| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 97.741544080691 -0.815049795615903X[t] + 1.87018159774291M1[t] + 4.29996328167822M2[t] + 13.7930268025441M3[t] + 7.1032140785195M4[t] + 6.04071323204974M5[t] + 13.6699054875868M6[t] -9.8692386652739M7[t] -0.254348328168483M8[t] + 14.0461607844849M9[t] + 15.7957292849124M10[t] + 7.6397334180042M11[t] + 0.114302764901383t + 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) | 97.741544080691 | 4.790567 | 20.4029 | 0 | 0 |
| X | -0.815049795615903 | 0.576386 | -1.4141 | 0.161081 | 0.080541 |
| M1 | 1.87018159774291 | 2.049273 | 0.9126 | 0.364092 | 0.182046 |
| M2 | 4.29996328167822 | 2.112714 | 2.0353 | 0.045014 | 0.022507 |
| M3 | 13.7930268025441 | 2.114485 | 6.5231 | 0 | 0 |
| M4 | 7.1032140785195 | 2.122793 | 3.3462 | 0.001233 | 0.000616 |
| M5 | 6.04071323204974 | 2.138728 | 2.8244 | 0.005929 | 0.002965 |
| M6 | 13.6699054875868 | 2.148476 | 6.3626 | 0 | 0 |
| M7 | -9.8692386652739 | 2.108615 | -4.6804 | 1.1e-05 | 6e-06 |
| M8 | -0.254348328168483 | 2.108411 | -0.1206 | 0.904272 | 0.452136 |
| M9 | 14.0461607844849 | 2.107866 | 6.6637 | 0 | 0 |
| M10 | 15.7957292849124 | 2.107358 | 7.4955 | 0 | 0 |
| M11 | 7.6397334180042 | 2.108595 | 3.6231 | 5e-04 | 0.00025 |
| t | 0.114302764901383 | 0.015436 | 7.4047 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.897678632759792 |
| R-squared | 0.80582692771349 |
| Adjusted R-squared | 0.77541427783729 |
| F-TEST (value) | 26.4964391788857 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 83 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.21420383050917 |
| Sum Squared Residuals | 1474.03965578149 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 98.8 | 94.591214730954 | 4.20878526904587 |
| 2 | 100.5 | 97.298309138915 | 3.20169086108504 |
| 3 | 110.4 | 106.905675424682 | 3.49432457531785 |
| 4 | 96.4 | 100.167155506436 | -3.76715550643581 |
| 5 | 101.9 | 99.2189574248674 | 2.68104257513259 |
| 6 | 106.2 | 107.206967383991 | -1.00696738399063 |
| 7 | 81 | 83.6191160369082 | -2.61911603690818 |
| 8 | 94.7 | 93.1852991797918 | 1.51470082020822 |
| 9 | 101 | 107.274091139100 | -6.27409113910019 |
| 10 | 109.4 | 108.567427547498 | 0.83257245250211 |
| 11 | 102.3 | 100.525734445491 | 1.77426555450891 |
| 12 | 90.7 | 92.9187988128267 | -2.21879881282667 |
| 13 | 96.2 | 94.903283175471 | 1.29671682452899 |
| 14 | 96.1 | 97.6103775834309 | -1.51037758343087 |
| 15 | 106 | 107.299248848760 | -1.29924884875968 |
| 16 | 103.1 | 100.886748848760 | 2.21325115124032 |
| 17 | 102 | 100.101560726314 | 1.89843927368552 |
| 18 | 104.7 | 107.926560726314 | -3.22656072631448 |
| 19 | 86 | 83.9311844814241 | 2.06881551857592 |
| 20 | 92.1 | 93.5788726038693 | -1.47887260386929 |
| 21 | 106.9 | 107.830674522301 | -0.930674522300902 |
| 22 | 112.6 | 109.531535828507 | 3.06846417149346 |
| 23 | 101.7 | 101.408337746938 | 0.291662253061851 |
