BANA 5368 Sam Houston State University Multiple Regression Model Paper

1. Now, you will do some model evaluation and model building. The goal in this section will beto examine various models using different sets of predictor variables to predict your dependentvariable. In general, your goal will be to create a model that: 1). is meaningful and potentiallyuseful for EFH, 2). has a reasonably high adjusted r-squared, and 3). has a residual plot thatindicates that no major regression assumptions are violated.
   1. (a) Determine a multiple linear regression model with at least four (4) X variables that youbelieve would be useful for predicting your dependent variable (if your dummy variable(s)from above were significant, you may include them here and count them toward therequirement of using at least four predictors). Thus, at the outset, you may need to add(at least) one more X variable. Explain your choice of X variable(s) conceptually (thatis, in a way that would be understandable to management and consistent with EFH’sgoals).
   2. (b) Fit the model.
   3. (c) Report R2 and adjusted R2 and explain, specifically, what they tell you about the fit ofyour model. Explain why adjusted r-squared should be the preferred measure of modelfit in this case.
   4. (d) Report the test statistic and p-value for the overall Model F test and explain what theconclusion tells you about your collection of X variables.

(e) Produce a plot of the residuals from the model.
do you see any violation(s) of the regression assumptions (e.g., non-constant error vari-ance, correlated errors, a pattern that indicates the regression function is not properlyspecified, outliers)? Explain what you see.

(f) Try to improve upon your model so that any violations of assumptions you noticed in theresidual plot are reduced or eliminated, and so adjusted r-squared is improved from thefirst model (this doesn’t have to be a dramatic improvement). Below are some specificideas. Which ones to use will depend on what variables you have been working with, sothere is no “one-size-fits-all” solution. You will need to experiment a bit. Most of thesetopics are covered in Chapter 16 of the textbook and in the “Special Regression Topics”handout and video.

1. If you see outliers, investigate these observations by examining the values of the pre-dictor variables associated with them in the original data set. Do these observationsappear to be legitimately unusual observations, or do you believe there might besome error in the data set? If the observations appear legitimate, you can continueon to the next model-building item below. If you believe the latter, you can removethese observations from the data set, but be sure to explain which observations youare removing and why.
2. If there appears to be any non-linearity in the residual plot, try log-transforming,squaring, and/or square rooting one or more predictor variables.
3. If there appears to be heteroscedasticity in the error terms, try log transformingyour response variable.
4. Add a predictor variable (categorical or numeric) that you have not yet used orremove one or more predictor variables that are not statistically significant.
5. Add an interaction term. Explain specifically why you believe those X vari-ables might interact. Keep in mind that interaction is NOT related to correlation:two X variables can interact significantly without being correlated at all. A decentexplanation of the difference can be found here: theanalysisfactor.com/interaction-association/ After you have tried the above and the issues, determine if the issues you identified in theresidual plot are, if not fixed, at least less pronounced. If not, resolve these remaining issues as best you can.equation, and the residual plot.

Then, display the output of the final model, the fitted model