| Multiple Linear Regression - Estimated Regression Equation |
| OPENVAC[t] = + 2250.36966939532 + 0.921167547866439Y1[t] + 0.147604467143337Y2[t] -0.0352136681864466Y3[t] -0.0684979108690105Y4[t] -1782.24140296891M1[t] -2244.99351674281M2[t] -1446.45969762698M3[t] -2768.68887159723M4[t] -3252.36709616257M5[t] -2662.16780990246M6[t] + 1003.87028803039M7[t] + 778.856112992519M8[t] + 901.696972060029M9[t] + 881.942687673479M10[t] -1391.42130378499M11[t] -2.68490575599361t + 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) | 2250.36966939532 | 1252.69288 | 1.7964 | 0.075222 | 0.037611 |
| Y1 | 0.921167547866439 | 0.095886 | 9.6069 | 0 | 0 |
| Y2 | 0.147604467143337 | 0.130041 | 1.1351 | 0.258863 | 0.129431 |
| Y3 | -0.0352136681864466 | 0.12807 | -0.275 | 0.783875 | 0.391938 |
| Y4 | -0.0684979108690105 | 0.095391 | -0.7181 | 0.474262 | 0.237131 |
| M1 | -1782.24140296891 | 733.338533 | -2.4303 | 0.016733 | 0.008367 |
| M2 | -2244.99351674281 | 729.357054 | -3.078 | 0.002641 | 0.001321 |
| M3 | -1446.45969762698 | 758.801315 | -1.9062 | 0.059277 | 0.029638 |
| M4 | -2768.68887159723 | 813.506152 | -3.4034 | 0.000935 | 0.000467 |
| M5 | -3252.36709616257 | 812.052227 | -4.0051 | 0.000114 | 5.7e-05 |
| M6 | -2662.16780990246 | 862.123173 | -3.0879 | 0.002562 | 0.001281 |
| M7 | 1003.87028803039 | 918.587877 | 1.0928 | 0.276895 | 0.138448 |
| M8 | 778.856112992519 | 927.154085 | 0.8401 | 0.402736 | 0.201368 |
| M9 | 901.696972060029 | 812.294747 | 1.1101 | 0.269438 | 0.134719 |
| M10 | 881.942687673479 | 743.516388 | 1.1862 | 0.238155 | 0.119078 |
| M11 | -1391.42130378499 | 743.95932 | -1.8703 | 0.064151 | 0.032075 |
| t | -2.68490575599361 | 5.368187 | -0.5002 | 0.617986 | 0.308993 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.982023446627715 |
| R-squared | 0.964370049726577 |
| Adjusted R-squared | 0.959091538574959 |
| F-TEST (value) | 182.697359544449 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 108 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1581.2481549845 |
| Sum Squared Residuals | 270037338.585324 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 40399 | 43191.945750204 | -2792.94575020402 |
| 2 | 36763 | 39213.245477128 | -2450.24547712803 |
| 3 | 37903 | 36020.7512010242 | 1882.24879897577 |
| 4 | 35532 | 35364.5990504630 | 167.400949536961 |
| 5 | 35533 | 33248.3482886415 | 2284.65171135847 |
| 6 | 32110 | 33695.7284672838 | -1585.72846728383 |
| 7 | 33374 | 34211.4767364604 | -837.4767364604 |
| 8 | 35462 | 34805.2566781403 | 656.743321859688 |
| 9 | 33508 | 37155.8504061575 | -3647.85040615747 |
| 10 | 36080 | 35831.6062271961 | 248.393772803855 |
| 11 | 34560 | 35476.2736357844 | -916.273635784363 |
| 12 | 38737 | 35770.2579202909 | 2966.74207970915 |
| 13 | 38144 | 37651.9650322087 | 492.034967791303 |
| 14 | 37594 | 37134.16766494 | 459.832335059972 |
| 15 | 36424 | 37292.8743104634 | -868.874310463432 |
| 16 | 36843 | 34543.7776743393 | 2299.22232566067 |
| 17 | 37246 | 34330.6732986642 | 2915.32670133581 |
| 18 | 38661 | 35430.1383154476 | 3230.86168455236 |
