| Multiple Linear Regression - Estimated Regression Equation |
| Y_1[t] = + 0.0224726367150805 + 0.245211414734055X_1[t] -0.245905863560043X_2[t] + 0.297769252859355X_3[t] + 0.234501188857809X_4[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) | 0.0224726367150805 | 0.14422 | 0.1558 | 0.876576 | 0.438288 |
| X_1 | 0.245211414734055 | 0.004431 | 55.341 | 0 | 0 |
| X_2 | -0.245905863560043 | 0.001714 | -143.4527 | 0 | 0 |
| X_3 | 0.297769252859355 | 0.026167 | 11.3796 | 0 | 0 |
| X_4 | 0.234501188857809 | 0.010393 | 22.5637 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.999209685999466 |
| R-squared | 0.998419996595152 |
| Adjusted R-squared | 0.998338970779519 |
| F-TEST (value) | 12322.2455558451 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 78 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.331699067978937 |
| Sum Squared Residuals | 8.58189319245143 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3 | 3.15923491782965 | -0.159234917829649 |
| 2 | 1 | 1.29085899510953 | -0.290858995109532 |
| 3 | 0 | -0.183187288598768 | 0.183187288598768 |
| 4 | 1 | 1.24801809160454 | -0.248018091604543 |
| 5 | 1 | 1.01589909165464 | -0.0158990916546393 |
| 6 | 3 | 3.25602255711191 | -0.25602255711191 |
| 7 | 5 | 4.98460158377852 | 0.0153984162214795 |
| 8 | 5 | 4.75357263905065 | 0.246427360949349 |
| 9 | 4 | 4.12382010922524 | -0.123820109225237 |
| 10 | 11 | 11.1280814798237 | -0.128081479823679 |
| 11 | 8 | 7.66051204304416 | 0.339487956955844 |
| 12 | -1 | -0.500689253128688 | -0.499310746871312 |
| 13 | 4 | 3.80485765774317 | 0.195142342256832 |
| 14 | 4 | 3.43311011500602 | 0.56688988499398 |
| 15 | 4 | 4.49765099844035 | -0.497650998440349 |
| 16 | 6 | 6.04944665858631 | -0.0494466585863094 |
| 17 | 6 | 5.43873239160548 | 0.561267608394519 |
| 18 | 6 | 5.70536425809203 | 0.29463574190797 |
| 19 | 6 | 5.66421109466896 | 0.335788905331036 |
| 20 | 4 | 3.39681809336487 | 0.60318190663513 |
| 21 | 1 | 0.955713014330505 | 0.0442869856694954 |
| 22 | 6 | 6.16435620770091 | -0.164356207700905 |
| 23 | 0 | 0.4047999161648 | -0.4047999161648 |
| 24 | 2 | 1.94280871270062 | 0.0571912872993809 |
| 25 | -2 | -2.1344816998038 | 0.134481699803803 |
| 26 | 0 | 0.0104702771529614 | -0.0104702771529614 |
| 27 | 1 | 1.1334950210506 | -0.133495021050604 |
| 28 | -3 | -2.58136917694094 | -0.418630823059058 |
| 29 | -3 | -3.29865960712451 | 0.298659607124511 |
| 30 | -5 | -5.63041072765218 | 0.630410727652183 |
| 31 | -7 | -7.07540297146563 | 0.0754029714656254 |
| 32 | -7 | -7.2514972381038 | 0.251497238103803 |
| 33 | -5 | -5.48414723692203 | 0.484147236922034 |
| 34 | -13 | -12.8574751189198 | -0.142524881080227 |
| 35 | -16 | -15.7063064431236 | -0.29369355687641 |
| 36 | -20 | -19.9313261822538 | -0.0686738177461811 |
| 37 | -18 | -17.401371243453 | -0.598628756546997 |
| 38 | -21 | -21.052272928617 | 0.0522729286170146 |
| 39 | -20 | -19.9513630852979 | -0.0486369147021487 |
| 40 | -16 | -16.1034192263829 | 0.103419226382897 |
| 41 | -14 | -13.2753908433493 | -0.724609156650734 |
| 42 | -12 | -12.3515685579242 | 0.351568557924213 |
| 43 | -10 | -10.2214165615559 | 0.221416561555944 |
| 44 | -3 | -3.49103038813387 | 0.491030388133873 |
| 45 | -4 | -3.97074299172574 | -0.0292570082742642 |
| 46 | -4 | -4.38718753131605 | 0.387187531316054 |
