| Multiple Linear Regression - Estimated Regression Equation |
| Ye[t] = + 27.2834214053944 + 0.397125190922649`Ye-1`[t] + 0.241628865980788`Ye-2`[t] -0.0721154477263936`Ye-3`[t] + 0.194553871149098`Ye-4`[t] -8.55123851482719M1[t] -2.43346143954193M2[t] + 8.75387561158733M3[t] -12.7401440949288M4[t] -2.18969425871734M5[t] -16.6086800675589M6[t] -17.5742918715359M7[t] + 23.4944770899369M8[t] + 3.14624069205249M9[t] -11.5904562802941M10[t] -13.6691227830971M11[t] -0.290723078985568t + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | 27.2834214053944 | 13.826997 | 1.9732 | 0.053163 | 0.026582 |
| `Ye-1` | 0.397125190922649 | 0.126329 | 3.1436 | 0.002612 | 0.001306 |
| `Ye-2` | 0.241628865980788 | 0.135726 | 1.7803 | 0.080182 | 0.040091 |
| `Ye-3` | -0.0721154477263936 | 0.134954 | -0.5344 | 0.595094 | 0.297547 |
| `Ye-4` | 0.194553871149098 | 0.123448 | 1.576 | 0.120373 | 0.060186 |
| M1 | -8.55123851482719 | 12.080546 | -0.7079 | 0.481824 | 0.240912 |
| M2 | -2.43346143954193 | 12.239001 | -0.1988 | 0.843081 | 0.42154 |
| M3 | 8.75387561158733 | 12.311775 | 0.711 | 0.479876 | 0.239938 |
| M4 | -12.7401440949288 | 12.466598 | -1.0219 | 0.31098 | 0.15549 |
| M5 | -2.18969425871734 | 12.734413 | -0.172 | 0.864065 | 0.432032 |
| M6 | -16.6086800675589 | 12.472345 | -1.3316 | 0.1881 | 0.09405 |
| M7 | -17.5742918715359 | 12.332299 | -1.4251 | 0.159408 | 0.079704 |
| M8 | 23.4944770899369 | 12.332275 | 1.9051 | 0.061642 | 0.030821 |
| M9 | 3.14624069205249 | 13.509236 | 0.2329 | 0.816649 | 0.408324 |
| M10 | -11.5904562802941 | 13.781157 | -0.841 | 0.403723 | 0.201862 |
| M11 | -13.6691227830971 | 13.151083 | -1.0394 | 0.302864 | 0.151432 |
| t | -0.290723078985568 | 0.13498 | -2.1538 | 0.03535 | 0.017675 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.819156252095656 |
| R-squared | 0.671016965347402 |
| Adjusted R-squared | 0.581801227136528 |
| F-TEST (value) | 7.52128468366599 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 59 |
| p-value | 3.64684837883544e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21.0468770596200 |
| Sum Squared Residuals | 26135.2910038028 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 30 | 48.7324279956963 | -18.7324279956963 |
| 2 | 43 | 47.086469936221 | -4.08646993622098 |
| 3 | 82 | 66.1103682427065 | 15.8896317572935 |
| 4 | 40 | 60.980613945781 | -20.9806139457810 |
| 5 | 47 | 62.0743382813179 | -15.0743382813179 |
| 6 | 19 | 39.7127912223652 | -20.7127912223652 |
| 7 | 52 | 39.6448028347573 | 12.3551971652427 |
| 8 | 136 | 78.086301047883 | 57.913698952117 |
| 9 | 80 | 102.160719820264 | -22.1607198202642 |
| 10 | 42 | 77.3637956525042 | -35.3637956525042 |
| 11 | 54 | 46.735012459634 | 7.26498754036598 |
| 12 | 66 | 76.0780077967497 | -10.0780077967497 |
| 13 | 81 | 66.7464651150316 | 14.2535348849684 |
| 14 | 63 | 73.171510890558 | -10.1715108905580 |
| 15 | 137 | 82.0135654968783 | 54.9864345031217 |
| 16 | 72 | 86.5196819898917 | -14.5196819898917 |