| 19 | 40454 | 40521.8162168609 | -67.8162168608912 |
| 20 | 44928 | 42111.7391374661 | 2816.26086253387 |
| 21 | 48441 | 46540.4215109561 | 1900.57848904394 |
| 22 | 48140 | 50254.3636515297 | -2114.36365152966 |
| 23 | 45998 | 47939.2151098277 | -1941.21510982765 |
| 24 | 47369 | 46880.2164061496 | 488.783593850354 |
| 25 | 49554 | 45812.0081901699 | 3741.99180983011 |
| 26 | 47510 | 47657.7335356086 | -147.733535608623 |
| 27 | 44873 | 46991.6763278354 | -2118.67632783545 |
| 28 | 45344 | 42765.0873927556 | 2578.91260724437 |
| 29 | 42413 | 42245.6700001467 | 167.329999853287 |
| 30 | 36912 | 40435.6321747027 | -3523.63217470272 |
| 31 | 43452 | 38763.0573461149 | 4688.94265388506 |
| 32 | 42142 | 43818.7706000473 | -1676.77060004726 |
| 33 | 44382 | 44092.0080462219 | 289.991953778116 |
| 34 | 43636 | 46086.1319290935 | -2450.13192909346 |
| 35 | 44167 | 43051.6796158126 | 1115.32038418737 |
| 36 | 44423 | 44830.2966957705 | -407.296695770532 |
| 37 | 42868 | 43232.4013274731 | -364.401327473056 |
| 38 | 43908 | 41404.7364983008 | 2503.26350169918 |
| 39 | 42013 | 42883.6876253067 | -870.687625306688 |
| 40 | 38846 | 40003.8914770501 | -1157.89147705007 |
| 41 | 35087 | 36390.3722938865 | -1303.37229388651 |
| 42 | 33026 | 33043.2465884273 | -17.2465884272728 |
| 43 | 34646 | 34494.5535007028 | 151.446499297158 |
| 44 | 37135 | 35804.2341031052 | 1330.76589689479 |
| 45 | 37985 | 38786.3543369174 | -801.354336917373 |
| 46 | 43121 | 39998.4231330201 | 3122.57686697995 |
| 47 | 43722 | 42380.3411229956 | 1341.65887700440 |
| 48 | 43630 | 44880.3728424291 | -1250.37284242906 |
| 49 | 42234 | 42860.3287800093 | -626.328780009342 |
| 50 | 39351 | 40722.3935678774 | -1371.39356787742 |
| 51 | 39327 | 38618.5330176471 | 708.466982352912 |
| 52 | 35704 | 36901.427326586 | -1197.42732658604 |
| 53 | 30466 | 33271.2757520878 | -2805.27575208782 |
| 54 | 28155 | 28697.2681374790 | -542.268137479045 |
| 55 | 29257 | 29587.8739973401 | -330.873997340107 |
| 56 | 29998 | 30466.8047557658 | -468.804755765845 |
| 57 | 32529 | 31872.3768291491 | 656.623170850894 |
| 58 | 34787 | 34410.2808224866 | 376.719177513448 |
| 59 | 33855 | 34486.2371287905 | -631.237128790494 |
| 60 | 34556 | 35209.8535128838 | -653.853512883788 |
| 61 | 31348 | 33680.2176166612 | -2332.21761666121 |
| 62 | 30805 | 30241.2966910508 | 563.703308949204 |
| 63 | 28353 | 30102.5917668545 | -1749.59176685455 |
| 64 | 24514 | 26503.7740461239 | -1989.77404612391 |
| 65 | 21106 | 22357.9848660009 | -1251.98486600087 |
| 66 | 21346 | 19363.0449740079 | 1982.95502599207 |
| 67 | 23335 | 23047.5845032668 | 287.415496733181 |
| 68 | 24379 | 25070.4844082993 | -691.484408299252 |
| 69 | 26290 | 26670.9141666083 | -380.91416660827 |
| 70 | 30084 | 28476.4457395047 | 1607.55426049527 |
| 71 | 29429 | 29804.3732413013 | -375.37324130135 |
| 72 | 30632 | 31010.9511049681 | -378.951104968099 |
| 73 | 27349 | 29973.0082655776 | -2624.00826557758 |
| 74 | 27264 | 26424.1302392007 | 839.869760799304 |
| 75 | 27474 | 26659.5985341512 | 814.401465848787 |
