| Multiple Linear Regression - Estimated Regression Equation |
| Passengersbrussels[t] = + 643506.889523468 + 33.0554647235123DJIA[t] -37601.179288474M1[t] -2084.93078149814M2[t] + 218151.003437736M3[t] + 386307.756645739M4[t] + 460143.964267434M5[t] + 489460.295892718M6[t] + 728273.668754439M7[t] + 612201.854211425M8[t] + 544958.341672279M9[t] + 395143.631685458M10[t] + 118806.647585149M11[t] + 3366.03286395014t + 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) | 643506.889523468 | 55597.882389 | 11.5743 | 0 | 0 |
| DJIA | 33.0554647235123 | 4.053388 | 8.155 | 0 | 0 |
| M1 | -37601.179288474 | 31091.216256 | -1.2094 | 0.232695 | 0.116347 |
| M2 | -2084.93078149814 | 31121.009248 | -0.067 | 0.946877 | 0.473438 |
| M3 | 218151.003437736 | 31033.333354 | 7.0296 | 0 | 0 |
| M4 | 386307.756645739 | 30907.22407 | 12.4989 | 0 | 0 |
| M5 | 460143.964267434 | 30859.091968 | 14.9111 | 0 | 0 |
| M6 | 489460.295892718 | 30867.966075 | 15.8566 | 0 | 0 |
| M7 | 728273.668754439 | 30811.808138 | 23.6362 | 0 | 0 |
| M8 | 612201.854211425 | 30785.045101 | 19.8863 | 0 | 0 |
| M9 | 544958.341672279 | 30773.524087 | 17.7087 | 0 | 0 |
| M10 | 395143.631685458 | 30760.584075 | 12.8458 | 0 | 0 |
| M11 | 118806.647585149 | 30752.229412 | 3.8634 | 0.000348 | 0.000174 |
| t | 3366.03286395014 | 388.608455 | 8.6618 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.987238960106177 |
| R-squared | 0.974640764351525 |
| Adjusted R-squared | 0.967474023842174 |
| F-TEST (value) | 135.994984481405 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 48619.1823506069 |
| Sum Squared Residuals | 108735945052.312 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 989236 | 956021.584720707 | 33214.4152792926 |
| 2 | 1008380 | 1004036.76044009 | 4343.23955991047 |
| 3 | 1207763 | 1218962.65969729 | -11199.6596972938 |
| 4 | 1368839 | 1380196.93237405 | -11357.9323740538 |
| 5 | 1469798 | 1466488.43399472 | 3309.56600527653 |
| 6 | 1498721 | 1492807.29097003 | 5913.70902996611 |
| 7 | 1761769 | 1747083.01345663 | 14685.9865433729 |
| 8 | 1653214 | 1629111.16569246 | 24102.8343075397 |
| 9 | 1599104 | 1568112.81699468 | 30991.1830053173 |
| 10 | 1421179 | 1417412.21544443 | 3766.78455557408 |
| 11 | 1163995 | 1156532.95320393 | 7462.04679607066 |
| 12 | 1037735 | 1038171.22706511 | -436.227065113023 |
| 13 | 1015407 | 1008807.13392225 | 6599.86607775436 |
| 14 | 1039210 | 1051938.69528338 | -12728.6952833793 |
| 15 | 1258049 | 1279372.12128267 | -21323.1212826655 |
| 16 | 1469445 | 1459417.26726964 | 10027.7327303650 |
| 17 | 1552346 | 1530047.08970430 | 22298.9102956958 |
| 18 | 1549144 | 1562131.48083669 | -12987.4808366895 |
| 19 | 1785895 | 1805483.03334146 | -19588.0333414567 |
| 20 | 1662335 | 1699238.60335190 | -36903.6033518976 |
| 21 | 1629440 | 1645209.00772713 | -15769.0077271301 |
| 22 | 1467430 | 1512037.38856511 | -44607.3885651054 |
| 23 | 1202209 | 1243733.86894771 | -41524.8689477072 |
| 24 | 1076982 | 1136266.89342711 | -59284.8934271138 |
| 25 | 1039367 | 1107272.36037986 | -67905.3603798555 |
| 26 | 1063449 | 1134484.07937550 | -71035.0793754983 |
| 27 | 1335135 | 1360919.56089478 | -25784.5608947817 |
| 28 | 1491602 | 1555864.12705123 | -64262.1270512271 |
| 29 | 1591972 | 1651733.78013018 | -59761.7801301816 |
| 30 | 1641248 | 1677176.33673567 | -35928.3367356715 |
| 31 | 1898849 | 1912856.04643276 | -14007.0464327586 |
| 32 | 1798580 | 1804968.09873715 | -6388.09873714658 |
| 33 | 1762444 | 1758870.82298208 | 3573.17701791966 |
| 34 | 1622044 | 1613558.59273640 | 8485.40726359599 |
