# Simple regression analysis and multiple regression model predict

Project Part III: Modeling Credit Balances for Pinnacle Fitness April 12, 2015

We are called upon by the senior management of Pinnacle Fitness to increase our credit volume. In order to do this, we will use linear regression analysis to identify those characteristics of our current credit customers.

Using MINITAB perform a simple regression analysis on the Pinnacle Fitness data. Use Credit Balance as the Dependent (Y) variable and Income as the Independent (X) variable. Be sure to answer the following.

1. Determine the equation of the "best fit" line, which describes the relationship between Credit Balance and Income.

2. Determine the coefficient of correlation. Interpret.

3. Determine the coefficient of determination. Interpret.

4. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value.

5. Based on your findings in 1-4, what is your opinion about the use of Income to predict Credit Balance? Explain.

In an effort to improve the model, do a multiple regression model predicting Credit Balance based on Income, Household Size, Years In Residence and Location.

Before we can do this, Indicator or "Dummy" Variables must be created for the variable Location. In other words, where Location = Rural for example, a new variable called "Rural" will be created where Rural = 1 if Location = "Rural", and 0 otherwise. Similar variables will be created for Suburban and Urban.

• In MINITAB, pull down the Calc menu.

• Select "Make Indicator Variables ...

• In the box, Indicator variable for:" put "Location"

• Minitab will show the values for Location and the proposed new variable names

• Change the names to Rural, Suburban, Urban (Eliminate "Location_".

• Click OK and the new variables will appear in the data sheet.

1. Using MINITAB run the multiple regression analysis using the variables Income, HH Size, Years, Urban, Suburban, and Rural to predict Credit Balance. State the equation for this multiple regression model.

2. Observe the Global Test for Utility (F-Test). Explain your conclusion.

3. Observe the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded from the model.

4. Re-run the model with only the independent variables selected from the first run.

5. What do the t-tests show for the new model?

6. What is the R2 for the new model?

7. Select example values for the independent variables in the final model and obtain the predicted Credit Balance for your example.

8. Select a confidence interval or prediction interval and interpret it. Describe it in terms that Senior Management will understand.

9. Write a brief Management summary.

Describe what data is currently unavailable but should be collected

recommendations going forward.

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The solution provides step by step method for the calculation of regression analysis. Formula for the calculation and interpretations of the results are also included.