| Multiple Linear Regression - Estimated Regression Equation |
| OPENVAC[t] = + 2916.22308407620 + 1.20727819032451Y1[t] -0.0769374964679657Y2[t] -0.295020374564640Y3[t] + 0.106069047767341Y4[t] -0.0190621316848944NWWZ[t] + 0.00830310174893315X1[t] + 0.0416925619993690X2[t] -0.0618940493708573X3[t] + 0.0255099935589280X4[t] + 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) | 2916.22308407620 | 2006.581725 | 1.4533 | 0.148856 | 0.074428 |
| Y1 | 1.20727819032451 | 0.096339 | 12.5315 | 0 | 0 |
| Y2 | -0.0769374964679657 | 0.152589 | -0.5042 | 0.615075 | 0.307538 |
| Y3 | -0.295020374564640 | 0.151992 | -1.941 | 0.054702 | 0.027351 |
| Y4 | 0.106069047767341 | 0.100092 | 1.0597 | 0.291495 | 0.145747 |
| NWWZ | -0.0190621316848944 | 0.019078 | -0.9992 | 0.319804 | 0.159902 |
| X1 | 0.00830310174893315 | 0.029625 | 0.2803 | 0.779768 | 0.389884 |
| X2 | 0.0416925619993690 | 0.031109 | 1.3402 | 0.18282 | 0.09141 |
| X3 | -0.0618940493708573 | 0.028573 | -2.1662 | 0.03236 | 0.01618 |
| X4 | 0.0255099935589280 | 0.018046 | 1.4136 | 0.160184 | 0.080092 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.967504886669294 |
| R-squared | 0.936065705728964 |
| Adjusted R-squared | 0.931062152264274 |
| F-TEST (value) | 187.080184579781 |
| F-TEST (DF numerator) | 9 |
| F-TEST (DF denominator) | 115 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2052.68504885078 |
| Sum Squared Residuals | 484554329.624184 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 40399 | 43416.6257715925 | -3017.62577159253 |
| 2 | 36763 | 37458.9019670443 | -695.901967044333 |
| 3 | 37903 | 35352.7419772328 | 2550.25802276717 |
| 4 | 35532 | 37651.0541878872 | -2119.05418788717 |
| 5 | 35533 | 35075.1970698027 | 457.802930197315 |
| 6 | 32110 | 34659.2299017477 | -2549.22990174765 |
| 7 | 33374 | 31446.4551582699 | 1927.54484173008 |
| 8 | 35462 | 33122.8235281537 | 2339.17647184635 |
| 9 | 33508 | 35444.2076110100 | -1936.20761100996 |
| 10 | 36080 | 33248.2794211605 | 2831.72057883955 |
| 11 | 34560 | 35934.414637528 | -1374.41463752797 |
| 12 | 38737 | 35357.7029998715 | 3379.2970001285 |
| 13 | 38144 | 38747.7204399171 | -603.72043991706 |
| 14 | 37594 | 37656.6730424655 | -62.6730424655093 |
| 15 | 36424 | 36891.2441405552 | -467.244140555227 |
| 16 | 36843 | 36182.4951281615 | 660.504871838538 |
| 17 | 37246 | 36605.818769037 | 640.181230962978 |
| 18 | 38661 | 37295.3752052028 | 1365.62479479720 |
| 19 | 40454 | 38964.2386959052 | 1489.76130409485 |
| 20 | 44928 | 40569.4455859193 | 4358.55441408066 |
| 21 | 48441 | 45363.7902928645 | 3077.20970713551 |
| 22 | 48140 | 49266.1249332942 | -1126.12493329416 |
| 23 | 45998 | 47383.0213269791 | -1385.02132697914 |
| 24 | 47369 | 45083.8298794291 | 2285.17012057089 |
| 25 | 49554 | 46580.6711588737 | 2973.32884112627 |
| 26 | 47510 | 48663.4924361199 | -1153.49243611992 |
| 27 | 44873 | 46872.1237603823 | -1999.12376038229 |
| 28 | 45344 | 43396.8484344880 | 1947.15156551195 |
| 29 | 42413 | 44298.3247197018 | -1885.32471970177 |
| 30 | 36912 | 41471.8652169968 | -4559.86521699679 |