| 17 | 107 | 93.0631935460354 | 13.9368064539646 |
| 18 | 58 | 67.7084772393128 | -9.70847723931278 |
| 19 | 36 | 74.5345088777169 | -38.5345088777169 |
| 20 | 52 | 79.565943831732 | -27.5659438317321 |
| 21 | 79 | 70.3081947868588 | 8.69180521314117 |
| 22 | 77 | 61.9226169098056 | 15.0773830901944 |
| 23 | 54 | 59.8489239987506 | -5.84892399875062 |
| 24 | 84 | 64.7759314294526 | 19.2240685705474 |
| 25 | 48 | 67.6874470622396 | -19.6874470622396 |
| 26 | 96 | 67.7364077201564 | 28.2635922798436 |
| 27 | 83 | 82.3581892130578 | 0.641810786942179 |
| 28 | 66 | 75.4417767652626 | -9.4417767652626 |
| 29 | 61 | 65.3437191668188 | -4.34371916681884 |
| 30 | 53 | 54.8167802383049 | -1.81678023830489 |
| 31 | 30 | 47.8720617844677 | -17.8720617844677 |
| 32 | 74 | 74.636358776985 | -0.636358776984946 |
| 33 | 69 | 65.517598009219 | 3.482401990781 |
| 34 | 59 | 59.2384464349425 | -0.238446434942508 |
| 35 | 42 | 44.041841877633 | -2.04184187763301 |
| 36 | 65 | 57.1737722454439 | 7.8262277545561 |
| 37 | 70 | 53.1063844426971 | 16.8936155573029 |
| 38 | 100 | 65.7569522110259 | 34.2430477889741 |
| 39 | 63 | 84.8093951335112 | -21.8093951335112 |
| 40 | 105 | 59.6940480610925 | 45.3059519389075 |
| 41 | 82 | 76.5020707197341 | 5.49792928026586 |
| 42 | 81 | 71.3117825122287 | 9.6882174877713 |
| 43 | 75 | 53.8735164837603 | 21.1264835162397 |
| 44 | 102 | 101.8571002407 | 0.142899759300056 |
| 45 | 121 | 86.0881241341539 | 34.9118758658461 |
| 46 | 98 | 85.3682009070425 | 12.6317990929575 |
| 47 | 76 | 75.3414400721609 | 0.658559927839122 |
| 48 | 77 | 78.3083826726402 | -1.30838267264018 |
| 49 | 63 | 69.9028900677126 | -6.90289006771262 |
| 50 | 37 | 67.5236210706274 | -30.5236210706274 |
| 51 | 35 | 60.3598753420447 | -25.3598753420447 |
| 52 | 23 | 32.7027017985157 | -9.70270179851573 |
| 53 | 40 | 36.8649159775072 | 3.13508402249283 |
| 54 | 29 | 21.0926191891718 | 7.90738081082816 |
| 55 | 37 | 20.0518755581521 | 16.9481244418479 |
| 56 | 51 | 57.788396377094 | -6.78839637709397 |
| 57 | 20 | 48.7429062355124 | -28.7429062355124 |
| 58 | 28 | 22.0703932248579 | 5.92960677514215 |
| 59 | 13 | 15.9343250260694 | -2.93432502606939 |
| 60 | 22 | 30.2482108697931 | -8.24821086979305 |
| 61 | 25 | 14.7478494171391 | 10.2521505828609 |
| 62 | 13 | 26.5791014651225 | -13.5791014651225 |
| 63 | 16 | 29.8677526473628 | -13.8677526473628 |
| 64 | 13 | 7.90947754002223 | 5.09052245997777 |
| 65 | 16 | 19.1517623085866 | -3.15176230858660 |
| 66 | 17 | 2.35754959861670 | 14.6424504013833 |
| 67 | 9 | 3.02323446114568 | 5.97676553885432 |
| 68 | 17 | 40.065899725606 | -23.065899725606 |
| 69 | 25 | 21.1824570139918 | 3.81754298600822 |
| 70 | 14 | 12.0365468708473 | 1.96345312915268 |
| 71 | 8 | 5.09845656575206 | 2.90154343424794 |
| 72 | 7 | 14.4156949859207 | -7.41569498592066 |
| 73 | 10 | 6.07653589948362 | 3.92346410051638 |
| 74 | 7 | 11.1459367062888 | -4.14593670628875 |
