| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.54167091765125 + 0.98059228033681X[t] + 0.387904499998967M1[t] -0.390548095699390M2[t] -0.792460059946535M3[t] -1.03691565041127M4[t] + 0.366721482980735M5[t] -1.14491108900953M6[t] -0.737442655419468M7[t] -0.821530714152305M8[t] -0.660810912706852M9[t] -0.358194409032587M10[t] -0.471564152213164M11[t] -0.0264160821289604t + 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) | 1.54167091765125 | 1.233414 | 1.2499 | 0.216348 | 0.108174 |
| X | 0.98059228033681 | 0.057471 | 17.0624 | 0 | 0 |
| M1 | 0.387904499998967 | 0.276379 | 1.4035 | 0.165792 | 0.082896 |
| M2 | -0.390548095699390 | 0.266241 | -1.4669 | 0.147806 | 0.073903 |
| M3 | -0.792460059946535 | 0.278754 | -2.8429 | 0.006163 | 0.003082 |
| M4 | -1.03691565041127 | 0.276503 | -3.7501 | 0.00041 | 0.000205 |
| M5 | 0.366721482980735 | 0.296309 | 1.2376 | 0.22084 | 0.11042 |
| M6 | -1.14491108900953 | 0.265079 | -4.3191 | 6.2e-05 | 3.1e-05 |
| M7 | -0.737442655419468 | 0.284798 | -2.5893 | 0.012137 | 0.006069 |
| M8 | -0.821530714152305 | 0.266386 | -3.084 | 0.003126 | 0.001563 |
| M9 | -0.660810912706852 | 0.267358 | -2.4716 | 0.016407 | 0.008203 |
| M10 | -0.358194409032587 | 0.291004 | -1.2309 | 0.223332 | 0.111666 |
| M11 | -0.471564152213164 | 0.264668 | -1.7817 | 0.080031 | 0.040015 |
| t | -0.0264160821289604 | 0.006086 | -4.3406 | 5.8e-05 | 2.9e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.98920334433598 |
| R-squared | 0.978523256445487 |
| Adjusted R-squared | 0.97370950357982 |
| F-TEST (value) | 203.276587675413 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 58 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.458137829416737 |
| Sum Squared Residuals | 12.1736357030754 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 18 | 17.984872733045 | 0.0151272669550136 |
| 2 | 19.6 | 18.5528332476892 | 1.04716675231082 |
| 3 | 23.3 | 22.5371704628287 | 0.762829537171278 |
| 4 | 23.7 | 22.7565949304034 | 0.943405069596563 |
| 5 | 20.3 | 19.7211507201508 | 0.578849279849173 |
| 6 | 22.8 | 22.2035304154125 | 0.596469584587477 |
| 7 | 24.3 | 24.0554711873788 | 0.244528812621157 |
| 8 | 21.5 | 21.3954271176413 | 0.104572882358660 |
| 9 | 23.5 | 23.1967377135304 | 0.303262286469589 |
| 10 | 22.2 | 21.9039904865368 | 0.296009513463182 |
| 11 | 20.9 | 21.5680862051599 | -0.668086205159919 |
| 12 | 22.2 | 21.7190565911431 | 0.480943408856922 |
| 13 | 19.5 | 19.1387681680027 | 0.361231831997348 |
| 14 | 21.1 | 21.0795578751184 | 0.0204421248815975 |
| 15 | 22 | 22.1221182492475 | -0.122118249247516 |
| 16 | 19.2 | 19.4978251038455 | -0.297825103845481 |
| 17 | 17.8 | 18.8158023664012 | -1.01580236640122 |
| 18 | 19.2 | 19.1408790449219 | 0.0591209550780661 |
| 19 | 19.9 | 20.6986421327872 | -0.79864213278721 |
| 20 | 19.6 | 19.6075457115886 | -0.0075457115885984 |
| 21 | 18.1 | 18.5651386945009 | -0.465138694500919 |