| 31 | 43452 | 34891.682845119 | 8560.31715488099 |
| 32 | 42142 | 43733.6434903281 | -1591.64349032808 |
| 33 | 44382 | 42686.6950249164 | 1695.30497508356 |
| 34 | 43636 | 43309.39243646 | 326.60756354 |
| 35 | 44167 | 43301.1296895678 | 865.870310432216 |
| 36 | 44423 | 44300.2625006992 | 122.737499300848 |
| 37 | 42868 | 43753.0939557405 | -885.093955740535 |
| 38 | 43908 | 40597.4538395836 | 3310.54616041637 |
| 39 | 42013 | 43978.84058619 | -1965.84058619004 |
| 40 | 38846 | 41392.1656887526 | -2546.16568875256 |
| 41 | 35087 | 37017.791381644 | -1930.79138164398 |
| 42 | 33026 | 33577.3314554256 | -551.331455425634 |
| 43 | 34646 | 32090.3441209996 | 2555.65587900044 |
| 44 | 37135 | 34441.5610123150 | 2693.43898768496 |
| 45 | 37985 | 37570.8246549117 | 414.175345088343 |
| 46 | 43121 | 37946.0129174278 | 5174.98708257222 |
| 47 | 43722 | 43933.5722035703 | -211.572203570289 |
| 48 | 43630 | 44165.625836671 | -535.625836671008 |
| 49 | 42234 | 42260.6748667514 | -26.6748667514262 |
| 50 | 39351 | 39978.9543501525 | -627.954350152471 |
| 51 | 39327 | 38509.470399822 | 817.529600178023 |
| 52 | 35704 | 38400.1228517099 | -2696.12285170990 |
| 53 | 30466 | 34464.0669654113 | -3998.06696541131 |
| 54 | 28155 | 28387.0565314575 | -232.056531457502 |
| 55 | 29257 | 26747.6648745963 | 2509.33512540367 |
| 56 | 29998 | 29864.9582644656 | 133.041735534424 |
| 57 | 32529 | 29873.3016325018 | 2655.69836749819 |
| 58 | 34787 | 33008.6483336249 | 1778.3516663751 |
| 59 | 33855 | 35273.5694529508 | -1418.56945295083 |
| 60 | 34556 | 34489.6469680959 | 66.3530319041103 |
| 61 | 31348 | 33480.6622956257 | -2132.66229562572 |
| 62 | 30805 | 29441.2727111412 | 1363.72728885883 |
| 63 | 28353 | 30613.2074945979 | -2260.20749459794 |
| 64 | 24514 | 28089.1841309380 | -3575.18413093796 |
| 65 | 21106 | 23286.0262818105 | -2180.02628181046 |
| 66 | 21346 | 20042.8350566098 | 1303.16494339020 |
| 67 | 23335 | 21701.1901531722 | 1633.80984682783 |
| 68 | 24379 | 24305.0684263475 | 73.931573652472 |
| 69 | 26290 | 24942.8790102659 | 1347.12098973408 |
| 70 | 30084 | 27004.7598185844 | 3079.24018141564 |
| 71 | 29429 | 31027.0994862747 | -1598.09948627472 |
| 72 | 30632 | 31111.81975047 | -479.819750469983 |
| 73 | 27349 | 29584.1452670640 | -2235.14526706404 |
| 74 | 27264 | 26045.0668343114 | 1218.93316568857 |
| 75 | 27474 | 27415.8222327852 | 58.1777672147815 |
| 76 | 24482 | 28144.9581758419 | -3662.95817584193 |
| 77 | 21453 | 24080.0249398751 | -2627.02493987509 |
| 78 | 18788 | 20595.9473655206 | -1807.94736552062 |
| 79 | 19282 | 18570.8307214822 | 711.169278517825 |
| 80 | 19713 | 19550.329341445 | 162.670658555016 |
| 81 | 21917 | 20462.9604278171 | 1454.0395721829 |
| 82 | 23812 | 23014.9130903398 | 797.086909660217 |
| 83 | 23785 | 25109.2281343581 | -1324.22813435808 |
| 84 | 24696 | 25347.8728647611 | -651.872864761088 |
| 85 | 24562 | 24668.8620498617 | -106.862049861737 |
| 86 | 23580 | 23907.6542605707 | -327.654260570681 |
| 87 | 24939 | 24510.9756013969 | 428.024398603075 |
| 88 | 23899 | 25745.7757619179 | -1846.77576191786 |
