| Multiple Linear Regression - Estimated Regression Equation |
| yt[t] = + 219.151207387327 + 0.532138256307442xt[t] + 3.48234302529478t + 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) | 219.151207387327 | 21.419773 | 10.2313 | 0 | 0 |
| xt | 0.532138256307442 | 0.053892 | 9.8742 | 0 | 0 |
| t | 3.48234302529478 | 0.304854 | 11.423 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.933737552987903 |
| R-squared | 0.871865817859836 |
| Adjusted R-squared | 0.869675489960005 |
| F-TEST (value) | 398.052646787162 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 117 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 80.8886789273304 |
| Sum Squared Residuals | 765528.470297224 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 384 | 359.87200671431 | 24.1279932856903 |
| 2 | 367.6 | 372.879624527508 | -5.27962452750764 |
| 3 | 457.1 | 399.563195527808 | 57.5368044721924 |
| 4 | 429.4 | 392.615628729477 | 36.7843712705234 |
| 5 | 442.2 | 412.753899177194 | 29.4461008228056 |
| 6 | 507.5 | 420.59977590421 | 86.9002240957899 |
| 7 | 348.5 | 355.063787086430 | -6.56378708642963 |
| 8 | 393.2 | 396.487587786445 | -3.28758778644505 |
| 9 | 426.8 | 402.417766790754 | 24.3822332092459 |
| 10 | 403 | 385.732069901997 | 17.2679300980032 |
| 11 | 454.8 | 403.848214975746 | 50.9517850242538 |
| 12 | 413 | 400.519188320306 | 12.4808116796943 |
| 13 | 388.9 | 406.928291755291 | -18.0282917552915 |
| 14 | 406.5 | 506.408376218449 | -99.9083762184489 |
| 15 | 447.4 | 571.193046370361 | -123.793046370361 |
| 16 | 474.4 | 459.307815428202 | 15.0921845717977 |
| 17 | 428.5 | 520.527159262855 | -92.0271592628546 |
| 18 | 472.8 | 507.672857819511 | -34.8728578195108 |
| 19 | 411 | 488.166828172324 | -77.1668281723241 |
| 20 | 463.9 | 492.553806233342 | -28.6538062333415 |
| 21 | 497.3 | 540.576121311569 | -43.2761213115693 |
| 22 | 474 | 508.72448411805 | -34.7244841180499 |
| 23 | 518.1 | 561.90854028246 | -43.8085402824597 |
| 24 | 566 | 498.288249187386 | 67.711750812614 |
| 25 | 509.4 | 469.629441531711 | 39.7705584682887 |
| 26 | 445.1 | 478.220311817558 | -33.1203118175575 |
| 27 | 466.6 | 480.372309202084 | -13.7723092020837 |
| 28 | 600.5 | 531.481026166895 | 69.0189738331054 |
| 29 | 538.7 | 517.349592908413 | 21.3504070915870 |
| 30 | 548 | 506.517416839038 | 41.4825831609624 |
| 31 | 591.9 | 530.912793337215 | 60.9872066627851 |
| 32 | 547.3 | 525.029503051499 | 22.2704969485013 |
| 33 | 610.2 | 556.076607753519 | 54.1233922464811 |
| 34 | 621.6 | 556.259693589708 | 65.3403064102925 |
| 35 | 582.4 | 564.956991526815 | 17.4430084731847 |
| 36 | 635.8 | 606.859716657507 | 28.9402833424925 |
| 37 | 663.9 | 599.060728649084 | 64.8392713509156 |
| 38 | 624.2 | 592.219589502015 | 31.9804104979853 |
| 39 | 654.1 | 602.300446905522 | 51.7995530944781 |
| 40 | 723.5 | 646.597794189597 | 76.9022058104025 |
| 41 | 641.2 | 619.482187477214 | 21.7178125227857 |
| 42 | 565.5 | 604.552546834272 | -39.0525468342716 |
| 43 | 698.6 | 601.329947830093 | 97.2700521699074 |