| 47 | -1 | -1.43285027340911 | 0.43285027340911 |
| 48 | -8 | -8.13557130458831 | 0.135571304588314 |
| 49 | -10 | -10.151209358238 | 0.151209358238035 |
| 50 | -11 | -10.7055947005337 | -0.294405299466322 |
| 51 | -7 | -6.44844428377471 | -0.551555716225288 |
| 52 | -2 | -1.99000806206519 | -0.00999193793480924 |
| 53 | -6 | -6.2578687047004 | 0.257868704700403 |
| 54 | -4 | -4.43210643235549 | 0.432106432355488 |
| 55 | 0 | 0.278779185834395 | -0.278779185834395 |
| 56 | 2 | 2.01638069829533 | -0.016380698295333 |
| 57 | 2 | 1.6916407520191 | 0.308359247980901 |
| 58 | 5 | 5.24290541329673 | -0.242905413296729 |
| 59 | 8 | 8.36223110556956 | -0.362231105569562 |
| 60 | 8 | 8.28964171334375 | -0.289641713343746 |
| 61 | 5 | 5.26271506321098 | -0.262715063210985 |
| 62 | 10 | 10.5646736517337 | -0.564673651733708 |
| 63 | 6 | 6.05884492505426 | -0.0588449250542619 |
| 64 | 6 | 5.76732036268528 | 0.232679637314718 |
| 65 | 9 | 9.35240344167357 | -0.352403441673572 |
| 66 | 5 | 5.0610390008079 | -0.0610390008079019 |
| 67 | 5 | 4.61831821662669 | 0.381681783373308 |
| 68 | -4 | -3.62456654686646 | -0.37543345313354 |
| 69 | -5 | -4.76546790908649 | -0.234532090913511 |
| 70 | -1 | -1.19694948901229 | 0.196949489012293 |
| 71 | -8 | -7.50117418822373 | -0.49882581177627 |
| 72 | -8 | -8.12685678905932 | 0.126856789059317 |
| 73 | -13 | -13.1103917110963 | 0.110391711096345 |
| 74 | -18 | -17.9640792737735 | -0.0359207262265295 |
| 75 | -8 | -7.98406019351559 | -0.0159398064844093 |
| 76 | -8 | -8.2185613823734 | 0.2185613823734 |
| 77 | -6 | -5.50735219272255 | -0.492647807277453 |
| 78 | -5 | -5.43060145648432 | 0.430601456484319 |
| 79 | -11 | -10.8046233416731 | -0.195376658326863 |
| 80 | -14 | -13.5928874589357 | -0.407112541064322 |
| 81 | -12 | -11.8189885758901 | -0.181011424109926 |
| 82 | -13 | -13.2185893740244 | 0.218589374024356 |
| 83 | -19 | -19.5298301507958 | 0.529830150795839 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.364479694449221 | 0.728959388898442 | 0.635520305550779 |
| 9 | 0.212440511089893 | 0.424881022179786 | 0.787559488910107 |
| 10 | 0.122466830739669 | 0.244933661479338 | 0.877533169260331 |
| 11 | 0.0922347236618886 | 0.184469447323777 | 0.907765276338111 |
| 12 | 0.169871748454013 | 0.339743496908026 | 0.830128251545987 |
| 13 | 0.105629070917073 | 0.211258141834145 | 0.894370929082927 |
| 14 | 0.157442693692984 | 0.314885387385967 | 0.842557306307016 |
| 15 | 0.417777841808863 | 0.835555683617726 | 0.582222158191137 |
| 16 | 0.393978437895667 | 0.787956875791333 | 0.606021562104333 |
| 17 | 0.474811255719061 | 0.949622511438121 | 0.525188744280939 |
| 18 | 0.416319554410667 | 0.832639108821334 | 0.583680445589333 |
| 19 | 0.351171124264022 | 0.702342248528044 | 0.648828875735978 |
| 20 | 0.322791590522698 | 0.645583181045395 | 0.677208409477302 |
| 21 | 0.42531306819099 | 0.850626136381981 | 0.57468693180901 |
| 22 | 0.466660095973394 | 0.933320191946788 | 0.533339904026606 |
| 23 | 0.555899501265811 | 0.888200997468377 | 0.444100498734189 |
| 24 | 0.481690207908274 | 0.963380415816548 | 0.518309792091726 |
| 25 | 0.411250831806577 | 0.822501663613153 | 0.588749168193423 |
| 26 | 0.339961442257649 | 0.679922884515298 | 0.660038557742351 |
