At first, an OLS model is investigated, summary output table is printed below:
| Estimate | Std. Error | t value | Pr(> |t|) | |
|---|---|---|---|---|
| (Intercept) | 10739.3519 | 323.2812 | 33.22 | 0.0000 |
| AREA_SQ_M | 0.0102 | 0.0025 | 4.04 | 0.0001 |
| HUBDISTBUS | -1.5666 | 0.9151 | -1.71 | 0.0870 |
| HUBDISTMET | -1.1445 | 0.1295 | -8.84 | 0.0000 |
| HUBDISTTRA | -0.0738 | 0.1357 | -0.54 | 0.5867 |
| HUBDISTTRAM | -0.4352 | 0.1164 | -3.74 | 0.0002 |
| Scores | F:65.78 (5,2302) | M. R^2: 0.125 | Adj. R^2: 0.1231 | AIC: 46814.1 |
With p value above 0.05, it can be concluded that bus and tram distance are not significant. This is most likely to be caused by multicolinearity of independent variables as all predictors are related with distance and even have the same unit. A model reduction is performed to have only significant variables. Summary table of the reduced model is printed below:
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 10304.5593 | 210.6201 | 48.92 | 0.0000 |
| AREA_SQ_M | 0.0101 | 0.0025 | 4.02 | 0.0001 |
| HUBDISTMET | -1.1507 | 0.1283 | -8.97 | 0.0000 |
| HUBDISTTRAM | -0.4400 | 0.1149 | -3.83 | 0.0001 |
| Scores | F:108.4 (3,2302) | M. R^2: 0.1237 | Adj. R^2: 0.1226 | AIC: 46813.49 |
Adjusted R squared metrics of the reduced model is 0.1226. It can be concluded that 12.26 percent of the variance in the data can be explained. Although model reduction was performed and model performance has slightly increased the model still fits poorly to the data.