Regression Model Building

To develop your project report follow the steps below.

1. Create an introductory "scenario" of just two to three sentences that describes the data file for your project and why you (the ?????? Corporation/Group) are building a regression model to predict \[Y\] based on the set of possible independent variables \[{{X}_{1}},{{X}_{2,}}...,{{X}_{k}}\]
2. As you learned in class in Week 2, first develop a simple linear regression model using one of the above predictors of \[Y\] .

1. Cut and paste into your report the scatterplot and theMinitab printout for this simple linear regression model.
2. Write the sample regression equation.
3. Interpret the meaning of the \[Y\] intercept and slope for your fitted model.
4. Interpret the meaning of the coefficient of determination \[{{r}^{2}}\] .
5. Interpret the meaning of the standard error of the estimate \[{{S}_{YX}}\] .
6. Obtain the residual plots andcut and paste them into the report. Brieflycomment on the appropriateness of your fitted model.

1. If the assumptions are met and the fitted model is appropriate continue to Step 2G.
2. If the linearity or normality assumptions are problematic state this but continue to Step 2G with caution. You do not need to check the assumption of independence in your project – that assumption is met.
3. If the equality of variance assumption appears to be seriously violated contact me.

1. Comment on the statistical significance of your fitted model. ( Note: Every team should have a fitted model that is statistically significant so contact me immediately if this is not so ).
2. Select a value for your independent variable in its relevant range:

1. Predict \[\hat{Y}\] .
2. Determine the 95% confidence interval estimate of the average value of \[Y\] for all occasions when the independent variable has the particular value you selected.Determine the 95% prediction interval estimate of \[Y\] for an individual occasion when the independent variable has the particular value you selected.

1. As you learned in class in Weeks3and 4, use the set of potentially meaningful numerical independent variables and one selected "two-category" dummy variable in your study to develop a "best" multiple regression model for predicting your numerical dependent variable \[Y\] .

1. Start by fitting a multiple regression model using the set of potentially meaningful numerical independent variables and the one selected two-category dummy variable as the predictor variables.
2. Cut and paste into your report the scatterplot matrix and the Minitab printout for this multiple regression model.
3. Look at the set of residual plots, cut and pasted them into the report, and briefly comment on the appropriateness of your fitted model.

1. If the assumptions are met and the fitted model is appropriate continue to Step 3D.
2. If the linearity or normality assumptions are problematic state this but continue to Step 3D with caution. You do not need to check the assumption of independence in your project – that assumption is met.
3. If the equality of variance assumption is violated either transform the dependent variable \[Y\] to log \[Y\] or transform the set of independent variables ( discuss this with me ) and rerun the multiple regression model as in Step A before going to Step 3D with your new fitted model.

1. Look at the VIF (Variance Inflationary Factor) values listed for eachpredictor variable.

1. If each predictor variable has a VIF less than or equal to 5.0 continue to Step 3E.
2. If one predictor variable has a VIF greater than 5.0 remove that variable and rerun the multiple regression model starting with Step 3A before goingto Step 3D.
3. If more than one independent variables have VIF values greater than 5.0 remove the variable with the highest VIF, rerun the multiple regression modelas in Step 3A before going to Step 3D.

1. Assess the significance of the overall fitted model.
2. Determine the contribution of each predictor variable via Stepwise Regression and Best Subsets approaches.

1. Cut and paste into your report the Minitab printout of the Stepwise Regression modeling approach:

• Using the Stepwise modeling criterion determine which numerical independent variable or variables should be included in your regression model.
• Using the Forward Selection modeling criterion determine which numerical independent variable or variables should be included in your regression model.
• Using the Backward Elimination modeling criterion determine which numerical independent variable or variables should be included in your regression model.

1. Briefly comment on the consistency of your findings in Step3F(1) and if there are discrepancies state which approach you would select and why.
2. Cut and paste into your report the Minitab printout of the Best Subsets modeling approach.

• Using the adjusted \[{{r}^{2}}\] criterion determine which numerical independent variable or variables should be included in your regression model.
• Using Minitab’s "predicted" \[{{r}^{2}}\] criterion determine which numerical independent variable or variables should be included in your regression model.
• Using the smallest \[{{S}_{YX}}\] criterion determine which numerical independent variable or variables should be included in your regression model.
• Using Mallows’ \[{{C}_{p}}\] criterion determine which numerical independent variable or variables should be included in your regression model.

1. Briefly comment on the consistency of your findings in Step3F(3) and if there are discrepancies state which approach you would select and why.
2. Based on your answers to Steps 3F(2) and 3F(4), which independent variable(s) should be included in your regression model to predict your numerical dependent variable \[Y\] ?

1. Cut and paste into your report the Minitab printout for this "best" multiple regression model and also cut and paste into your report the Minitab printout for the scatterplot matrixforeach of the predictor variables with your selected dependent variable \[Y\] .
2. Cut and paste all the residual plots into the report and briefly comment on the appropriateness of your fitted model.

1. If the assumptions are met and the fitted model is appropriate continue to Step 3I.
2. If the linearity or normality assumptions are problematic state this but continue to Step3I with caution. You do not need to check the assumption of independence in your project – that assumption is met.
3. If the equality of variance assumption is violated because of one or more numerical independent variable adata transformationwill be needed (be sure to contact me). You will then need to refit the multiple regression model one last time – starting as in Step 3A and continuing to Step 3I.

1. Perform influence analysis to determine if any one or more of the observations demonstrates significant influence on the fitted model.

1. If "yes," remove such data points and rerun the model on the smaller sample of observations starting with Step 3A and continuing through Step 3I.
2. If "no," you are ready to use your "best" model for prediction.

1. Write the sample multiple regression equation for the "best" model you have developed.

1. Select one value for each of your independent variables in theirrespective relevant ranges:

1. Predict \[\hat{Y}\] .( If you used log Y take the antilog so you are back in units of Y ).
2. Determine the 95% confidence interval estimate of the average value of \[Y\] for all occasions when the independent variables have the particular values you selected.

(If your lower and upper boundaries are in units of log \[Y\] convert back to \[Y\] by taking the antilogs).

1. Determine the 95% prediction interval estimate of \[Y\] for an individual occasion when the independent variables have the particular values you selected. (If your lower and upper boundaries are in units of log \[Y\] convert back to \[Y\] by taking the antilogs).

1. Interpret the meaning of the \[Y\] intercept and all the slopes for your fitted model (but do this in whatever units you used for Y to build the model).
2. Interpret the meaning of the coefficient of multiple determination \[{{r}^{2}}\] .
3. Interpret the meaning of the standard error of the estimate \[{{S}_{YX}}\] (in the units you used to build the model).
4. Very briefly comment on how much \[{{r}^{2}}\] has changed from the simple regression model in Step 2D to the "final" multiple regression model in Step 4C.
5. If, in the influence analysis of Step 3I, one or more observations had been deemed "influential" and removed from the model, very briefly comment on how much \[{{r}^{2}}\] changed from a model with at least one influential observation to the "final fitted" model in Step 4C.

Price: $36.17

Solution: The downloadable solution consists of 24 pages, 1217 words and 13 charts.
Deliverable: Word Document