1. (10 pts) Test your independent variables (through ) for potential multicollinearity. Report the variance inflation factor (VIF) for each independent variable, and state your conclusion. If your test suggests that you should remove an independent variable from your analysis, then remove it and test the remaining independent variables for multicollinearity again.

2. (10 pts) Run a regression with consumption expenditure as your dependent variable and the remaining X variables as your independent variables. Check if any of the regression coefficients are insignificantly different from zero. If so, remove the corresponding independent variables (one at a time) from your analysis and arrive at a model where all regression coefficients are statistically significant. Only state your final regression results.

3. (10 pts) Using your results from question 2, perform a partial residual analysis by testing the linearity assumption of your regression. Does there appear to be a pattern in any of the relationships between the residuals and your independent variables? If so, then extend your dataset by adding a nonlinear term of the independent variable in question (i.e.add a squared term). State your final regression results which successfully pass a residual analysis.

4.b. Interpret each of the relationships between consumption expenditure and the independent variables. In the occurrence of a linear and quadratic term, be sure to interpret both terms jointly and not separately.

4.c. Test the following hypothesis: For every $1 increase in income on average, a household will increase their consumption expenditure by MORE THAN $0.25. Be sure to state the null and alternative hypotheses, the p-value of the test, and your conclusion.