| 89 | 21454 | 24263.4356575387 | -2809.43565753869 |
| 90 | 19761 | 21200.928372505 | -1439.92837250498 |
| 91 | 19815 | 19784.1451619030 | 30.8548380970458 |
| 92 | 20780 | 20190.8470845858 | 589.152915414245 |
| 93 | 23462 | 21734.8823317012 | 1727.11766829877 |
| 94 | 25005 | 24633.3948383678 | 371.605161632174 |
| 95 | 24725 | 26385.8202111246 | -1660.82021112457 |
| 96 | 26198 | 26124.1738129710 | 73.8261870290377 |
| 97 | 27543 | 26382.5950911317 | 1160.40490886832 |
| 98 | 26471 | 27354.8210694773 | -883.8210694773 |
| 99 | 26558 | 27570.8488477490 | -1012.84884774904 |
| 100 | 25317 | 26697.1700996389 | -1380.17009963886 |
| 101 | 22896 | 25629.7474073438 | -2733.74740734385 |
| 102 | 22248 | 22564.7013919538 | -316.701391953801 |
| 103 | 23406 | 22518.8537379387 | 887.146262061253 |
| 104 | 25073 | 24151.2808331886 | 921.719166811442 |
| 105 | 27691 | 25976.043109844 | 1714.95689015598 |
| 106 | 30599 | 29143.4830609818 | 1455.51693901824 |
| 107 | 31948 | 32000.0952743487 | -52.0952743486932 |
| 108 | 32946 | 33302.1774809776 | -356.177480977608 |
| 109 | 34012 | 32806.4767195555 | 1205.52328044449 |
| 110 | 32936 | 33711.8992424468 | -775.899242446798 |
| 111 | 32974 | 33581.4363516315 | -607.436351631457 |
| 112 | 30951 | 32843.4550054186 | -1892.45500541863 |
| 113 | 29812 | 30656.9684964223 | -844.968496422295 |
| 114 | 29010 | 29531.7407406632 | -521.740740663159 |
| 115 | 31068 | 29236.0614016933 | 1831.93859830666 |
| 116 | 32447 | 31437.0327763678 | 1009.96722363224 |
| 117 | 34844 | 33218.2903269012 | 1625.70967309881 |
| 118 | 35676 | 35234.8157557156 | 441.184244284417 |
| 119 | 35387 | 36307.0378494799 | -920.03784947986 |
| 120 | 36488 | 36337.6141961388 | 150.385803861180 |
| 121 | 35652 | 35409.3136557818 | 242.686344218198 |
| 122 | 33488 | 34934.6546951543 | -1446.65469515425 |
| 123 | 32914 | 33430.2448256227 | -516.244825622688 |
| 124 | 29781 | 32487.0279540819 | -2706.02795408193 |
| 125 | 27951 | 29138.8169170118 | -1187.81691701180 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 13 | 0.26396105538585 | 0.5279221107717 | 0.73603894461415 |
| 14 | 0.169935920964145 | 0.339871841928290 | 0.830064079035855 |
| 15 | 0.1220414442955 | 0.244082888591 | 0.8779585557045 |
| 16 | 0.0915569663803196 | 0.183113932760639 | 0.90844303361968 |
| 17 | 0.0887004358553361 | 0.177400871710672 | 0.911299564144664 |
| 18 | 0.0691735527789837 | 0.138347105557967 | 0.930826447221016 |
| 19 | 0.0456963840022256 | 0.0913927680044512 | 0.954303615997774 |
| 20 | 0.282987371850506 | 0.565974743701012 | 0.717012628149494 |
| 21 | 0.469459280875637 | 0.938918561751274 | 0.530540719124363 |
| 22 | 0.418729690015385 | 0.83745938003077 | 0.581270309984615 |
| 23 | 0.339586990345283 | 0.679173980690567 | 0.660413009654717 |
| 24 | 0.295449580014708 | 0.590899160029415 | 0.704550419985292 |
| 25 | 0.330310949561031 | 0.660621899122063 | 0.669689050438969 |
| 26 | 0.268467270515653 | 0.536934541031307 | 0.731532729484346 |
| 27 | 0.441924834765926 | 0.883849669531852 | 0.558075165234074 |