| 24 | 92 | 93.8014021142738 | -1.80140211427375 |
| 25 | 97.4 | 95.7043814973565 | 1.69561850264354 |
| 26 | 97 | 98.3299709257547 | -1.32997092575474 |
| 27 | 105.4 | 108.100347170645 | -2.70034717064514 |
| 28 | 102.7 | 101.606342191084 | 1.09365780891645 |
| 29 | 98.1 | 100.9026590482 | -2.80265904819995 |
| 30 | 104.5 | 108.646154068638 | -4.14615406863835 |
| 31 | 87.4 | 84.650777823748 | 2.74922217625205 |
| 32 | 89.9 | 94.2984659461931 | -4.39846594619314 |
| 33 | 109.8 | 108.713277823748 | 1.08672217625204 |
| 34 | 111.7 | 110.577149089077 | 1.12285091092324 |
| 35 | 98.6 | 102.53545598707 | -3.93545598706998 |
| 36 | 96.9 | 94.847015374844 | 2.05298462515603 |
| 37 | 95.1 | 96.5869847988035 | -1.48698479880352 |
| 38 | 97 | 99.2125742272018 | -2.21257422720179 |
| 39 | 112.7 | 109.227465410777 | 3.47253458922304 |
| 40 | 102.9 | 103.303995288147 | -0.403995288146497 |
| 41 | 97.4 | 102.600312145263 | -5.20031214526289 |
| 42 | 111.4 | 110.180797206578 | 1.21920279342188 |
| 43 | 87.4 | 85.6148861047566 | 1.78511389524341 |
| 44 | 96.8 | 94.9365543089554 | 1.86344569104457 |
| 45 | 114.1 | 109.351366186510 | 4.74863381348976 |
| 46 | 110.3 | 111.704267329209 | -1.40426732920859 |
| 47 | 103.9 | 104.070099125010 | -0.170099125009744 |
| 48 | 101.6 | 96.4631634923453 | 5.13683650765465 |
| 49 | 94.6 | 98.2846378958665 | -3.68463789586648 |
| 50 | 95.9 | 100.747217365142 | -4.84721736514156 |
| 51 | 104.7 | 110.436088630470 | -5.73608863047037 |
| 52 | 102.8 | 104.105093610032 | -1.30509361003197 |
| 53 | 98.1 | 103.238400508025 | -5.13840050802518 |
| 54 | 113.9 | 111.144905487587 | 2.75509451241324 |
| 55 | 80.9 | 87.1495292426964 | -6.24952924269637 |
| 56 | 95.7 | 96.7972173651416 | -1.09721736514157 |
| 57 | 113.2 | 111.212029242696 | 1.98797075730363 |
| 58 | 105.9 | 113.238910467148 | -7.33891046714835 |
| 59 | 108.8 | 105.278722344703 | 3.52127765529684 |
| 60 | 102.3 | 97.6717867120388 | 4.62821328796124 |
| 61 | 99 | 99.49326111556 | -0.493261115559886 |
| 62 | 100.7 | 102.037345564397 | -1.33734556439657 |
| 63 | 115.5 | 111.726216829725 | 3.77378317027462 |
| 64 | 100.7 | 105.232211850164 | -4.53221185016378 |
| 65 | 109.9 | 104.447023727719 | 5.45297627228142 |
| 66 | 114.6 | 112.435033686842 | 2.16496631315823 |
| 67 | 85.4 | 88.8471823397593 | -3.44718233975931 |
| 68 | 100.5 | 98.6578804213277 | 1.84211957867230 |
| 69 | 114.8 | 113.072692298883 | 1.72730770111749 |
| 70 | 116.5 | 115.018068543773 | 1.48193145622709 |
| 71 | 112.9 | 107.057880421328 | 5.8421195786723 |
| 72 | 102 | 99.5324497682249 | 2.46755023177511 |
| 73 | 106 | 101.435429151308 | 4.56457084869239 |
| 74 | 105.3 | 103.979513600144 | 1.32048639985570 |
| 75 | 118.8 | 113.668384865473 | 5.13161513452689 |
| 76 | 106.1 | 107.011369926788 | -0.911369926788338 |
| 77 | 109.3 | 106.307686783905 | 2.99231321609527 |