| 44 | 651 | 633.122046090943 | 17.8779539090567 |
| 45 | 721.6 | 628.835170574149 | 92.7648294258506 |
| 46 | 643.5 | 588.788604233495 | 54.7113957665046 |
| 47 | 604 | 641.866232746644 | -37.8662327466438 |
| 48 | 618.2 | 671.90227476168 | -53.70227476168 |
| 49 | 783.5 | 638.294581322346 | 145.205418677654 |
| 50 | 672.9 | 646.300099526254 | 26.5999004737459 |
| 51 | 726.7 | 680.273964637965 | 46.4260353620348 |
| 52 | 738.6 | 695.090852522609 | 43.5091474773914 |
| 53 | 692.2 | 673.669125152715 | 18.5308748472850 |
| 54 | 669.5 | 649.427065024392 | 20.0729349756079 |
| 55 | 546.2 | 658.284004438392 | -112.084004438392 |
| 56 | 715 | 713.862682756185 | 1.13731724381453 |
| 57 | 789.8 | 779.55198794382 | 10.2480120561797 |
| 58 | 684 | 696.88114727294 | -12.8811472729401 |
| 59 | 639 | 651.619626020473 | -12.6196260204732 |
| 60 | 768.5 | 753.97325706769 | 14.5267429323093 |
| 61 | 643.8 | 707.274962523194 | -63.4749625231937 |
| 62 | 623 | 722.411133361621 | -99.4111333616214 |
| 63 | 692.8 | 726.798111422639 | -33.9981114226389 |
| 64 | 936.5 | 775.991130664743 | 160.508869335257 |
| 65 | 795.9 | 784.475573299328 | 11.4244267006723 |
| 66 | 695.7 | 749.21825126544 | -53.5182512654406 |
| 67 | 648.3 | 806.340130526526 | -158.040130526526 |
| 68 | 675.2 | 830.150154942765 | -154.950154942765 |
| 69 | 826.5 | 898.127654632522 | -71.6276546325215 |
| 70 | 742.4 | 835.571640050063 | -93.1716400500627 |
| 71 | 793.9 | 1115.39337957581 | -321.493379575812 |
| 72 | 685.3 | 876.806029806852 | -191.506029806852 |
| 73 | 756.1 | 728.735397435787 | 27.3646025642133 |
| 74 | 704 | 766.008519736604 | -62.0085197366041 |
| 75 | 860.6 | 796.04456175164 | 64.5554382483598 |
| 76 | 795.9 | 794.737660470168 | 1.16233952983195 |
| 77 | 816.7 | 830.999720084001 | -14.2997200840012 |
| 78 | 777.9 | 782.864652247474 | -4.96465224747415 |
| 79 | 746.4 | 718.712222896093 | 27.687777103907 |
| 80 | 694.7 | 742.681888789224 | -47.9818887892243 |
| 81 | 909.2 | 795.706303476742 | 113.493696523258 |
| 82 | 783.6 | 730.542811438377 | 53.0571885616234 |
| 83 | 730.4 | 758.397086602552 | -27.9970866025523 |
| 84 | 847.7 | 802.85407536352 | 44.8459246364799 |
| 85 | 758.7 | 751.845460942933 | 6.85453905706722 |
| 86 | 839.2 | 798.909927159807 | 40.2900728401929 |
| 87 | 784.8 | 840.493369336715 | -55.6933693367149 |
| 88 | 906.1 | 814.814535916362 | 91.2854640836383 |
| 89 | 838.2 | 870.286786582894 | -32.0867865828936 |
| 90 | 729 | 811.934664225264 | -82.9346642252636 |
| 91 | 768.1 | 813.554523353482 | -45.4545233534823 |
| 92 | 710.5 | 833.160655544893 | -122.660655544893 |
| 93 | 863 | 832.332678694097 | 30.6673213059029 |
| 94 | 778.3 | 797.713922567779 | -19.4139225677791 |
| 95 | 827.7 | 809.657263868362 | 18.0427361316379 |
| 96 | 853.1 | 895.514608970049 | -42.4146089700489 |
| 97 | 859.3 | 877.126069661108 | -17.8260696611080 |
| 98 | 779.2 | 855.172204034907 | -75.9722040349069 |
| 99 | 724.6 | 841.945405812148 | -117.345405812148 |
| 100 | 829.2 | 869.852894801954 | -40.6528948019543 |