| 75 | 10 | 20.4808539244387 | -10.4808539244387 |
| 76 | 3 | -1.24830010056577 | 4.24830010056577 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.996099335949888 | 0.00780132810022442 | 0.00390066405011221 |
| 21 | 0.997024245112129 | 0.00595150977574312 | 0.00297575488787156 |
| 22 | 0.997010201153075 | 0.00597959769385076 | 0.00298979884692538 |
| 23 | 0.997975637239023 | 0.00404872552195301 | 0.00202436276097650 |
| 24 | 0.996893357106895 | 0.00621328578620933 | 0.00310664289310467 |
| 25 | 0.998285676495904 | 0.00342864700819255 | 0.00171432350409628 |
| 26 | 0.998646560570466 | 0.00270687885906715 | 0.00135343942953357 |
| 27 | 0.99898245301392 | 0.00203509397215923 | 0.00101754698607962 |
| 28 | 0.998989207834904 | 0.00202158433019232 | 0.00101079216509616 |
| 29 | 0.998622536587734 | 0.00275492682453228 | 0.00137746341226614 |
| 30 | 0.99733822958538 | 0.00532354082923934 | 0.00266177041461967 |
| 31 | 0.997549177556421 | 0.00490164488715757 | 0.00245082244357879 |
| 32 | 0.996572155052906 | 0.00685568989418842 | 0.00342784494709421 |
| 33 | 0.993491044187745 | 0.0130179116245098 | 0.00650895581225492 |
| 34 | 0.991527495424926 | 0.0169450091501476 | 0.00847250457507381 |
| 35 | 0.990574988283061 | 0.0188500234338774 | 0.0094250117169387 |
| 36 | 0.98320276505002 | 0.0335944698999592 | 0.0167972349499796 |
| 37 | 0.97468372855773 | 0.0506325428845392 | 0.0253162714422696 |
| 38 | 0.987462119912082 | 0.0250757601758366 | 0.0125378800879183 |
| 39 | 0.993952748110382 | 0.0120945037792358 | 0.00604725188961791 |
| 40 | 0.998617267523335 | 0.00276546495332905 | 0.00138273247666452 |
| 41 | 0.997799467942049 | 0.00440106411590238 | 0.00220053205795119 |
| 42 | 0.995644240347678 | 0.00871151930464418 | 0.00435575965232209 |
| 43 | 0.99429148746791 | 0.0114170250641821 | 0.00570851253209106 |
| 44 | 0.995401906397139 | 0.00919618720572168 | 0.00459809360286084 |
| 45 | 0.999896049871661 | 0.000207900256677033 | 0.000103950128338516 |
| 46 | 0.999862297511302 | 0.000275404977396668 | 0.000137702488698334 |
| 47 | 0.99962162047816 | 0.000756759043680463 | 0.000378379521840231 |
| 48 | 0.999428230221577 | 0.00114353955684585 | 0.000571769778422925 |
| 49 | 0.999298053114472 | 0.00140389377105624 | 0.000701946885528119 |
| 50 | 0.998815280229245 | 0.00236943954150934 | 0.00118471977075467 |
| 51 | 0.99758863707142 | 0.00482272585716041 | 0.00241136292858021 |
| 52 | 0.993688658217002 | 0.0126226835659961 | 0.00631134178299806 |
| 53 | 0.986947335476286 | 0.0261053290474277 | 0.0130526645237139 |
| 54 | 0.964516471543372 | 0.0709670569132558 | 0.0354835284566279 |
| 55 | 0.948650159108347 | 0.102699681783305 | 0.0513498408916527 |
| 56 | 0.995325050457116 | 0.00934989908576899 | 0.00467494954288449 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 25 | 0.675675675675676 | NOK |
| 5% type I error level | 34 | 0.918918918918919 | NOK |
| 10% type I error level | 36 | 0.972972972972973 | NOK |
