Regression Analysis, Stat 3776/5776
The student project for this course will have you perform a statistical regression analysis on a data set of interest to you. You will turn in a type-written project paper by noon on November 25 that details your analysis. Your data set should have a continuous or discrete response variable (Y) and at least five covariates (X’s). These covariates should be continuous, discrete, ordinal or binary – anything except purely categorical. You also need to have at least 30 observations.
Basic elements of your analysis to be provided in your paper will include: motivation – why do you need a regression analysis of this data set?; a detailed explanation of the data set, what exploratory data analysis tools did you use?; what model building techniques did you employ?; what are your results?; model checking diagnostics; prediction for some interesting covariates and what interesting questions arose from the analysis of your data?
To ensure that your problem is not overly challenging, you are required to submit a short proposal that consists of a detailed data description together with the motivation for why a regression analysis is reasonable for your data. This proposal should consist of a page or two and your submission should also include your data set. The proposal is due by the end of the day on Friday, October 16, 2020. You may turn in your project proposal early, however, do not start significant work on your project until I have had a chance to approve your proposal!
A perfect regression written report would include a detailed data description (you may borrow it from your project proposal) together with all statistical analyses and conclusions. The statistical analysis has several components. First would be model building (e.ge. forward, backwards and stepwise procedures, plot, MSE plot, C(p) criterion). Provide a results chart for your final model: what variables are statistically significant and what are their interpretations?
Once a suitable model is chosen, the six model assumptions need to be graphically and formally checked (normal probability plot of the residuals, predicted versus residual plot, correlation test, runs test, Breusch-Pagan tests) at the macro level together with a check for multicollinearity. Another wave of model residual diagnostics at the micro level identifies influential observations, large residuals and high leverage points together with a discussion of why certain data values are damaging.
Next, you should use your model to predict for a few new observations; remember to include a plus/minus factor or confidence interval for your prediction. You can always predict for a hypothetical observation using the best values of each covariate, the worst values and the mean values. You should then summarize your conclusions from the regression analysis and add your comments (for example, I didn’t realize that errors committed would be such an important predictor of team wins and losses in baseball).
Summarize your findings in the written report, and please feel free to include as much SAS or R/Splus output with any comments you wish to support your analysis AS APPENDICES. Do NOT include running annotated SAS or R/Splus output in the body of your written report. As far as report length guidelines, I think that it would be very difficult to produce an outstanding paper with less than four or five typed pages (excluding your computer output).
Lastly, you will make a PowerPoint presentation of your project during finals week. Professor Ecker will provide you with more information regarding your presentation as the end of the semester draws near.
SIGNIFICANT PROJECT DATES:
Project Proposal Due October 16
Presentation During Finals Week
Written Report Due November 25
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