| 101 | 862.9 | 930.274031252146 | -67.3740312521455 |
| 102 | 601.6 | 839.940399690438 | -238.340399690438 |
| 103 | 964.9 | 870.189297007997 | 94.7107029920027 |
| 104 | 766.3 | 863.986723768497 | -97.6867237684967 |
| 105 | 847.8 | 895.19346994741 | -47.3934699474092 |
| 106 | 992.7 | 868.450360014441 | 124.249639985559 |
| 107 | 865.3 | 864.855264230847 | 0.444735769152932 |
| 108 | 1054.1 | 983.226256792919 | 70.8737432070812 |
| 109 | 972.5 | 999.799200923376 | -27.2992009233765 |
| 110 | 857.4 | 906.432381300717 | -49.0323813007168 |
| 111 | 1043.3 | 968.024221914784 | 75.2757780852157 |
| 112 | 1061 | 1012.32156919886 | 48.6784308011401 |
| 113 | 989.4 | 1041.24012087565 | -51.8401208756504 |
| 114 | 963.2 | 982.08979113356 | -18.8897911335591 |
| 115 | 1181.9 | 1125.57770939334 | 56.322290606658 |
| 116 | 1256.4 | 1188.23382652002 | 68.1661734799757 |
| 117 | 1492.7 | 1217.57808880186 | 275.121911198139 |
| 118 | 1360.8 | 1214.83441422836 | 145.965585771641 |
| 119 | 1342.8 | 1201.34154687745 | 141.458453122554 |
| 120 | 1464 | 1360.79361282645 | 103.206387173548 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.0482969383243491 | 0.0965938766486982 | 0.95170306167565 |
| 7 | 0.0131112783144921 | 0.0262225566289843 | 0.986888721685508 |
| 8 | 0.00694115232480782 | 0.0138823046496156 | 0.993058847675192 |
| 9 | 0.00184702905241157 | 0.00369405810482313 | 0.998152970947588 |
| 10 | 0.00054915889029487 | 0.00109831778058974 | 0.999450841109705 |
| 11 | 0.000237341331530692 | 0.000474682663061384 | 0.99976265866847 |
| 12 | 6.52204849877258e-05 | 0.000130440969975452 | 0.999934779515012 |
| 13 | 5.99641144538465e-05 | 0.000119928228907693 | 0.999940035885546 |
| 14 | 0.00424114022511286 | 0.00848228045022573 | 0.995758859774887 |
| 15 | 0.00260652466488635 | 0.00521304932977270 | 0.997393475335114 |
| 16 | 0.00228794050717802 | 0.00457588101435604 | 0.997712059492822 |
| 17 | 0.00119438242176369 | 0.00238876484352738 | 0.998805617578236 |
| 18 | 0.000660808454100489 | 0.00132161690820098 | 0.9993391915459 |
| 19 | 0.000351521762927541 | 0.000703043525855082 | 0.999648478237072 |
| 20 | 0.00018681373453912 | 0.00037362746907824 | 0.999813186265461 |
| 21 | 0.000120173088176547 | 0.000240346176353094 | 0.999879826911823 |
| 22 | 5.80579087332107e-05 | 0.000116115817466421 | 0.999941942091267 |
| 23 | 3.91642662870171e-05 | 7.83285325740342e-05 | 0.999960835733713 |
| 24 | 0.000201620736895328 | 0.000403241473790655 | 0.999798379263105 |
| 25 | 0.000115365034704946 | 0.000230730069409893 | 0.999884634965295 |
| 26 | 7.39834310907211e-05 | 0.000147966862181442 | 0.99992601656891 |
| 27 | 3.47716427367558e-05 | 6.95432854735115e-05 | 0.999965228357263 |
| 28 | 0.000127442505536665 | 0.000254885011073330 | 0.999872557494463 |
| 29 | 7.13613674250322e-05 | 0.000142722734850064 | 0.999928638632575 |
| 30 | 4.22318871063767e-05 | 8.44637742127535e-05 | 0.999957768112894 |
| 31 | 4.22761034192644e-05 | 8.45522068385288e-05 | 0.99995772389658 |
