysis (symbolic regression) on your data set using Eureqa Desktop software. Compare and contrast your multiple linear regression model to your symbolic regression model. Which model makes the most sense based on the data? Why?

Symbolic Regression (SR) is a relative newcomer to statistical model building, having its roots in Genetic Programming algorithms. SR can be summarized as an algorithm for automated generation of mathematical expressions in the form of Y=f(x) to fit a set of data. Model fitness can be evaluated with common statistics like Absolute Error, R², PRESS, and Mallow’s Cp that are already familiar to statistics practitioners. The advantage computer assisted SR offers over standard regression methods like multiple linear regression is that the computers can run a search process of potential models while simultaneously evaluating each of them in multiple criteria with the aim of finding a model with satisfactory predictive accuracy (lower error is better) and low complexity (less variables are better). The inner workings of software with SR capabilities continue to mature with highly active industrial researchers in the Genetic Programming field reporting on improvements made to SR algorithms and implementation challenges particularly in the chemical industry.

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