Table 1
Initial regression straight line model
| Variable | Coefficient (βj ) | Standard error | t-test | p-value | |
|---|---|---|---|---|---|
| Constant | 5930.39 | 1565.32 | 3.789 | 0.0005 | *** |
| Number of axles | −3964.05 | 727.26 | −5.451 | 2.61e−06 | *** |
| Permissible maximum weight | 1364.78 | 70.65 | 19.32 | 3.34e−022 | *** |
| Determination coefficient | 0.914668 | ||||
| Adjusted determination coefficient | 0.910506 | ||||
| F (2.41) | 219.7387 | ||||
| P-value (F) | 1.22e−22 | ||||
| rX1X2 = rX2X1 | 0.6146 |
Figure 1
Straight line model residuals versus number of axles
Source: Gretl, own calculation
Figure 2
Straight line model residuals versus permissible maximum weight
Source: Gretl, own calculation
Table 2
Regression model completed with a 2nd degree polynomial in variable X2
| Variable | Coefficient ( βj ) | Standard error | t-test | p-value | |
|---|---|---|---|---|---|
| Constant | 8369.13 | 1676.89 | 4.991 | 1.22e−05 | *** |
| Number of axles | −3954.80 | 670.88 | −5.895 | 6.64e−07 | *** |
| Permissible maximum weight | 848.59 | 191.867 | 4.423 | 7.29e−05 | *** |
| Sq Permissible maximum weight | 16.39 | 5.73 | 2.860 | 0.0067 | *** |
| Determination coefficient | 0.929158 | ||||
| Adjusted determination coefficient | 0.923845 | ||||
| F (2.41) | 174.8793 | ||||
| P-value (F) | 5.03e−23 |
Table 3
Linear regression specification tests
| Specification tests | Test variant | p-value |
|---|---|---|
| RESET test | Squared and cubed powers Squared powers only Cubed powers only | 9.47e−016 1.27e−007 0.0021 |
| LM test | Squared powers Logarithms | 0.0022 0.0014 |
Table 4
Residual normality test of the linear regression model
| Residual normality test | p-value |
|---|---|
| Chi-Square test | 0.03451 |
| Doornik-Hansen test | 0.03450 |
| Shapiro-Wilk W-test | 0.01051 |
| Jarque-Bery test | 0.10149 |
Figure 3
Graph of dependent variable Y and independent variable X2
Source: Gretl, own calculation
Annex 1
Calculation of rate per ton of permissible maximum weight of the vehicle for annual taxes under the ART
| from | to | ||||
|---|---|---|---|---|---|
| 1 | 1.0 | 1 800 | 1.00 | 1 800.00 | |
| 1.0 | 2.0 | 2 700 | 1.50 | 1 800.00 | |
| 2.0 | 3.5 | 3 900 | 2.75 | 1 418.18 | |
| 3.5 | 5.0 | 5 400 | 4.25 | 1 270.59 | |
| 5.0 | 6.5 | 6 900 | 5.75 | 1 200.00 | |
| 6.5 | 8.0 | 8 400 | 7.25 | 1 158.62 | |
| 8.0 | – | 9 600 | – | – | |
| 2 | – | 1.0 | 1 800 | 1.00 | 1 800.00 |
| 1.0 | 2.0 | 2 400 | 1.50 | 1 600.00 | |
| 2.0 | 3.5 | 3 600 | 2.75 | 1 309.09 | |
| 3.5 | 5.0 | 4 800 | 4.25 | 1 129.41 | |
| 5.0 | 6.5 | 6 000 | 5.75 | 1 043.48 | |
| 6.5 | 8.0 | 7 200 | 7.25 | 993.10 | |
| 8.0 | 9.5 | 8 400 | 8.75 | 960.00 | |
| 9.5 | 11 | 9 600 | 10.25 | 936.59 | |
| 11 | 12 | 10 800 | 11.50 | 939.13 | |
| 12 | 13 | 12 600 | 12.50 | 1 008.00 | |
| 13 | 14 | 14 700 | 13.50 | 1 088.89 | |
| 14 | 15 | 16 500 | 14.50 | 1 137.93 | |
| 15 | 18 | 23 700 | 16.50 | 1 436.36 | |
| 18 | 21 | 29 100 | 19.50 | 1 492.31 | |
| 21 | 24 | 35 100 | 22.50 | 1 560.00 | |
| 24 | 27 | 40 500 | 25.50 | 1 588.24 | |
| 27 | – | 46 200 | – | – | |
| 3 | – | 1.0 | 1 800 | 1.00 | 1 800.00 |
| 1.0 | 3.5 | 2 400 | 2.25 | 1 066.67 | |
| 3.5 | 6.0 | 3 600 | 4.75 | 757.89 | |
| 6.0 | 8.5 | 6 000 | 7.25 | 827.59 | |
| 8.5 | 11 | 7 200 | 9.75 | 738.46 | |
| 11 | 13 | 8 400 | 12.00 | 700.00 | |
| 13 | 15 | 10 500 | 14.00 | 750.00 | |
| 15 | 17 | 13 200 | 16.00 | 825.00 | |
| 17 | 19 | 15 900 | 18.00 | 883.33 | |
| 19 | 21 | 17 400 | 20.00 | 870.00 | |
| 21 | 23 | 21 300 | 22.00 | 968.18 | |
| 23 | 26 | 27 300 | 24.50 | 1 114.29 | |
| 26 | 31 | 36 600 | 28.50 | 1 284.21 | |
| 31 | 36 | 43 500 | 33.50 | 1 298.51 | |
| 36 | – | 50 400 | – | – | |
| 4 plus | – | 18 | 8 400 | 9.00 | 466.67 |
| 18 | 21 | 10 500 | 19.50 | 538.46 | |
| 21 | 23 | 14 100 | 22.00 | 640.91 | |
| 23 | 25 | 17 700 | 24.00 | 737.50 | |
| 25 | 27 | 22 200 | 26.00 | 853.85 | |
| 27 | 29 | 28 200 | 28.00 | 1 007.14 | |
| 29 | 32 | 33 300 | 30.50 | 1 091.80 | |
| 32 | 36 | 39 300 | 34.00 | 1 155.88 | |
| 36 | – | 44 100 | – | – |