| 76 | 24482 | 25548.7867456504 | -1066.78674565042 |
| 77 | 21453 | 22565.1590533916 | -1112.15905339161 |
| 78 | 18788 | 19919.2518178201 | -1131.25181782013 |
| 79 | 19282 | 20771.5742978871 | -1489.57429788711 |
| 80 | 19713 | 20917.1740310591 | -1204.17403105911 |
| 81 | 21917 | 21808.594402009 | 108.405597991021 |
| 82 | 23812 | 24045.1773930847 | -233.177393084652 |
| 83 | 23785 | 23791.0461857034 | -6.04618570336439 |
| 84 | 24696 | 25327.4880009091 | -631.488000909115 |
| 85 | 24562 | 24160.0607109091 | 401.939289090947 |
| 86 | 23580 | 23576.8021374769 | 3.19786252310590 |
| 87 | 24939 | 23418.0553121103 | 1520.94468788971 |
| 88 | 23899 | 23142.3773779351 | 756.622622064904 |
| 89 | 21454 | 21942.353010896 | -488.353010895997 |
| 90 | 19761 | 20143.5136644456 | -382.513664445586 |
| 91 | 19815 | 21829.9708299620 | -2014.97082996202 |
| 92 | 20780 | 21559.4556798989 | -779.455679898907 |
| 93 | 23462 | 22803.6030904417 | 658.396909558336 |
| 94 | 25005 | 25508.2389994894 | -503.238999489397 |
| 95 | 24725 | 25011.7467325244 | -286.746732524439 |
| 96 | 26198 | 26209.7663678884 | -11.7663678883515 |
| 97 | 27543 | 25502.3445194082 | 2040.65548059179 |
| 98 | 26471 | 26397.4667824821 | 73.5332175178714 |
| 99 | 26558 | 26371.6617746416 | 186.338225358382 |
| 100 | 25317 | 24820.3974763813 | 496.602523618725 |
| 101 | 22896 | 23149.3263699762 | -253.326369976211 |
| 102 | 22248 | 21393.8831446902 | 854.116855309849 |
| 103 | 23406 | 24140.7101948693 | -734.71019486931 |
| 104 | 25073 | 25054.3336378637 | 18.6663621362638 |
| 105 | 27691 | 27069.6537656193 | 621.346234380717 |
| 106 | 30599 | 29708.4970810022 | 890.502918997767 |
| 107 | 31948 | 30359.6101423115 | 1588.38985768848 |
| 108 | 32946 | 33213.8599521344 | -267.859952134403 |
| 109 | 34012 | 32265.6484046153 | 1746.35159538469 |
| 110 | 32936 | 32682.7900861295 | 253.209913870508 |
| 111 | 32974 | 32517.2621573475 | 456.737842652531 |
| 112 | 30951 | 30962.6313524599 | -11.6313524598961 |
| 113 | 29812 | 28583.2263765385 | 1228.77362346155 |
| 114 | 29010 | 27895.2927156957 | 1114.70728430431 |
| 115 | 31068 | 30720.3823765356 | 347.61762346444 |
| 116 | 32447 | 32448.7469683542 | -1.74696835424703 |
| 117 | 34844 | 34249.2234459199 | 594.776554080096 |
| 118 | 35676 | 36620.8350235931 | -944.835023593117 |
| 119 | 35387 | 35275.4770849486 | 111.522915051416 |
| 120 | 36488 | 36341.9371965762 | 146.062803423847 |
| 121 | 35652 | 35335.0714027636 | 316.928597236367 |
| 122 | 33488 | 34215.2373198051 | -727.237319805074 |
| 123 | 32914 | 32875.307972618 | 38.6920273820277 |
| 124 | 29781 | 30656.2500802553 | -875.250080255301 |
| 125 | 27951 | 27332.6106897701 | 618.3893102299 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.385204799851253 | 0.770409599702506 | 0.614795200148747 |
| 21 | 0.851225311715645 | 0.29754937656871 | 0.148774688284355 |
| 22 | 0.926500072001927 | 0.146999855996146 | 0.073499927998073 |
| 23 | 0.940498180643078 | 0.119003638713844 | 0.0595018193569219 |