| 32 | 2.04252209052502e-05 | 4.08504418105004e-05 | 0.999979574779095 |
| 33 | 1.86962480364268e-05 | 3.73924960728535e-05 | 0.999981303751964 |
| 34 | 1.75035743914682e-05 | 3.50071487829363e-05 | 0.999982496425609 |
| 35 | 8.42158648904236e-06 | 1.68431729780847e-05 | 0.99999157841351 |
| 36 | 5.78830673002131e-06 | 1.15766134600426e-05 | 0.99999421169327 |
| 37 | 6.18319614534959e-06 | 1.23663922906992e-05 | 0.999993816803855 |
| 38 | 3.13157578148031e-06 | 6.26315156296063e-06 | 0.999996868424219 |
| 39 | 1.98495320834875e-06 | 3.96990641669749e-06 | 0.999998015046792 |
| 40 | 3.50940531517262e-06 | 7.01881063034524e-06 | 0.999996490594685 |
| 41 | 1.72172743621085e-06 | 3.44345487242169e-06 | 0.999998278272564 |
| 42 | 2.20538759850763e-06 | 4.41077519701526e-06 | 0.999997794612401 |
| 43 | 2.43312394403445e-06 | 4.8662478880689e-06 | 0.999997566876056 |
| 44 | 1.23854610755725e-06 | 2.47709221511449e-06 | 0.999998761453892 |
| 45 | 1.41000497269454e-06 | 2.82000994538909e-06 | 0.999998589995027 |
| 46 | 8.74758698595195e-07 | 1.74951739719039e-06 | 0.999999125241301 |
| 47 | 1.05965728917715e-06 | 2.11931457835431e-06 | 0.99999894034271 |
| 48 | 1.09661722792096e-06 | 2.19323445584192e-06 | 0.999998903382772 |
| 49 | 5.83672091453394e-06 | 1.16734418290679e-05 | 0.999994163279085 |
| 50 | 3.68821031203128e-06 | 7.37642062406255e-06 | 0.999996311789688 |
| 51 | 2.54721112262536e-06 | 5.09442224525073e-06 | 0.999997452788877 |
| 52 | 1.78793511501615e-06 | 3.5758702300323e-06 | 0.999998212064885 |
| 53 | 1.18749628052936e-06 | 2.37499256105871e-06 | 0.99999881250372 |
| 54 | 9.71036115575942e-07 | 1.94207223115188e-06 | 0.999999028963884 |
| 55 | 1.58530341336100e-05 | 3.17060682672199e-05 | 0.999984146965866 |
| 56 | 9.87652389175888e-06 | 1.97530477835178e-05 | 0.999990123476108 |
| 57 | 6.7230009628663e-06 | 1.34460019257326e-05 | 0.999993276999037 |
| 58 | 5.00767098244217e-06 | 1.00153419648843e-05 | 0.999994992329018 |
| 59 | 5.00140162200815e-06 | 1.00028032440163e-05 | 0.999994998598378 |
| 60 | 3.39087726827611e-06 | 6.78175453655223e-06 | 0.999996609122732 |
| 61 | 4.48877385642188e-06 | 8.97754771284376e-06 | 0.999995511226144 |
| 62 | 9.5674389812725e-06 | 1.9134877962545e-05 | 0.999990432561019 |
| 63 | 6.65410746920935e-06 | 1.33082149384187e-05 | 0.99999334589253 |
| 64 | 0.000198417837595922 | 0.000396835675191844 | 0.999801582162404 |
| 65 | 0.000164384807496668 | 0.000328769614993336 | 0.999835615192503 |
| 66 | 0.000146853745884525 | 0.000293707491769050 | 0.999853146254115 |
| 67 | 0.000438720507934309 | 0.000877441015868618 | 0.999561279492066 |
| 68 | 0.000790695625055718 | 0.00158139125011144 | 0.999209304374944 |
| 69 | 0.00049493147994228 | 0.00098986295988456 | 0.999505068520058 |
| 70 | 0.000374213032274554 | 0.000748426064549108 | 0.999625786967725 |
| 71 | 0.0144716128544935 | 0.028943225708987 | 0.985528387145507 |
| 72 | 0.0922024104862427 | 0.184404820972485 | 0.907797589513757 |
| 73 | 0.0746711257540403 | 0.149342251508081 | 0.92532887424596 |