| 22 | 20.4 | 21.1947605888546 | -0.794760588854571 |
| 23 | 18.1 | 18.7015532907367 | -0.601553290736686 |
| 24 | 18.6 | 19.4408790449219 | -0.84087904492193 |
| 25 | 17.6 | 18.2334198142530 | -0.633419814253042 |
| 26 | 19.4 | 20.0761502933351 | -0.676150293335115 |
| 27 | 19.3 | 19.5497630189253 | -0.249763018925326 |
| 28 | 18.6 | 18.8866544341969 | -0.286654434196911 |
| 29 | 16.9 | 17.0279209603485 | -0.127920960348478 |
| 30 | 16.4 | 16.8627014987008 | -0.462701498700789 |
| 31 | 19 | 19.4010568669029 | -0.401056866902873 |
| 32 | 18.7 | 18.8983158139064 | -0.19831581390635 |
| 33 | 17.1 | 16.8753165164819 | 0.224683483518142 |
| 34 | 21.5 | 20.9758268313407 | 0.524173168659272 |
| 35 | 17.8 | 17.6000864809197 | 0.199913519080287 |
| 36 | 18.1 | 17.7510568669029 | 0.348943133097128 |
| 37 | 19 | 18.6028414249413 | 0.397158575058714 |
| 38 | 18.9 | 18.8766242554845 | 0.0233757445155378 |
| 39 | 16.8 | 17.0754670166368 | -0.275467016636818 |
| 40 | 18.1 | 18.2754837645483 | -0.175483764548342 |
| 41 | 15.7 | 15.6322764664305 | 0.0677235335695386 |
| 42 | 15.1 | 15.2709385487154 | -0.170938548715409 |
| 43 | 18.3 | 17.9073531449512 | 0.392646855048824 |
| 44 | 16.5 | 16.4240198116178 | 0.075980188382158 |
| 45 | 16.9 | 17.1466788991364 | -0.246678899136424 |
| 46 | 18.4 | 18.6976492851196 | -0.297649285119583 |
| 47 | 16.4 | 16.1063827589680 | 0.293617241031981 |
| 48 | 15.7 | 15.9631754608501 | -0.263175460850134 |
| 49 | 16.9 | 17.0110784749559 | -0.111078474955908 |
| 50 | 16.6 | 16.8926243933644 | -0.292624393364354 |
| 51 | 16.7 | 16.9545924871567 | -0.254592487156657 |
| 52 | 16.6 | 16.5856615865293 | 0.0143384134707157 |
| 53 | 14.4 | 14.1385727444788 | 0.261427255521237 |
| 54 | 14.5 | 14.5617086510332 | -0.0617086510331594 |
| 55 | 17.5 | 16.9039455631679 | 0.596054436832118 |
| 56 | 14.3 | 14.3419607214641 | -0.0419607214640582 |
| 57 | 15.4 | 15.4568567211174 | -0.0568567211173608 |
| 58 | 17.2 | 17.2039455631679 | -0.00394556316788222 |
| 59 | 14.6 | 14.5146198089826 | 0.0853801910173616 |
| 60 | 14.2 | 14.2733532828311 | -0.0733532828310736 |
| 61 | 14.9 | 14.9290193848021 | -0.0290193848021241 |
| 62 | 14.1 | 14.2222099350085 | -0.122209935008487 |
| 63 | 15.6 | 15.4608887652050 | 0.13911123479504 |
| 64 | 14.6 | 14.7977801804765 | -0.197780180476546 |
| 65 | 11.9 | 11.6642767421903 | 0.235723257809746 |
| 66 | 13.5 | 13.4602418412162 | 0.0397581587838143 |
| 67 | 14.2 | 14.233531104812 | -0.033531104812014 |
| 68 | 13.7 | 13.6327308237818 | 0.0672691762181886 |
| 69 | 14.4 | 14.1592714552330 | 0.240728544766973 |
| 70 | 15.3 | 15.0238272449804 | 0.276172755019582 |
| 71 | 14.3 | 13.6092714552330 | 0.690728544766975 |
| 72 | 14.5 | 14.1524787533509 | 0.347521246649088 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.969419796284642 | 0.061160407430716 | 0.030580203715358 |
