| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = + 25.8050372634699 + 0.428060309492314X_1t[t] -0.450777521641689X_2t[t] -0.0776137468286691X_3t[t] -0.816444705642473X_4t[t] + 0.00518584246664621X_5t[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) | 25.8050372634699 | 4.064581 | 6.3488 | 0 | 0 |
| X_1t | 0.428060309492314 | 0.059689 | 7.1715 | 0 | 0 |
| X_2t | -0.450777521641689 | 0.064245 | -7.0166 | 0 | 0 |
| X_3t | -0.0776137468286691 | 0.062086 | -1.2501 | 0.2151 | 0.10755 |
| X_4t | -0.816444705642473 | 0.204637 | -3.9897 | 0.000151 | 7.6e-05 |
| X_5t | 0.00518584246664621 | 0.080931 | 0.0641 | 0.949077 | 0.474539 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.913826048354758 |
| R-squared | 0.835078046651673 |
| Adjusted R-squared | 0.824227918141914 |
| F-TEST (value) | 76.9648069975043 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 76 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.06840558070266 |
| Sum Squared Residuals | 1257.94622165103 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | -3 | -6.59954720802944 | 3.59954720802944 |
| 2 | -4 | -4.04238554131172 | 0.042385541311725 |
| 3 | -7 | -4.18692568802895 | -2.81307431197105 |
| 4 | -7 | -5.77560591157472 | -1.22439408842528 |
| 5 | -7 | -4.3950629527413 | -2.6049370472587 |
| 6 | -3 | -1.87936678170078 | -1.12063321829922 |
| 7 | 0 | -0.784574834408368 | 0.784574834408368 |
| 8 | -5 | -2.36867028107771 | -2.63132971892229 |
| 9 | -3 | -1.992704158679 | -1.007295841321 |
| 10 | 3 | 1.08339958747001 | 1.91660041252999 |
| 11 | 2 | -2.01771087511798 | 4.01771087511798 |
| 12 | -7 | -6.91676631850706 | -0.0832336814929382 |
| 13 | -1 | -0.63648578144448 | -0.36351421855552 |
| 14 | 0 | -1.37332165391951 | 1.37332165391951 |
| 15 | -3 | 0.431395802096771 | -3.43139580209677 |
| 16 | 4 | 3.21475186784712 | 0.785248132152878 |
| 17 | 2 | 1.21173474469973 | 0.788265255300269 |
| 18 | 3 | 1.66769810880807 | 1.33230189119193 |
| 19 | 0 | -2.0672476771596 | 2.0672476771596 |
| 20 | -10 | -3.08155910621677 | -6.91844089378323 |
| 21 | -10 | -6.0593856352502 | -3.9406143647498 |
| 22 | -9 | -4.53232868741676 | -4.46767131258324 |
| 23 | -22 | -13.3483955350016 | -8.65160446499836 |
| 24 | -16 | -14.4227893412048 | -1.57721065879525 |
| 25 | -18 | -16.8742196881066 | -1.1257803118934 |
| 26 | -14 | -15.5241766274711 | 1.52417662747114 |
| 27 | -12 | -17.2603815582053 | 5.26038155820532 |
| 28 | -17 | -22.160493453965 | 5.16049345396497 |
| 29 | -23 | -20.8787992110669 | -2.1212007889331 |
| 30 | -28 | -22.3383570905218 | -5.66164290947817 |
| 31 | -31 | -26.4443318401902 | -4.55566815980979 |
| 32 | -21 | -25.4809775839612 | 4.48097758396124 |
| 33 | -19 | -23.0145540554349 | 4.01455405543492 |
| 34 | -22 | -25.187920009853 | 3.18792000985297 |
| 35 | -22 | -23.7029302856021 | 1.70293028560211 |
| 36 | -25 | -25.2644985483671 | 0.264498548367052 |
| 37 | -16 | -19.456639647296 | 3.456639647296 |
| 38 | -22 | -19.7121897772169 | -2.2878102227831 |
| 39 | -21 | -14.7568573620567 | -6.24314263794334 |
| 40 | -10 | -14.7275531336478 | 4.7275531336478 |
| 41 | -7 | -10.8053847914406 | 3.80538479144063 |
| 42 | -5 | -10.349627622989 | 5.34962762298898 |
| 43 | -4 | -3.59062077548652 | -0.409379224513484 |
| 44 | 7 | -1.23589768771843 | 8.23589768771843 |