| 74 | 0.0784264657484766 | 0.156852931496953 | 0.921573534251523 |
| 75 | 0.0724411096068096 | 0.144882219213619 | 0.92755889039319 |
| 76 | 0.0561233674800129 | 0.112246734960026 | 0.943876632519987 |
| 77 | 0.0473790932451497 | 0.0947581864902993 | 0.95262090675485 |
| 78 | 0.0365464826476332 | 0.0730929652952663 | 0.963453517352367 |
| 79 | 0.0309062125388938 | 0.0618124250777876 | 0.969093787461106 |
| 80 | 0.0307126128491256 | 0.0614252256982512 | 0.969287387150874 |
| 81 | 0.0452549196908142 | 0.0905098393816283 | 0.954745080309186 |
| 82 | 0.0471610866599937 | 0.0943221733199874 | 0.952838913340006 |
| 83 | 0.0401631443861017 | 0.0803262887722035 | 0.959836855613898 |
| 84 | 0.0356566432537477 | 0.0713132865074954 | 0.964343356746252 |
| 85 | 0.0322889898180621 | 0.0645779796361242 | 0.967711010181938 |
| 86 | 0.0317968513986253 | 0.0635937027972507 | 0.968203148601375 |
| 87 | 0.025158795018496 | 0.050317590036992 | 0.974841204981504 |
| 88 | 0.0506309756728946 | 0.101261951345789 | 0.949369024327105 |
| 89 | 0.0373738686854182 | 0.0747477373708364 | 0.962626131314582 |
| 90 | 0.0361799442420293 | 0.0723598884840586 | 0.96382005575797 |
| 91 | 0.0292015402184211 | 0.0584030804368423 | 0.970798459781579 |
| 92 | 0.0387085759409324 | 0.0774171518818649 | 0.961291424059068 |
| 93 | 0.0376886396965243 | 0.0753772793930486 | 0.962311360303476 |
| 94 | 0.0328046735358659 | 0.0656093470717319 | 0.967195326464134 |
| 95 | 0.0380187277175276 | 0.0760374554350552 | 0.961981272282472 |
| 96 | 0.0271794906956656 | 0.0543589813913312 | 0.972820509304335 |
| 97 | 0.0221924722041526 | 0.0443849444083053 | 0.977807527795847 |
| 98 | 0.0170726279288523 | 0.0341452558577046 | 0.982927372071148 |
| 99 | 0.0171245387814764 | 0.0342490775629529 | 0.982875461218524 |
| 100 | 0.0116926753530876 | 0.0233853507061751 | 0.988307324646912 |
| 101 | 0.00766437809354823 | 0.0153287561870965 | 0.992335621906452 |
| 102 | 0.139444270544404 | 0.278888541088807 | 0.860555729455596 |
| 103 | 0.185707371572141 | 0.371414743144281 | 0.81429262842786 |
| 104 | 0.205117077130152 | 0.410234154260304 | 0.794882922869848 |
| 105 | 0.193490596313687 | 0.386981192627374 | 0.806509403686313 |
| 106 | 0.350854682792999 | 0.701709365585997 | 0.649145317207001 |
| 107 | 0.28506086379761 | 0.57012172759522 | 0.71493913620239 |
| 108 | 0.297983186584334 | 0.595966373168668 | 0.702016813415666 |
| 109 | 0.228328596767070 | 0.456657193534141 | 0.77167140323293 |
| 110 | 0.167973640855358 | 0.335947281710716 | 0.832026359144642 |
| 111 | 0.173068908286844 | 0.346137816573688 | 0.826931091713156 |
| 112 | 0.145698785261421 | 0.291397570522842 | 0.854301214738579 |
| 113 | 0.119960669113158 | 0.239921338226317 | 0.880039330886841 |
| 114 | 0.0989935958174117 | 0.197987191634823 | 0.901006404182588 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 62 | 0.568807339449541 | NOK |
| 5% type I error level | 70 | 0.642201834862385 | NOK |
| 10% type I error level | 90 | 0.825688073394495 | NOK |