| 28 | 0.383886591386948 | 0.767773182773896 | 0.616113408613052 |
| 29 | 0.36401243225999 | 0.72802486451998 | 0.63598756774001 |
| 30 | 0.68526663324998 | 0.629466733500041 | 0.314733366750021 |
| 31 | 0.979666421037737 | 0.0406671579245256 | 0.0203335789622628 |
| 32 | 0.973999684806378 | 0.0520006303872442 | 0.0260003151936221 |
| 33 | 0.972508193256625 | 0.0549836134867493 | 0.0274918067433746 |
| 34 | 0.96330810862539 | 0.073383782749221 | 0.0366918913746105 |
| 35 | 0.968982683845746 | 0.0620346323085073 | 0.0310173161542536 |
| 36 | 0.959056459189792 | 0.0818870816204156 | 0.0409435408102078 |
| 37 | 0.950725112860462 | 0.0985497742790757 | 0.0492748871395378 |
| 38 | 0.971812687875747 | 0.0563746242485059 | 0.0281873121242530 |
| 39 | 0.966281964559772 | 0.0674360708804553 | 0.0337180354402276 |
| 40 | 0.974051426185437 | 0.0518971476291259 | 0.0259485738145630 |
| 41 | 0.979845495750663 | 0.0403090084986746 | 0.0201545042493373 |
| 42 | 0.976462280123743 | 0.0470754397525132 | 0.0235377198762566 |
| 43 | 0.979037651173844 | 0.0419246976523115 | 0.0209623488261557 |
| 44 | 0.985062456899752 | 0.0298750862004965 | 0.0149375431002483 |
| 45 | 0.982817696951763 | 0.0343646060964737 | 0.0171823030482368 |
| 46 | 0.99940457586399 | 0.00119084827201893 | 0.000595424136009464 |
| 47 | 0.999207639189122 | 0.00158472162175539 | 0.000792360810877696 |
| 48 | 0.998774076744931 | 0.00245184651013738 | 0.00122592325506869 |
| 49 | 0.99826822732815 | 0.00346354534370062 | 0.00173177267185031 |
| 50 | 0.997500435323756 | 0.00499912935248732 | 0.00249956467624366 |
| 51 | 0.997760119202982 | 0.00447976159403599 | 0.00223988079701800 |
| 52 | 0.997517078440004 | 0.00496584311999237 | 0.00248292155999618 |
| 53 | 0.998994088402842 | 0.0020118231943166 | 0.0010059115971583 |
| 54 | 0.998634859258037 | 0.00273028148392597 | 0.00136514074196299 |
| 55 | 0.999342420992295 | 0.00131515801540917 | 0.000657579007704587 |
| 56 | 0.998969170878137 | 0.00206165824372581 | 0.00103082912186291 |
| 57 | 0.999330222649929 | 0.00133955470014200 | 0.000669777350071002 |
| 58 | 0.999376459752946 | 0.00124708049410809 | 0.000623540247054047 |
| 59 | 0.99915136362185 | 0.00169727275629940 | 0.000848636378149701 |
| 60 | 0.999105833410853 | 0.00178833317829446 | 0.00089416658914723 |
| 61 | 0.999171962721738 | 0.00165607455652367 | 0.000828037278261835 |
| 62 | 0.999460654694405 | 0.00107869061118948 | 0.000539345305594742 |
| 63 | 0.999535348783286 | 0.000929302433428292 | 0.000464651216714146 |
| 64 | 0.999882083920874 | 0.000235832158252843 | 0.000117916079126422 |
| 65 | 0.999916595324605 | 0.000166809350790950 | 8.34046753954748e-05 |
| 66 | 0.999932741812482 | 0.000134516375035804 | 6.72581875179022e-05 |
| 67 | 0.999922062740187 | 0.000155874519625368 | 7.79372598126838e-05 |
| 68 | 0.999881241911406 | 0.000237516177187685 | 0.000118758088593843 |
| 69 | 0.99988204550608 | 0.000235908987840403 | 0.000117954493920201 |
| 70 | 0.99997555106421 | 4.88978715793147e-05 | 2.44489357896574e-05 |
| 71 | 0.999967980563166 | 6.40388736684042e-05 | 3.20194368342021e-05 |