| 18 | 0.973064147663213 | 0.0538717046735742 | 0.0269358523367871 |
| 19 | 0.959679575717558 | 0.0806408485648837 | 0.0403204242824419 |
| 20 | 0.974141172351366 | 0.0517176552972673 | 0.0258588276486336 |
| 21 | 0.95401102196195 | 0.0919779560760979 | 0.0459889780380489 |
| 22 | 0.950672927941168 | 0.0986541441176636 | 0.0493270720588318 |
| 23 | 0.981731697190842 | 0.0365366056183158 | 0.0182683028091579 |
| 24 | 0.992183450950955 | 0.0156330980980893 | 0.00781654904904467 |
| 25 | 0.990059551496419 | 0.0198808970071630 | 0.00994044850358148 |
| 26 | 0.989221567956466 | 0.021556864087067 | 0.0107784320435335 |
| 27 | 0.988251896256424 | 0.0234962074871514 | 0.0117481037435757 |
| 28 | 0.98418897485796 | 0.0316220502840807 | 0.0158110251420403 |
| 29 | 0.994950907063593 | 0.0100981858728132 | 0.00504909293640658 |
| 30 | 0.991882273241995 | 0.0162354535160091 | 0.00811772675800454 |
| 31 | 0.997859830745627 | 0.00428033850874624 | 0.00214016925437312 |
| 32 | 0.99806991215124 | 0.00386017569751857 | 0.00193008784875928 |
| 33 | 0.999744201365175 | 0.000511597269649726 | 0.000255798634824863 |
| 34 | 0.999977950883756 | 4.40982324873151e-05 | 2.20491162436576e-05 |
| 35 | 0.999989773203158 | 2.04535936849318e-05 | 1.02267968424659e-05 |
| 36 | 0.99999736921699 | 5.2615660195967e-06 | 2.63078300979835e-06 |
| 37 | 0.999999578742039 | 8.42515922650204e-07 | 4.21257961325102e-07 |
| 38 | 0.999999113394834 | 1.77321033240766e-06 | 8.8660516620383e-07 |
| 39 | 0.999997822990196 | 4.35401960696193e-06 | 2.17700980348097e-06 |
| 40 | 0.999993115379134 | 1.37692417315975e-05 | 6.88462086579875e-06 |
| 41 | 0.999984452375507 | 3.10952489858162e-05 | 1.55476244929081e-05 |
| 42 | 0.999969071414684 | 6.18571706325659e-05 | 3.09285853162829e-05 |
| 43 | 0.999976226822488 | 4.75463550246575e-05 | 2.37731775123287e-05 |
| 44 | 0.999963257938099 | 7.34841238029508e-05 | 3.67420619014754e-05 |
| 45 | 0.999891974218634 | 0.000216051562731430 | 0.000108025781365715 |
| 46 | 0.99981783901238 | 0.000364321975242393 | 0.000182160987621196 |
| 47 | 0.999687792692782 | 0.000624414614436992 | 0.000312207307218496 |
| 48 | 0.999063004926787 | 0.00187399014642539 | 0.000936995073212693 |
| 49 | 0.99736137059735 | 0.00527725880529884 | 0.00263862940264942 |
| 50 | 0.995850406008542 | 0.00829918798291619 | 0.00414959399145809 |
| 51 | 0.992294394148183 | 0.0154112117036349 | 0.00770560585181744 |
| 52 | 0.98435221770368 | 0.0312955645926384 | 0.0156477822963192 |
| 53 | 0.964582858053298 | 0.0708342838934042 | 0.0354171419467021 |
| 54 | 0.91734968438905 | 0.165300631221901 | 0.0826503156109505 |
| 55 | 0.969029732279413 | 0.0619405354411746 | 0.0309702677205873 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 20 | 0.512820512820513 | NOK |
| 5% type I error level | 30 | 0.769230769230769 | NOK |
| 10% type I error level | 38 | 0.974358974358974 | NOK |
