Scenario: You have put together a time-series data set that includes numerous financial and economic variables. The data runs quarterly from the years 2000 through 2016. Before doing more complex econometric modeling, you are interested in seeing if there is a basic predictive model that can be created from your data for Gross Domestic Product (GDP). Therefore, you are interested in utilizing GDP as a dependent variable and several predictor (independent) variables to generate a statistically significant regression model.
Research Question: What financial and economic variables effect quarterly Gross Domestic Product?
Resources: Utilize the data set (Excel file), PHStat, textbook and mortgage example as primary resources for completing the assignment. This assignment should be completed individually.
Three separate files:
1. Word document which includes part #1, Part#2, and Part #3
2. Best subset Regression Excel file generated for part# 1: lastname-firstinitial part1
3. Multiple regression Excel file generated for part# 2: lastname-firstinitial part2
Part 1 (24 points)
Utilizing PHStat, run a Best Subsets regression for GDP. Use the following 5 variables as predictors: S&P Quarterly Close, 10yr Treasury, M2 Supply, Unemployment Rate and Housing Starts. Use 95% confidence level.
TIPS: When selecting columns of data, start with the title cell in Row 3 so your output is labeled. To select multiple columns of cell data not next to each other hold down the appropriate keyboard key prior to selecting the next group of cells (i.e. use the Control key for Windows PC and Command key if using a Mac).
Submit for Part #1:
a.) Using adjusted R-squared as the key metric, identify the most significant model. Copy and paste the Excel sheet output (regression stats and ANOVA) for the best model (the info from column A to I only) into a Word document. Change the Word page orientation to landscape so it all fits on the page?Layout menu, Orientation drop down, select Landscape.
b.) Write the identified best model name from the column A of the "Bestsubsets" tab on the word document. For example: X1X2X3
c.) Submit excel file for Best Subsets generated for part#1. Name the file: lastname- first initial part 1
Part 2 (24 points)
Utilizing PHStat, run a regular Multiple Regression for GDP using the same 5 predictor variables as in part 1. In the options part of the input table select ANOVA and Coefficients Table, Durbin-Watson Statistic and VIF. Use 95% confidence level.
TIP: The regression statistics and ANOVA output should match your identified Best Subsets model output. Submit for Part #2: Submit the excel file for generated part # 2. Name the file lastname first initial part2
Copy and paste the following Excel items into your Word document.
1. Durbin-Watson Statistic output.
2. VIF output (from columns A & B only) for the lowest VIF score.
3. VIF output (from columns A & B only) for the highest VIF score.
4. Using an Excel function, calculate the Critical F-score for the model and include the result in your Word document. Write the excel function used including the values of the variables.
Part 3 (52 points)
Submit for Part #3: Answer the following questions related to your output from parts 1 and 2. Include them in the same Word document you used for the other parts.
1. Based on the ANOVA coefficients (use 4 decimal places) and variables in the output, type the regression equation for this model utilizing the proper format (y = b0 + b1x1 + b2x2....)
2. Using the estimated regression equation and all the variables in the model, calculate (show your work) the expected change in GDP when:
S&P 500 index declines by 2.25%
10-year Treasury rate average is 2.9%
M2 money supply increases 1.9%
Unemployment rate declines by 1.5%
Housing starts increase by 3% Show the calculation.
3. Which independent variable(s) in the model are statistically significant and how did you make that determination?
4. Which independent variable(s) in the model are statistically insignificant and how did you make that determination?
5. For any statistically insignificant variables in the model how could the lack of significance be indicated from the 95% confidence intervals in the output?
6. For any of the independent variables, if the 95% confidence range (lower and upper levels) was not given, how could you approximate it based on the other information in the table?
7. Interpret the coefficients for Treasury and M2 Supply by typing a statement for each that describes their respective effects on GDP due to a 1% change in the independent variable.
8. What is the Adjusted R-square value and what does it mean?
9. What is the F-statistic for the model and what does it mean?
10. Show the basic mathematical equations and solutions, using the data in the ANOVA output, for: Mean Square Regression (MSR) Mean Square Error (MSE) F-statistic
11. Is the overall model reliable/significant? How did you make that determination?
12. Is multicollinearity a concern for this model? Why?
13. Is autocorrelation a concern for this model? Why?
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