For my project, I decided to test the effect that changes in income would have on the consumption of used cars. I used data from the FRED database, using Real Personal Disposable Income per capita (using 2009 as a base year) as my independent variable and the net purchase of used cars (in billions of dollars) as my dependent variable. The data set gives annual reports on both these variables starting on January 1^{st}, 1969 all the way through January 1, 2016, giving us a total of 47 observations. The following is the data collected from an OLS regression using these 2 variables.

We find that there is a very high correlation between changes in income and changes in the consumption of used cars. The high t-statistic of 16 plus the high value of R^{2} and adjusted R^{2}, coupled with a low p-value tells us that these 2 variables are highly correlated. As income goes up, the consumption of used cars also increases. The high F-statistic also provides evidence that both variables are positively correlated.

To account for heteroscedasticity and/or any outliers, I used the natural log of the observations in the data set for both variables; and the resulting regression gave positive results. In the end, the regression yielded a R^{2} of .83 (.05 higher than the previous regression) and a higher adjusted R^{2} as well. The F-statistic and t-statistic are both much higher than in the previous regression (even when both statistics were high to begin with), which gives us confidence that both variables being tested are highly correlated.

The graph above represents the Engle Curve of used cars, with real disposable income per capita on the x-axis and the net purchase of used cars on the y-axis. Plotting the natural log of the observations in the data set for both variables, we get an upward sloping Engle Curve. Using the natural log as a means to capture the Engle curve is a good measure because any changes in the natural log are approximately equal to a percent change. The upward slope of the curve also tells us that used cars are normal goods, since the demand for a normal good goes up as income rises.

The graph above represents the Engle Curve of used cars, with real disposable income per capita on the x-axis and the net purchase of used cars on the y-axis. Plotting the natural log of the observations in the data set for both variables, we get an upward sloping Engle Curve. Using the natural log as a means to capture the Engle curve is a good measure because any changes in the natural log are approximately equal to a percent change. The upward slope of the curve also tells us that used cars are normal goods, since the demand for a normal good goes up as income rises.