Scenario: You are working as a business consultant. Part of your job is to conduct data analyses of economic indicators and patterns to provide insight and guidance to your clients. One measure of interest is the number of business applications (i.e. applications to obtain an employer identification number, EIN, indicating the formation of a new business). Your boss has asked you to create a model that predicts the number of business applications in a quarter and to write a short report explaining and justifying the model that you have created. You have scoured the data available through the US Census Bureau and have found three potential variables for your model: X1: Total retail sales, excluding cars, gas, and auto parts X2: Total construction spending X3: Total value of manufacturing shipments. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.969314655 0.939570901 0.936549446 22849.42799 64 ANOVA Significance F df 3 1.6622E-36 Regression Residual Total SS MS F 4.87063E+11 1.62354E+11 310.9663757 31325781569 522096359.5 5.18389E+11 60 63 Lower 95% Intercept Total Retail, Excl. Cars&Gas Total Construction Spending Coefficients 85269.08725 0.589427738 0.067978016 Standard Error t Stat P-value 34851.09425 2.446668866 0.017365233 0.053861249 10.94344734 6.30402E-16 0.006822362 9.964000023 2.44996E-14 15556.51932 0.481689199 0.05433126 Total Value Manufacturing Shipments -0.08801356 0.041685793 2.111356265 0.03891611 -0.17139756 7. Often, when collinearity exists between a pair of variables, we consider eliminating one of the variables from the model. Explore what happens when we eliminate one of the variables that exhibits multicollinearity. a. Eliminate one of the variables exhibiting multicollinearity and fit a regression with the remaining two variables i. How good is the model fit? How does this compare to the model with all three variables? ii. What is the statistical significance (p-value) of each of the variables in the model? How do these compare to the model with all three variables? b. Next, eliminate the other variable exhibiting multicollinearity and fit a regression with the remaining two variables. How good is the fit of each model? i. How good is the model fit? How does this compare to the model with all three variables? ii. What is the statistical significance (p-value) of each of the variables in the model? How do these compare to the model with all three variables? Scenario: You are working as a business consultant. Part of your job is to conduct data analyses of economic indicators and patterns to provide insight and guidance to your clients. One measure of interest is the number of business applications (i.e. applications to obtain an employer identification number, EIN, indicating the formation of a new business). Your boss has asked you to create a model that predicts the number of business applications in a quarter and to write a short report explaining and justifying the model that you have created. You have scoured the data available through the US Census Bureau and have found three potential variables for your model: X1: Total retail sales, excluding cars, gas, and auto parts X2: Total construction spending X3: Total value of manufacturing shipments. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.969314655 0.939570901 0.936549446 22849.42799 64 ANOVA Significance F df 3 1.6622E-36 Regression Residual Total SS MS F 4.87063E+11 1.62354E+11 310.9663757 31325781569 522096359.5 5.18389E+11 60 63 Lower 95% Intercept Total Retail, Excl. Cars&Gas Total Construction Spending Coefficients 85269.08725 0.589427738 0.067978016 Standard Error t Stat P-value 34851.09425 2.446668866 0.017365233 0.053861249 10.94344734 6.30402E-16 0.006822362 9.964000023 2.44996E-14 15556.51932 0.481689199 0.05433126 Total Value Manufacturing Shipments -0.08801356 0.041685793 2.111356265 0.03891611 -0.17139756 7. Often, when collinearity exists between a pair of variables, we consider eliminating one of the variables from the model. Explore what happens when we eliminate one of the variables that exhibits multicollinearity. a. Eliminate one of the variables exhibiting multicollinearity and fit a regression with the remaining two variables i. How good is the model fit? How does this compare to the model with all three variables? ii. What is the statistical significance (p-value) of each of the variables in the model? How do these compare to the model with all three variables? b. Next, eliminate the other variable exhibiting multicollinearity and fit a regression with the remaining two variables. How good is the fit of each model? i. How good is the model fit? How does this compare to the model with all three variables? ii. What is the statistical significance (p-value) of each of the variables in the model? How do these compare to the model with all three variables