| 45 | 6 | 2.82250118084961 | 3.17749881915039 |
| 46 | 3 | 5.31669705358583 | -2.31669705358583 |
| 47 | 10 | 5.37011134522243 | 4.62988865477757 |
| 48 | 0 | 6.93873033374168 | -6.93873033374168 |
| 49 | -2 | 2.23410743481298 | -4.23410743481298 |
| 50 | -1 | 2.95416054332851 | -3.95416054332851 |
| 51 | 2 | -1.15483734794894 | 3.15483734794894 |
| 52 | 8 | 3.51516867667222 | 4.48483132332778 |
| 53 | -6 | -2.06519411818378 | -3.93480588181622 |
| 54 | -4 | -0.171539167740823 | -3.82846083225918 |
| 55 | 4 | 2.62127900839007 | 1.37872099160993 |
| 56 | 7 | 6.24641507957019 | 0.753584920429807 |
| 57 | 3 | 2.26187485592748 | 0.738125144072518 |
| 58 | 3 | -2.32867038301426 | 5.32867038301426 |
| 59 | 8 | 0.131211356079738 | 7.86878864392026 |
| 60 | 3 | -0.568772194694807 | 3.56877219469481 |
| 61 | -3 | -1.11158397629969 | -1.88841602370031 |
| 62 | 4 | 1.16552536463973 | 2.83447463536027 |
| 63 | -5 | -6.32609905129461 | 1.3260990512946 |
| 64 | -1 | -2.52466813186927 | 1.52466813186927 |
| 65 | 5 | -0.684765548795895 | 5.6847655487959 |
| 66 | 0 | -1.52821665584315 | 1.52821665584315 |
| 67 | -6 | -3.32611965588727 | -2.67388034411273 |
| 68 | -13 | -10.4591317048472 | -2.54086829515285 |
| 69 | -15 | -5.17945787658978 | -9.82054212341022 |
| 70 | -8 | -9.56062769291811 | 1.56062769291811 |
| 71 | -20 | -16.1456716845769 | -3.85432831542307 |
| 72 | -10 | -15.1042192353235 | 5.10421923532349 |
| 73 | -22 | -17.0947361380775 | -4.9052638619225 |
| 74 | -25 | -19.6750396379465 | -5.32496036205349 |
| 75 | -10 | -14.9320542845294 | 4.93205428452936 |
| 76 | -8 | -14.0236480654591 | 6.02364806545906 |
| 77 | -9 | -8.58907072826565 | -0.410929271734354 |
| 78 | -5 | -6.60134902005303 | 1.60134902005303 |
| 79 | -7 | -3.14841206506453 | -3.85158793493547 |
| 80 | -11 | -6.63865552952591 | -4.36134447047409 |
| 81 | -11 | -6.99403092817307 | -4.00596907182693 |
| 82 | -16 | -13.0029468014317 | -2.99705319856833 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.202875461266384 | 0.405750922532769 | 0.797124538733616 |
| 10 | 0.0971702778136047 | 0.194340555627209 | 0.902829722186395 |
| 11 | 0.0460849200280974 | 0.0921698400561947 | 0.953915079971903 |
| 12 | 0.0181930656362408 | 0.0363861312724817 | 0.981806934363759 |
| 13 | 0.0177471682418844 | 0.0354943364837687 | 0.982252831758116 |
| 14 | 0.00890819900147295 | 0.0178163980029459 | 0.991091800998527 |
| 15 | 0.0201177750938574 | 0.0402355501877148 | 0.979882224906143 |
| 16 | 0.00947835452836863 | 0.0189567090567373 | 0.990521645471631 |
| 17 | 0.00437018201554107 | 0.00874036403108213 | 0.995629817984459 |
| 18 | 0.00211763275382705 | 0.00423526550765409 | 0.997882367246173 |
| 19 | 0.000906193904011683 | 0.00181238780802337 | 0.999093806095988 |
| 20 | 0.017995412211996 | 0.0359908244239921 | 0.982004587788004 |
| 21 | 0.0123156301932144 | 0.0246312603864287 | 0.987684369806786 |
| 22 | 0.00893455716296862 | 0.0178691143259372 | 0.991065442837031 |
| 23 | 0.00889160226192911 | 0.0177832045238582 | 0.991108397738071 |
| 24 | 0.025040499477024 | 0.050080998954048 | 0.974959500522976 |
| 25 | 0.0310438939961506 | 0.0620877879923011 | 0.968956106003849 |
| 26 | 0.0431938051237705 | 0.0863876102475409 | 0.95680619487623 |
| 27 | 0.0899097418417071 | 0.179819483683414 | 0.910090258158293 |