| 24 | 0.969887297932574 | 0.0602254041348515 | 0.0301127020674258 |
| 25 | 0.96900625987987 | 0.0619874802402586 | 0.0309937401201293 |
| 26 | 0.967503989598452 | 0.0649920208030962 | 0.0324960104015481 |
| 27 | 0.992436951501128 | 0.0151260969977433 | 0.00756304849887164 |
| 28 | 0.991225756809333 | 0.0175484863813335 | 0.00877424319066673 |
| 29 | 0.997591801300552 | 0.00481639739889507 | 0.00240819869944754 |
| 30 | 0.999907840703867 | 0.000184318592265376 | 9.2159296132688e-05 |
| 31 | 0.999997961622033 | 4.07675593405603e-06 | 2.03837796702801e-06 |
| 32 | 0.999999201569368 | 1.59686126486285e-06 | 7.98430632431423e-07 |
| 33 | 0.999998175245544 | 3.64950891174452e-06 | 1.82475445587226e-06 |
| 34 | 0.999999351983103 | 1.29603379487977e-06 | 6.48016897439887e-07 |
| 35 | 0.999998990080976 | 2.01983804891930e-06 | 1.00991902445965e-06 |
| 36 | 0.9999990621595 | 1.87568099831732e-06 | 9.37840499158658e-07 |
| 37 | 0.99999914071709 | 1.71856582108583e-06 | 8.59282910542915e-07 |
| 38 | 0.999999683158712 | 6.33682575389931e-07 | 3.16841287694966e-07 |
| 39 | 0.99999950121033 | 9.97579338842651e-07 | 4.98789669421326e-07 |
| 40 | 0.99999982113977 | 3.57720458603036e-07 | 1.78860229301518e-07 |
| 41 | 0.999999944786376 | 1.10427248114406e-07 | 5.52136240572031e-08 |
| 42 | 0.999999873128208 | 2.53743583224956e-07 | 1.26871791612478e-07 |
| 43 | 0.999999827949426 | 3.4410114869186e-07 | 1.7205057434593e-07 |
| 44 | 0.999999853944578 | 2.92110844676388e-07 | 1.46055422338194e-07 |
| 45 | 0.999999752631394 | 4.94737211531031e-07 | 2.47368605765516e-07 |
| 46 | 0.999999993214097 | 1.35718066136823e-08 | 6.78590330684113e-09 |
| 47 | 0.999999994620702 | 1.07585962471232e-08 | 5.37929812356159e-09 |
| 48 | 0.999999994110197 | 1.17796053158051e-08 | 5.88980265790255e-09 |
| 49 | 0.999999991398961 | 1.72020777302895e-08 | 8.60103886514477e-09 |
| 50 | 0.999999985731774 | 2.8536451970047e-08 | 1.42682259850235e-08 |
| 51 | 0.999999983022465 | 3.39550697183265e-08 | 1.69775348591633e-08 |
| 52 | 0.999999976633691 | 4.67326173996472e-08 | 2.33663086998236e-08 |
| 53 | 0.999999995467071 | 9.06585728423044e-09 | 4.53292864211522e-09 |
| 54 | 0.999999989173584 | 2.16528327544464e-08 | 1.08264163772232e-08 |
| 55 | 0.999999985581314 | 2.88373713889153e-08 | 1.44186856944576e-08 |
| 56 | 0.9999999715014 | 5.69972012206241e-08 | 2.84986006103121e-08 |
| 57 | 0.99999995336087 | 9.32782584453115e-08 | 4.66391292226557e-08 |
| 58 | 0.999999929072731 | 1.41854537231043e-07 | 7.09272686155216e-08 |
| 59 | 0.99999984389663 | 3.12206738130407e-07 | 1.56103369065204e-07 |
| 60 | 0.999999735509784 | 5.28980430968667e-07 | 2.64490215484334e-07 |
| 61 | 0.999999800294723 | 3.99410554321873e-07 | 1.99705277160936e-07 |
| 62 | 0.999999809334827 | 3.81330345136359e-07 | 1.90665172568179e-07 |
| 63 | 0.999999823241028 | 3.53517943953992e-07 | 1.76758971976996e-07 |
| 64 | 0.99999982576346 | 3.48473077983412e-07 | 1.74236538991706e-07 |
| 65 | 0.999999640650287 | 7.18699425100235e-07 | 3.59349712550117e-07 |