| 78 | 117.2 | 114.458706702151 | 2.74129329784892 |
| 79 | 92.5 | 90.789350375507 | 1.71064962449295 |
| 80 | 104.2 | 100.681553436637 | 3.51844656336298 |
| 81 | 112.5 | 115.340880252877 | -2.84088025287660 |
| 82 | 122.4 | 117.204751518205 | 5.19524848179461 |
| 83 | 113.3 | 109.163058416199 | 4.13694158380138 |
| 84 | 100 | 101.474617803973 | -1.47461780397262 |
| 85 | 110.7 | 103.377597187055 | 7.32240281294466 |
| 86 | 112.8 | 106.084691595015 | 6.7153084049848 |
| 87 | 109.8 | 115.936572819467 | -6.1365728194672 |
| 88 | 117.3 | 109.687082778590 | 7.61291722140962 |
| 89 | 109.1 | 108.983399635707 | 0.116600364293227 |
| 90 | 115.9 | 116.400874737899 | -0.500874737898805 |
| 91 | 96 | 91.9979735952005 | 4.00202640479954 |
| 92 | 99.8 | 101.564156738084 | -1.76415673808407 |
| 93 | 116.8 | 116.304988533885 | 0.495011466114762 |
| 94 | 115.7 | 118.657889676584 | -2.95788967658358 |
| 95 | 99.4 | 110.860711513262 | -11.4607115132616 |
| 96 | 94.3 | 103.090765921474 | -8.79076592147399 |
| 97 | 91 | 104.423210447626 | -13.4232104476256 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.223105237931204 | 0.446210475862408 | 0.776894762068796 |
| 18 | 0.13311395570591 | 0.26622791141182 | 0.86688604429409 |
| 19 | 0.240801131624693 | 0.481602263249386 | 0.759198868375307 |
| 20 | 0.149062227509721 | 0.298124455019443 | 0.850937772490279 |
| 21 | 0.154453197672434 | 0.308906395344869 | 0.845546802327566 |
| 22 | 0.0944037259190161 | 0.188807451838032 | 0.905596274080984 |
| 23 | 0.0642078344450043 | 0.128415668890009 | 0.935792165554996 |
| 24 | 0.0359339605552340 | 0.0718679211104679 | 0.964066039444766 |
| 25 | 0.0202194504380543 | 0.0404389008761085 | 0.979780549561946 |
| 26 | 0.0111505554688626 | 0.0223011109377251 | 0.988849444531137 |
| 27 | 0.00830157050777617 | 0.0166031410155523 | 0.991698429492224 |
| 28 | 0.00498667148896423 | 0.00997334297792846 | 0.995013328511036 |
| 29 | 0.0061768230848428 | 0.0123536461696856 | 0.993823176915157 |
| 30 | 0.00358186468775765 | 0.0071637293755153 | 0.996418135312242 |
| 31 | 0.00359143928641604 | 0.00718287857283207 | 0.996408560713584 |
| 32 | 0.00291338607523676 | 0.00582677215047352 | 0.997086613924763 |
| 33 | 0.00360106719579675 | 0.0072021343915935 | 0.996398932804203 |
| 34 | 0.0020103221341131 | 0.0040206442682262 | 0.997989677865887 |
| 35 | 0.00212876696928205 | 0.00425753393856409 | 0.997871233030718 |
| 36 | 0.00210287813096675 | 0.00420575626193351 | 0.997897121869033 |
| 37 | 0.00142450998058553 | 0.00284901996117106 | 0.998575490019414 |
| 38 | 0.00079359966790419 | 0.00158719933580838 | 0.999206400332096 |
| 39 | 0.000797486067621148 | 0.00159497213524230 | 0.999202513932379 |
| 40 | 0.000418313473088073 | 0.000836626946176146 | 0.999581686526912 |
| 41 | 0.000664628846908569 | 0.00132925769381714 | 0.999335371153091 |
| 42 | 0.000717033306184243 | 0.00143406661236849 | 0.999282966693816 |