| 28 | 0.112654217073144 | 0.225308434146289 | 0.887345782926856 |
| 29 | 0.0808856432918578 | 0.161771286583716 | 0.919114356708142 |
| 30 | 0.075252349002586 | 0.150504698005172 | 0.924747650997414 |
| 31 | 0.0738125471113036 | 0.147625094222607 | 0.926187452888696 |
| 32 | 0.17142643412423 | 0.34285286824846 | 0.82857356587577 |
| 33 | 0.190238633003991 | 0.380477266007981 | 0.809761366996009 |
| 34 | 0.175402209994659 | 0.350804419989318 | 0.824597790005341 |
| 35 | 0.134521926633726 | 0.269043853267452 | 0.865478073366274 |
| 36 | 0.101580988188662 | 0.203161976377323 | 0.898419011811338 |
| 37 | 0.0910175065313968 | 0.182035013062794 | 0.908982493468603 |
| 38 | 0.0781610628217295 | 0.156322125643459 | 0.92183893717827 |
| 39 | 0.0854754050092668 | 0.170950810018534 | 0.914524594990733 |
| 40 | 0.124600827458463 | 0.249201654916926 | 0.875399172541537 |
| 41 | 0.156745070845734 | 0.313490141691467 | 0.843254929154266 |
| 42 | 0.183784987429925 | 0.367569974859849 | 0.816215012570075 |
| 43 | 0.146480098960381 | 0.292960197920761 | 0.853519901039619 |
| 44 | 0.33292436599509 | 0.665848731990179 | 0.66707563400491 |
| 45 | 0.336393610979271 | 0.672787221958543 | 0.663606389020729 |
| 46 | 0.312562609111112 | 0.625125218222224 | 0.687437390888888 |
| 47 | 0.416160773170425 | 0.83232154634085 | 0.583839226829575 |
| 48 | 0.484476571037421 | 0.968953142074841 | 0.515523428962579 |
| 49 | 0.466687907184494 | 0.933375814368988 | 0.533312092815506 |
| 50 | 0.424739515112936 | 0.849479030225872 | 0.575260484887064 |
| 51 | 0.42408581071147 | 0.848171621422939 | 0.57591418928853 |
| 52 | 0.476280589781819 | 0.952561179563638 | 0.523719410218181 |
| 53 | 0.428178505568047 | 0.856357011136093 | 0.571821494431953 |
| 54 | 0.373308203238638 | 0.746616406477276 | 0.626691796761362 |
| 55 | 0.343423623445546 | 0.686847246891092 | 0.656576376554454 |
| 56 | 0.335440141861722 | 0.670880283723444 | 0.664559858138278 |
| 57 | 0.293019048420869 | 0.586038096841739 | 0.706980951579131 |
| 58 | 0.31354088575599 | 0.62708177151198 | 0.68645911424401 |
| 59 | 0.455771970019767 | 0.911543940039533 | 0.544228029980233 |
| 60 | 0.50340743330105 | 0.993185133397899 | 0.49659256669895 |
| 61 | 0.429228489545152 | 0.858456979090304 | 0.570771510454848 |
| 62 | 0.438649811649092 | 0.877299623298184 | 0.561350188350908 |
| 63 | 0.417841934359165 | 0.835683868718331 | 0.582158065640835 |
| 64 | 0.344829658459965 | 0.68965931691993 | 0.655170341540035 |
| 65 | 0.358307101609135 | 0.71661420321827 | 0.641692898390865 |
| 66 | 0.340708714264841 | 0.681417428529682 | 0.659291285735159 |
| 67 | 0.265855943648465 | 0.531711887296929 | 0.734144056351535 |
| 68 | 0.344745344739116 | 0.689490689478232 | 0.655254655260884 |
| 69 | 0.657631507773855 | 0.684736984452289 | 0.342368492226145 |
| 70 | 0.575562089368095 | 0.848875821263809 | 0.424437910631904 |
| 71 | 0.475225632338187 | 0.950451264676374 | 0.524774367661813 |
| 72 | 0.558985870248048 | 0.882028259503904 | 0.441014129751952 |
| 73 | 0.853444425915225 | 0.29311114816955 | 0.146555574084775 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 3 | 0.0461538461538462 | NOK |
| 5% type I error level | 12 | 0.184615384615385 | NOK |
| 10% type I error level | 16 | 0.246153846153846 | NOK |
