Project: Regression and Correlation Analysis
Using MINITAB perform the regression and correlation analysis for the data on CREDIT BALANCE (Y) and SIZE (X) by answering the following.
1. Generate a scatterplot for INCOME ($1000) vs. CREDIT BALANCE($), including the graph of the "best fit" line. Interpret.
2. Determine the equation of the "best fit" line, which describes the relationship between INCOME and CREDIT BALANCE.
3. Determine the coefficient of correlation. Interpret.
4. Determine the coefficient of determination. Interpret.
5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value.
6. Based on your findings in 1-5, what is your opinion about using CREDIT BALANCE to predict INCOME? Explain.
7. Compute the 95% confidence interval for beta-1 (the population slope). Interpret this interval.
8. Using an interval, estimate the average income for customers that have credit balance of $4,000. Interpret this interval.
9. Using an interval, predict the income for a customer that has a credit balance of $4,000. Interpret this interval.
10. What can we say about the income for a customer that has a credit balance of $10,000? Explain your answer.
11. In an attempt to improve the model, we attempt to do a multiple regression model predicting INCOME based on CREDIT BALANCE, YEARS and SIZE.
Using MINITAB run the multiple regression analysis using the variables CREDIT BALANCE, YEARS and SIZE to predict INCOME. State the equation for this multiple regression model.
12. Perform the Global Test for Utility (F-Test). Explain your conclusion.
13. Perform 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.
14. Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain.