The purpose of this assignment was to estimate an Engel curve on used car purchases. Using data from the Bureau of Labor Statistics, I was able to estimate that a $1 increase in income will increase the average amount spent on used cars by 1.6 cents. However, there were difficulties model in gathering data. The new estimate predicted that a $1 increase in income will increase the average amount spent on used cars by 1.48 cents. While this was not a huge change in the model’s predictive power, it did show some improvement.
The first issue was obtaining the proper data. Luckily, the Bureau of Labor Statistics maintains consumer expenditure surveys. Each survey contained nine income categories, with the average amount spent on used cars in each income category. I used the after-tax income for this model. Also, I used the data from 2012-2015. This gave me a data set of 36 observations.
The first model that I created estimated had Income as the independent variable and average dollars spent on used cars per person as the dependent variable.
The model’s equation looked like: UsedCarsi = β0 + β1Incomei + ui
After I ran the regression, the equation looked like: UsedCars = 700.198 + .01609 Income with an R-Square of 0.7918. This model had very good predictive power. This model predicted that an $1 increase in average income increased the average spent on used cars by 1.609 cents.
| Number of Observations Read | 36 |
| Number of Observations Used | 36 |
| Analysis of Variance | |||||
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 1 | 21594706 | 21594706 | 129.34 | <.0001 |
| Error | 34 | 5676572 | 166958 | ||
| Corrected Total | 35 | 27271278 | |||
| Root MSE | 408.60494 | R-Square | 0.7918 |
| Dependent Mean | 1442.77778 | Adj R-Sq | 0.7857 |
| Coeff Var | 28.32071 |
| Parameter Estimates | |||||
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 700.19803 | 94.34524 | 7.42 | <.0001 |
| Income | 1 | 0.01609 | 0.00141 | 11.37 | <.0001 |
However, I realized that gasoline prices might influence car purchases. There is a possibility that in times of high gas prices, consumers might be more hesitant to purchase a car. I thought that there might be an omitted variable bias.
I then found data on the average gas price in the United States in the years used in the previous model. The data was taken from energy.gov.
The new model’s equation looked like: UsedCarsi = β0 + β1Incomei + β2GasPrice + ui
I then ran a new regression. UsedCars = 1779.424 + .01482 Income – 307.739 GasPrice. This model had a slightly better R-Square at .8208. What is very interesting about this model is that it predicted that gas prices have a significant deterrent effect. This model predicted that a $1 increase in average income increased the average amount spent on used cars by 1.482 cents, holding gas prices constant.
| Number of Observations Read | 36 |
| Number of Observations Used | 36 |
| Analysis of Variance | |||||
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 2 | 22385244 | 11192622 | 75.59 | <.0001 |
| Error | 33 | 4886034 | 148062 | ||
| Corrected Total | 35 | 27271278 | |||
| Root MSE | 384.78779 | R-Square | 0.8208 |
| Dependent Mean | 1442.77778 | Adj R-Sq | 0.8100 |
| Coeff Var | 26.66993 |
| Parameter Estimates | |||||
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 1779.42456 | 475.43512 | 3.74 | 0.0007 |
| Income | 1 | 0.01482 | 0.00144 | 10.30 | <.0001 |
| GasPrice | 1 | -307.73931 | 133.18121 | -2.31 | 0.0272 |
After analyzing the data and regression results, I found that increased income has a positive effect on used car sales. In addition, increased gas prices had a negative effect on used car sales.