| 66 | 0.999999879525101 | 2.40949798295866e-07 | 1.20474899147933e-07 |
| 67 | 0.999999868228691 | 2.63542617196725e-07 | 1.31771308598363e-07 |
| 68 | 0.999999702195095 | 5.95609809569991e-07 | 2.97804904784996e-07 |
| 69 | 0.999999333830248 | 1.33233950305508e-06 | 6.66169751527541e-07 |
| 70 | 0.999999931382903 | 1.37234194177596e-07 | 6.86170970887978e-08 |
| 71 | 0.999999831974763 | 3.36050473354638e-07 | 1.68025236677319e-07 |
| 72 | 0.999999686941485 | 6.2611702926028e-07 | 3.1305851463014e-07 |
| 73 | 0.999999982484084 | 3.50318320843567e-08 | 1.75159160421783e-08 |
| 74 | 0.999999999711027 | 5.77945377908789e-10 | 2.88972688954394e-10 |
| 75 | 0.999999999352597 | 1.29480517919056e-09 | 6.4740258959528e-10 |
| 76 | 0.999999998118803 | 3.76239460874773e-09 | 1.88119730437386e-09 |
| 77 | 0.99999999446584 | 1.10683197889301e-08 | 5.53415989446507e-09 |
| 78 | 0.999999987736055 | 2.45278889018674e-08 | 1.22639444509337e-08 |
| 79 | 0.999999973797255 | 5.24054897947432e-08 | 2.62027448973716e-08 |
| 80 | 0.999999932961754 | 1.34076492492214e-07 | 6.7038246246107e-08 |
| 81 | 0.999999823592898 | 3.52814204479853e-07 | 1.76407102239926e-07 |
| 82 | 0.999999576478867 | 8.4704226698811e-07 | 4.23521133494055e-07 |
| 83 | 0.999998889901608 | 2.22019678473166e-06 | 1.11009839236583e-06 |
| 84 | 0.999997106124435 | 5.78775112923357e-06 | 2.89387556461679e-06 |
| 85 | 0.999994352182856 | 1.12956342888460e-05 | 5.64781714442301e-06 |
| 86 | 0.999988884292922 | 2.22314141569687e-05 | 1.11157070784843e-05 |
| 87 | 0.999993448680009 | 1.31026399821181e-05 | 6.55131999105904e-06 |
| 88 | 0.999991281339698 | 1.74373206043069e-05 | 8.71866030215347e-06 |
| 89 | 0.999984183443482 | 3.16331130351706e-05 | 1.58165565175853e-05 |
| 90 | 0.99997526781381 | 4.94643723777128e-05 | 2.47321861888564e-05 |
| 91 | 0.999980490080907 | 3.90198381866265e-05 | 1.95099190933132e-05 |
| 92 | 0.999947840371039 | 0.000104319257922885 | 5.21596289614426e-05 |
| 93 | 0.999886220743953 | 0.000227558512093389 | 0.000113779256046694 |
| 94 | 0.999700689592857 | 0.000598620814285722 | 0.000299310407142861 |
| 95 | 0.999608171195381 | 0.000783657609237939 | 0.000391828804618969 |
| 96 | 0.998997193665068 | 0.00200561266986315 | 0.00100280633493157 |
| 97 | 0.998687037287753 | 0.00262592542449377 | 0.00131296271224689 |
| 98 | 0.99678561969262 | 0.00642876061475802 | 0.00321438030737901 |
| 99 | 0.993273427960491 | 0.0134531440790175 | 0.00672657203950876 |
| 100 | 0.985993789080785 | 0.0280124218384297 | 0.0140062109192149 |
| 101 | 0.989820371888146 | 0.0203592562237079 | 0.0101796281118539 |
| 102 | 0.976958205919829 | 0.046083588160343 | 0.0230417940801715 |
| 103 | 0.981458063333466 | 0.0370838733330684 | 0.0185419366665342 |
| 104 | 0.956664008517439 | 0.0866719829651226 | 0.0433359914825613 |
| 105 | 0.991884407286382 | 0.0162311854272357 | 0.00811559271361785 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 70 | 0.813953488372093 | NOK |
| 5% type I error level | 78 | 0.906976744186046 | NOK |
| 10% type I error level | 82 | 0.953488372093023 | NOK |