| 27 | 0.310949056975964 | 0.621898113951928 | 0.689050943024036 |
| 28 | 0.34160098655035 | 0.6832019731007 | 0.65839901344965 |
| 29 | 0.367784010117059 | 0.735568020234119 | 0.63221598988294 |
| 30 | 0.535432400446829 | 0.929135199106341 | 0.464567599553171 |
| 31 | 0.473041867800471 | 0.946083735600941 | 0.526958132199529 |
| 32 | 0.438610156316206 | 0.877220312632412 | 0.561389843683794 |
| 33 | 0.548100367351986 | 0.903799265296028 | 0.451899632648014 |
| 34 | 0.541530470141385 | 0.916939059717229 | 0.458469529858615 |
| 35 | 0.497208234006977 | 0.994416468013954 | 0.502791765993023 |
| 36 | 0.431888050970303 | 0.863776101940606 | 0.568111949029697 |
| 37 | 0.504111265949592 | 0.991777468100815 | 0.495888734050408 |
| 38 | 0.478686684232099 | 0.957373368464198 | 0.521313315767901 |
| 39 | 0.429543512895028 | 0.859087025790055 | 0.570456487104972 |
| 40 | 0.378646023056308 | 0.757292046112616 | 0.621353976943692 |
| 41 | 0.619940239795642 | 0.760119520408716 | 0.380059760204358 |
| 42 | 0.645081309779647 | 0.709837380440707 | 0.354918690220353 |
| 43 | 0.591115799038807 | 0.817768401922386 | 0.408884200961193 |
| 44 | 0.61209576864085 | 0.7758084627183 | 0.38790423135915 |
| 45 | 0.559312887539712 | 0.881374224920576 | 0.440687112460288 |
| 46 | 0.556648527099736 | 0.886702945800527 | 0.443351472900264 |
| 47 | 0.594086471836637 | 0.811827056326725 | 0.405913528163363 |
| 48 | 0.537877922084744 | 0.924244155830512 | 0.462122077915256 |
| 49 | 0.48536496110864 | 0.970729922217279 | 0.51463503889136 |
| 50 | 0.488208528671485 | 0.976417057342971 | 0.511791471328515 |
| 51 | 0.675297413145536 | 0.649405173708928 | 0.324702586854464 |
| 52 | 0.6192998962727 | 0.7614002074546 | 0.3807001037273 |
| 53 | 0.560406425146929 | 0.879187149706142 | 0.439593574853071 |
| 54 | 0.610013510299441 | 0.779972979401118 | 0.389986489700559 |
| 55 | 0.613753405836634 | 0.772493188326733 | 0.386246594163366 |
| 56 | 0.552732196879264 | 0.894535606241473 | 0.447267803120736 |
| 57 | 0.564593710315768 | 0.870812579368463 | 0.435406289684232 |
| 58 | 0.51904929647235 | 0.961901407055299 | 0.48095070352765 |
| 59 | 0.511808977705068 | 0.976382044589864 | 0.488191022294932 |
| 60 | 0.476182590048426 | 0.952365180096852 | 0.523817409951574 |
| 61 | 0.438385467924141 | 0.876770935848282 | 0.561614532075859 |
| 62 | 0.559550135396795 | 0.88089972920641 | 0.440449864603205 |
| 63 | 0.478014809970571 | 0.956029619941142 | 0.521985190029429 |
| 64 | 0.4317011391143 | 0.8634022782286 | 0.5682988608857 |
| 65 | 0.421944519596106 | 0.843889039192213 | 0.578055480403894 |
| 66 | 0.35755265488225 | 0.7151053097645 | 0.64244734511775 |
| 67 | 0.448188280247692 | 0.896376560495383 | 0.551811719752308 |
| 68 | 0.387224196153286 | 0.774448392306572 | 0.612775803846714 |
| 69 | 0.305478052237206 | 0.610956104474413 | 0.694521947762794 |
| 70 | 0.292288502910513 | 0.584577005821026 | 0.707711497089487 |
| 71 | 0.41523338680673 | 0.83046677361346 | 0.58476661319327 |
| 72 | 0.417852377705332 | 0.835704755410663 | 0.582147622294668 |
| 73 | 0.408021700041143 | 0.816043400082286 | 0.591978299958857 |
| 74 | 0.284637496523726 | 0.569274993047453 | 0.715362503476274 |
| 75 | 0.18149771538363 | 0.36299543076726 | 0.81850228461637 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