| 35 | 1368955 | 1322133.10609956 | 46821.8939004439 |
| 36 | 1262973 | 1203158.86219941 | 59814.1378005865 |
| 37 | 1195650 | 1148612.45492088 | 47037.5450791198 |
| 38 | 1269530 | 1174802.42950192 | 94727.5704980807 |
| 39 | 1479279 | 1398288.70245857 | 80990.297541429 |
| 40 | 1607819 | 1588231.31569305 | 19587.6843069455 |
| 41 | 1712466 | 1659423.74213732 | 53042.2578626821 |
| 42 | 1721766 | 1649520.42086860 | 72245.5791313965 |
| 43 | 1949843 | 1892625.71016118 | 57217.2898388197 |
| 44 | 1821326 | 1785391.5995578 | 35934.4004422005 |
| 45 | 1757802 | 1698610.31893033 | 59191.6810696714 |
| 46 | 1590367 | 1501730.57205203 | 88636.4279479687 |
| 47 | 1260647 | 1212365.10197675 | 48281.8980232471 |
| 48 | 1149235 | 1095184.11703786 | 54050.8829621392 |
| 49 | 1016367 | 1035313.46605631 | -18946.4660563113 |
| 50 | 1027885 | 1043192.03539911 | -15307.0353991136 |
| 51 | 1262159 | 1284841.95566669 | -22682.955666688 |
| 52 | 1520854 | 1474849.35761203 | 46004.6423879704 |
| 53 | 1544144 | 1563032.95403347 | -18888.9540334729 |
| 54 | 1564709 | 1593952.47058900 | -29243.4705890016 |
| 55 | 1821776 | 1860084.19660798 | -38308.1966079773 |
| 56 | 1741365 | 1758110.53266070 | -16745.5326606960 |
| 57 | 1623386 | 1701373.03336578 | -77987.0333657784 |
| 58 | 1498658 | 1554939.23120203 | -56281.2312020333 |
| 59 | 1241822 | 1302862.96977205 | -61040.9697720544 |
| 60 | 1136029 | 1190172.9002705 | -54143.9002704989 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00587755359110589 | 0.0117551071822118 | 0.994122446408894 |
| 18 | 0.00357038066369307 | 0.00714076132738613 | 0.996429619336307 |
| 19 | 0.00141650247659 | 0.00283300495318 | 0.99858349752341 |
| 20 | 0.00507617235053519 | 0.0101523447010704 | 0.994923827649465 |
| 21 | 0.00284292498918308 | 0.00568584997836615 | 0.997157075010817 |
| 22 | 0.00111709418141948 | 0.00223418836283896 | 0.99888290581858 |
| 23 | 0.000383523561019023 | 0.000767047122038047 | 0.99961647643898 |
| 24 | 0.00014805048839746 | 0.00029610097679492 | 0.999851949511603 |
| 25 | 0.000109808546066683 | 0.000219617092133366 | 0.999890191453933 |
| 26 | 8.6238630538108e-05 | 0.000172477261076216 | 0.999913761369462 |
| 27 | 0.000139771707031106 | 0.000279543414062212 | 0.999860228292969 |
| 28 | 0.000142706439452857 | 0.000285412878905714 | 0.999857293560547 |
| 29 | 0.000169866324540954 | 0.000339732649081908 | 0.99983013367546 |
| 30 | 0.00055434663858781 | 0.00110869327717562 | 0.999445653361412 |
| 31 | 0.00180745806162467 | 0.00361491612324934 | 0.998192541938375 |
| 32 | 0.00923550108382033 | 0.0184710021676407 | 0.99076449891618 |
| 33 | 0.0189438027098674 | 0.0378876054197348 | 0.981056197290133 |
| 34 | 0.136645162767549 | 0.273290325535097 | 0.863354837232451 |
| 35 | 0.390811885137579 | 0.781623770275158 | 0.609188114862421 |
| 36 | 0.736873932598083 | 0.526252134803833 | 0.263126067401917 |
| 37 | 0.702227461456783 | 0.595545077086435 | 0.297772538543217 |
| 38 | 0.79221125729994 | 0.415577485400118 | 0.207788742700059 |
| 39 | 0.818465003667327 | 0.363069992665346 | 0.181534996332673 |
| 40 | 0.95398264705338 | 0.09203470589324 | 0.04601735294662 |
| 41 | 0.90360358776734 | 0.192792824465320 | 0.0963964122326599 |
| 42 | 0.817030298259474 | 0.365939403481053 | 0.182969701740526 |
| 43 | 0.671832693773745 | 0.65633461245251 | 0.328167306226255 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 13 | 0.481481481481481 | NOK |
| 5% type I error level | 17 | 0.62962962962963 | NOK |
| 10% type I error level | 18 | 0.666666666666667 | NOK |