| 43 | 0.000422794851364416 | 0.000845589702728831 | 0.999577205148636 |
| 44 | 0.000347623777441791 | 0.000695247554883583 | 0.999652376222558 |
| 45 | 0.000731676901023386 | 0.00146335380204677 | 0.999268323098977 |
| 46 | 0.000462091014492731 | 0.000924182028985461 | 0.999537908985507 |
| 47 | 0.000252305323157075 | 0.00050461064631415 | 0.999747694676843 |
| 48 | 0.000358996046849122 | 0.000717992093698245 | 0.999641003953151 |
| 49 | 0.000400137209974444 | 0.000800274419948889 | 0.999599862790026 |
| 50 | 0.000467204067856567 | 0.000934408135713134 | 0.999532795932143 |
| 51 | 0.00078294570679655 | 0.0015658914135931 | 0.999217054293204 |
| 52 | 0.000483431941026912 | 0.000966863882053825 | 0.999516568058973 |
| 53 | 0.000754160958005082 | 0.00150832191601016 | 0.999245839041995 |
| 54 | 0.000811656364315824 | 0.00162331272863165 | 0.999188343635684 |
| 55 | 0.00210200050089299 | 0.00420400100178599 | 0.997897999499107 |
| 56 | 0.00163273286029716 | 0.00326546572059432 | 0.998367267139703 |
| 57 | 0.00116440592690678 | 0.00232881185381357 | 0.998835594073093 |
| 58 | 0.00484054835322773 | 0.00968109670645546 | 0.995159451646772 |
| 59 | 0.00457895594372798 | 0.00915791188745596 | 0.995421044056272 |
| 60 | 0.00430291946687428 | 0.00860583893374856 | 0.995697080533126 |
| 61 | 0.00300308086143475 | 0.0060061617228695 | 0.996996919138565 |
| 62 | 0.00300035669764804 | 0.00600071339529607 | 0.996999643302352 |
| 63 | 0.00260560780577954 | 0.00521121561155909 | 0.99739439219422 |
| 64 | 0.00488445790205607 | 0.00976891580411215 | 0.995115542097944 |
| 65 | 0.00596535846027948 | 0.0119307169205590 | 0.99403464153972 |
| 66 | 0.00412544007389114 | 0.00825088014778227 | 0.99587455992611 |
| 67 | 0.0116386887059827 | 0.0232773774119653 | 0.988361311294017 |
| 68 | 0.0108488757209146 | 0.0216977514418293 | 0.989151124279085 |
| 69 | 0.00728890441581026 | 0.0145778088316205 | 0.99271109558419 |
| 70 | 0.00636439535978418 | 0.0127287907195684 | 0.993635604640216 |
| 71 | 0.00516724199270997 | 0.0103344839854199 | 0.99483275800729 |
| 72 | 0.00283375703817047 | 0.00566751407634095 | 0.99716624296183 |
| 73 | 0.00158667438271847 | 0.00317334876543694 | 0.998413325617282 |
| 74 | 0.00196005991343260 | 0.00392011982686521 | 0.998039940086567 |
| 75 | 0.00256697018317846 | 0.00513394036635693 | 0.997433029816821 |
| 76 | 0.00607174664230603 | 0.0121434932846121 | 0.993928253357694 |
| 77 | 0.00398111839975299 | 0.00796223679950598 | 0.996018881600247 |
| 78 | 0.00383489627703424 | 0.00766979255406848 | 0.996165103722966 |
| 79 | 0.008090213912916 | 0.016180427825832 | 0.991909786087084 |
| 80 | 0.00315763761347364 | 0.00631527522694729 | 0.996842362386526 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 44 | 0.6875 | NOK |
| 5% type I error level | 56 | 0.875 | NOK |
| 10% type I error level | 57 | 0.890625 | NOK |
