Table 4.
The effect of the size of the perturbation
| Computed | 5 % | 10 % | 50 % | 200 % | |
| a10 | 0 | 0.0000 | 0.0000 | 0.0001 | 0.0008 |
| a11 | -14.6780 | -14.3647 | -14.1817 | -13.1496 | -11.3439 |
| a12 | 0 | -0.1466 | -0.1429 | -0.0671 | 0.5735 |
| a13 | 7.3390 | 7.3414 | 7.3438 | 7.3598 | 7.3735 |
| a14 | 0 | -0.2165 | -0.3673 | -1.2462 | -2.7619 |
| a15 | -7.3390 | -7.1723 | -7.0780 | -6.4846 | -5.2501 |
| a20 | 0 | 0.0000 | 0.0000 | 0.0000 | -0.0003 |
| a21 | 14.6780 | 14.6119 | 14.5748 | 14.4207 | 14.5029 |
| a22 | -14.6780 | -14.6540 | -14.6623 | -14.7503 | -15.1862 |
| a23 | 0 | -0.0009 | -0.0016 | -0.0054 | -0.0070 |
| a24 | 0 | 0.0494 | 0.0839 | 0.2494 | 0.3462 |
| a25 | 0 | -0.0309 | -0.0464 | -0.1119 | -0.0951 |
| a30 | 0 | 0.0000 | 0.0000 | 0.0004 | 0.0038 |
| a31 | 0 | -2.3527 | -4.5412 | -18.2307 | -46.8953 |
| a32 | 0 | 1.3989 | 2.6336 | 9.8422 | 24.4004 |
| a33 | -27.2517 | -27.9204 | -28.5955 | -34.0204 | -54.4047 |
| a34 | 0 | 1.7491 | 3.4009 | 14.0961 | 39.3252 |
| a35 | 0 | -0.9955 | -1.8949 | -7.0627 | -15.4759 |
| a40 | 0 | 0.0000 | 0.0000 | -0.0001 | 0.0001 |
| a41 | 0 | 2.0843 | 3.7814 | 14.7316 | 41.5863 |
| a42 | 0 | -1.0925 | -1.7693 | -5.5766 | -13.2688 |
| a43 | 18.5664 | 19.0295 | 19.4964 | 23.2397 | 37.1866 |
| a44 | -18.5664 | -20.2112 | -21.6608 | -31.4631 | -58.1065 |
| a45 | -9.2832 | -8.3594 | -7.6404 | -3.2226 | 6.5808 |
| a50 | 0 | 0.0000 | 0.0000 | -0.0001 | -0.0015 |
| a51 | 0 | -0.4026 | -0.6581 | -2.5848 | -10.1097 |
| a52 | 0 | 0.1384 | 0.0830 | -0.1317 | 0.1582 |
| a53 | 0 | -0.0059 | -0.0110 | -0.0435 | -0.0879 |
| a54 | 18.5664 | 18.8987 | 19.1602 | 21.0620 | 27.2722 |
| a55 | -18.5664 | -18.7852 | -18.9201 | -20.0013 | -24.0836 |
Overall, the estimated coefficients deviate more strongly from the corresponding computed values as the perturbation increases. However, there are substantial differences between variables. The coefficients associated with variable X2, for example, are hardly influenced, while the coefficients associated with X3 are strongly affected. Overall, the method seems to produce the best results for perturbation up to 10%. The datasets for the regression consisted of 401 data points in the interval [0,4] and the method of linearization was option II.