| 72 | 0.999950754233856 | 9.84915322875772e-05 | 4.92457661437886e-05 |
| 73 | 0.999963988115047 | 7.20237699050586e-05 | 3.60118849525293e-05 |
| 74 | 0.999990686741118 | 1.86265177638103e-05 | 9.31325888190513e-06 |
| 75 | 0.99998484172608 | 3.03165478389833e-05 | 1.51582739194917e-05 |
| 76 | 0.99999946118442 | 1.07763116139596e-06 | 5.38815580697978e-07 |
| 77 | 0.999999490621832 | 1.01875633693122e-06 | 5.0937816846561e-07 |
| 78 | 0.99999921808218 | 1.56383563932901e-06 | 7.81917819664507e-07 |
| 79 | 0.999998881588902 | 2.23682219511868e-06 | 1.11841109755934e-06 |
| 80 | 0.999997772187298 | 4.45562540433131e-06 | 2.22781270216566e-06 |
| 81 | 0.999997158073451 | 5.68385309759361e-06 | 2.84192654879680e-06 |
| 82 | 0.999995472242184 | 9.05551563160702e-06 | 4.52775781580351e-06 |
| 83 | 0.99999180744228 | 1.63851154396464e-05 | 8.19255771982318e-06 |
| 84 | 0.999983650931475 | 3.26981370495917e-05 | 1.63490685247958e-05 |
| 85 | 0.999968991103825 | 6.20177923500867e-05 | 3.10088961750433e-05 |
| 86 | 0.999945755040294 | 0.000108489919411729 | 5.42449597058644e-05 |
| 87 | 0.99992176451106 | 0.000156470977881502 | 7.82354889407512e-05 |
| 88 | 0.99996712647743 | 6.57470451418735e-05 | 3.28735225709367e-05 |
| 89 | 0.999988109999 | 2.37800020006994e-05 | 1.18900010003497e-05 |
| 90 | 0.999976829809693 | 4.63403806148295e-05 | 2.31701903074148e-05 |
| 91 | 0.999952510927484 | 9.497814503213e-05 | 4.7489072516065e-05 |
| 92 | 0.999896378604274 | 0.000207242791452132 | 0.000103621395726066 |
| 93 | 0.9998509372477 | 0.000298125504599554 | 0.000149062752299777 |
| 94 | 0.999683341233495 | 0.000633317533009445 | 0.000316658766504723 |
| 95 | 0.999659739045886 | 0.0006805219082273 | 0.00034026095411365 |
| 96 | 0.99931981952228 | 0.00136036095544036 | 0.000680180477720181 |
| 97 | 0.998648555455595 | 0.00270288908881022 | 0.00135144454440511 |
| 98 | 0.997737932827712 | 0.00452413434457542 | 0.00226206717228771 |
| 99 | 0.99654000996348 | 0.00691998007303889 | 0.00345999003651945 |
| 100 | 0.994389177287684 | 0.0112216454246322 | 0.00561082271231611 |
| 101 | 0.999440583938905 | 0.00111883212219093 | 0.000559416061095465 |
| 102 | 0.998670820355731 | 0.00265835928853711 | 0.00132917964426855 |
| 103 | 0.997560396205637 | 0.00487920758872602 | 0.00243960379436301 |
| 104 | 0.996526314451948 | 0.00694737109610481 | 0.00347368554805240 |
| 105 | 0.9927072068061 | 0.0145855863877997 | 0.00729279319389984 |
| 106 | 0.984280612611973 | 0.031438774776054 | 0.015719387388027 |
| 107 | 0.974158736792042 | 0.0516825264159156 | 0.0258412632079578 |
| 108 | 0.992060004890779 | 0.0158799902184424 | 0.00793999510922121 |
| 109 | 0.985586469058196 | 0.0288270618836089 | 0.0144135309418044 |
| 110 | 0.98153769347169 | 0.0369246130566213 | 0.0184623065283106 |
| 111 | 0.966773609672855 | 0.0664527806542896 | 0.0332263903271448 |
| 112 | 0.916913178381475 | 0.166173643237051 | 0.0830868216185254 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 58 | 0.58 | NOK |
| 5% type I error level | 70 | 0.7 | NOK |
| 10% type I error level | 82 | 0.82 | NOK |
