For this project, I decided to look at the effects of median household income on the consumption of motor vehicles and parts. Both of these data sets were received from the Federal Reserve Bank of St. Louie’s online database, FRED. My general intuition is that motor vehicles and their parts are normal goods, therefore when income rises, consumption on these goods should rise as well. I would expect after running an ordinary least squares regression for these variables to be positively correlated. This is an Engel Curve, and therefore the explanatory variable will be household income and the dependent variable will be the consumption of motor vehicles and parts. Here are is a graph of the two variables, before I do anything in SAS.

As you can see, they do both seem to be positively correlated. Now let’s look at the data using SAS. The first thing to look at is a PROC MEANS of the data. Below is the data from that procedure.

As shown above, the mean for median household income is $53,897, and the means for consumption of motor vehicles is $309.7 billion. This is a time series, and each variable is measured annually from 1984-2015. Overall this gives us 32 years of data. Next I will run an ordinary least squares regression on the data to achieve the Engel Curve.

These regression results suggest that median household income affects consumption of motor vehicles and parts. For this sample, an increase in $0.03 was associated with an additional $1 billion on the consumption of motor vehicles and parts. The coefficient on the income variable was highly statistically significant (p<.0001) The regression as a whole fit reasonable well (R^{2} = 0.62, adjusted R^{2} = 0.60) and was highly statistically significant (F = 48.45, p<.0001).

One problem that may be present in this model is autocorrelation since it is a time series. To test for this we use SAS to find our Durbin-Watson statistic, and this is shown below.

From this data it seems we do have a problem of autocorrelation, as the D value is way below our target of 2. To help mediate this problem, I will run a general least squares in SAS lagging the data. From this autoreg procedure, we achieve the following results.

Running a general least squares helped our autocorrelation, bringing our D statistic up to .93, and changed the coefficient on median household income slightly as well. Income may not be as influential as originally thought, the coefficient went from being .030 to .014 when adjusted for autocorrelation. It is however, still highly statistically significant (p=.0007). The model has now also become a much better fit of the data, the R^{2} went from .618 to .935.

In conclusion, the model does support the idea that motor vehicles and parts are normal goods, as when income goes up so does the consumption of these items. This Engel curve is flawed however, there could be many other problems with the model such as omitted variable bias and more autocorrelation. A simple regression does not tell the whole story, but this model is a good start and shows some interesting points.