SAS Assignment #1
Engel Curve: Illustrating the effects of real personal disposable income on real personal consumption of musical instruments
The curve was derived using SAS. An index of real personal consumption of musical instruments is the dependent variable and average real personal disposable income is the explanatory variable. Both sets of time-series data came from the U.S. Bureau of Economic Analysis.
Initial Regression Equation: IPC = -.53161 + .00444*RI + µ
IPC = Percentage of real personal consumption consisting of musical instruments in a given year in the U.S.
RI = Average Real Personal Disposable Income in a given year in the U.S.
In this given sample, in any given year, an additional 1$ increase in overall real personal disposable income results in a .0044% increase in musical instruments purchased in the United States.
| Analysis of Variance | |||||
| Source | DF | Sum of | Mean Square | F Value | Pr > F |
| Model | 1 | 7.35460 | 7.35460 | 672.89 | <.0001 |
| Error | 55 | 0.60115 | 0.01093 | ||
| Corrected Total | 56 | 7.95574 | |||
| Root MSE | 0.10455 | R-Square | 0.9244 |
| Dependent Mean | 0.55759 | Adj R-Sq | 0.9231 |
| Coeff Var | 18.74968 |
| Parameter Estimates | ||||||
| Variable | Label | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| |
| Intercept | Intercept | 1 | -0.53161 | 0.04421 | -12.02 | <.0001 |
| RI | RI | 1 | 0.00004440 | 0.00000171 | 25.94 | <.0001 |
| Ordinary Least Squares Estimates | |||
| SSE | 6015.07544 | DFE | 55 |
| MSE | 109.36501 | Root MSE | 10.45777 |
| SBC | 435.406551 | AIC | 431.320448 |
| MAE | 8.70880226 | AICC | 431.54267 |
| MAPE | 25.3737896 | HQC | 432.908447 |
| Durbin-Watson | 0.1073 | Total R-Square | 0.9244 |
| Durbin-Watson Statistics | |||
| Order | DW | Pr < DW | Pr > DW |
| 1 | 0.1073 | <.0001 | 1.0000 |
| NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation. |
| Parameter Estimates | ||||||
| Variable | DF | Estimate | Standard Error | t Value | Approx Pr > |t| | Variable Label |
| Intercept | 1 | -53.1807 | 4.4227 | -12.02 | <.0001 | |
| RI | 1 | 0.004442 | 0.000171 | 25.94 | <.0001 | RI |
The problem with my first regression: There is positive autocorrelation between my explanatory variable and dependent variable. In the second regression, I corrected this autocorrelation by using the “nlag” command. I also changed the dependent variable and explanatory variable so that the dependent variable would be expressed as a dollar amount rather than a percentage of consumption. The dependent variable changed from real personal consumption of instruments as an index to real personal consumption of instruments in billions of dollars. The explanatory variable changed from overall real personal disposable income to real personal disposable income per capita.
New Regression Equation: IPC = -3.151 + .00022*RI + µ
IPC = Real Consumption of Musical Instruments in Billions of dollars in a given year in the U.S.
RI = Real Personal Disposable Income Per Capita
In this given sample, an additional 1$ increase in average real personal disposable income results in a $220,000 increase in musical instruments purchased in the aggregate across in the United States in a given year.
| Number of Observations Read | 57 |
| Number of Observations Used | 57 |
| Analysis of Variance | |||||
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
| Model | 1 | 190.41259 | 190.41259 | 932.31 | <.0001 |
| Error | 55 | 11.23303 | 0.20424 | ||
| Corrected Total | 56 | 201.64561 | |||
| Root MSE | 0.45193 | R-Square | 0.9443 |
| Dependent Mean | 2.39123 | Adj R-Sq | 0.9433 |
| Coeff Var | 18.89932 |
| Parameter Estimates | ||||||
| Variable | Label | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| |
| Intercept | Intercept | 1 | -3.15128 | 0.19114 | -16.49 | <.0001 |
| RI | RI | 1 | 0.00022594 | 0.00000740 | 30.53 | <.0001 |
After changes my variables and accounting for autocorrelation, this is the refined Engel Curve for Musical Instruments using time-series data from 1959-2015.
IPC = -3.151 + .00022*RI + µ
IPC = Real Consumption of Musical Instruments in Billions of dollars in a given year in the U.S.
RI = Real Personal Disposable Income Per Capita