| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.81400771388499 + 0.978786816269285X[t] + 0.778727208976158M1[t] + 0.577454417952314M2[t] + 0.333211781206171M3[t] + 0.0510904628330994M4[t] -0.0642426367461433M5[t] -0.2170301542777M6[t] -0.354484572230014M7[t] -0.476181626928472M8[t] -0.599151472650772M9[t] -0.663818373071529M10[t] -0.448061009817672M11[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) | 1.81400771388499 | 1.1641 | 1.5583 | 0.125873 | 0.062936 |
| X | 0.978786816269285 | 0.153824 | 6.363 | 0 | 0 |
| M1 | 0.778727208976158 | 0.464792 | 1.6754 | 0.100491 | 0.050246 |
| M2 | 0.577454417952314 | 0.465067 | 1.2417 | 0.220524 | 0.110262 |
| M3 | 0.333211781206171 | 0.4673 | 0.7131 | 0.479336 | 0.239668 |
| M4 | 0.0510904628330994 | 0.46917 | 0.1089 | 0.913749 | 0.456875 |
| M5 | -0.0642426367461433 | 0.465718 | -0.1379 | 0.890875 | 0.445437 |
| M6 | -0.2170301542777 | 0.465199 | -0.4665 | 0.64299 | 0.321495 |
| M7 | -0.354484572230014 | 0.466418 | -0.76 | 0.451042 | 0.225521 |
| M8 | -0.476181626928472 | 0.465525 | -1.0229 | 0.311595 | 0.155798 |
| M9 | -0.599151472650772 | 0.464741 | -1.2892 | 0.203632 | 0.101816 |
| M10 | -0.663818373071529 | 0.465525 | -1.426 | 0.160489 | 0.080245 |
| M11 | -0.448061009817672 | 0.468362 | -0.9567 | 0.343637 | 0.171818 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.75488037601094 |
| R-squared | 0.569844382086419 |
| Adjusted R-squared | 0.460017415810612 |
| F-TEST (value) | 5.18856526233614 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 1.87317418973709e-05 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.734756187946033 |
| Sum Squared Residuals | 25.3737328190743 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 11.1 | 10.4230294530154 | 0.676970546984578 |
| 2 | 10.9 | 10.3196353436185 | 0.580364656381486 |
| 3 | 10 | 9.68387798036466 | 0.316122019635345 |
| 4 | 9.2 | 9.20599929873773 | -0.00599929873772784 |
| 5 | 9.2 | 9.18854488078541 | 0.0114551192145857 |
| 6 | 9.5 | 9.23151472650771 | 0.268485273492286 |
| 7 | 9.6 | 9.0940603085554 | 0.5059396914446 |
| 8 | 9.5 | 8.97236325385694 | 0.527636746143058 |
| 9 | 9.1 | 8.55575736325386 | 0.544242636746143 |
| 10 | 8.9 | 8.4910904628331 | 0.4089095371669 |
| 11 | 9 | 8.31533309957924 | 0.684666900420758 |
| 12 | 10.1 | 9.15490883590463 | 0.94509116409537 |
| 13 | 10.3 | 9.93363604488079 | 0.366363955119214 |
| 14 | 10.2 | 9.83024193548387 | 0.369758064516129 |
| 15 | 9.6 | 9.68387798036466 | -0.0838779803646572 |
| 16 | 9.2 | 9.40175666199159 | -0.201756661991586 |
| 17 | 9.3 | 9.4821809256662 | -0.182180925666199 |
| 18 | 9.4 | 9.5251507713885 | -0.125150771388499 |
| 19 | 9.4 | 9.48557503506311 | -0.0855750350631127 |
| 20 | 9.2 | 9.36387798036466 | -0.163877980364656 |
| 21 | 9 | 9.24090813464236 | -0.240908134642356 |
| 22 | 9 | 8.88260518934081 | 0.117394810659186 |
| 23 | 9 | 8.5110904628331 | 0.4889095371669 |
| 24 | 9.8 | 8.56763674614306 | 1.23236325385694 |
| 25 | 10 | 9.05272791023843 | 0.94727208976157 |
| 26 | 9.8 | 8.94933380084152 | 0.850666199158486 |
| 27 | 9.3 | 8.90084852734923 | 0.399151472650771 |
| 28 | 9 | 8.71660589060309 | 0.283394109396914 |
| 29 | 9 | 8.69915147265077 | 0.300848527349229 |
| 30 | 9.1 | 8.64424263674614 | 0.455757363253856 |
| 31 | 9.1 | 8.4089095371669 | 0.691090462833099 |
| 32 | 9.1 | 8.09145511921459 | 1.00854488078541 |
| 33 | 9.2 | 8.06636395511921 | 1.13363604488078 |
| 34 | 8.8 | 7.8059396914446 | 0.9940603085554 |
| 35 | 8.3 | 7.63018232819074 | 0.669817671809257 |
| 36 | 8.4 | 8.3718793828892 | 0.0281206171107995 |
| 37 | 8.1 | 9.05272791023843 | -0.95272791023843 |
| 38 | 7.7 | 8.65569775596073 | -0.955697755960729 |
| 39 | 7.9 | 8.31357643758766 | -0.413576437587657 |
| 40 | 7.9 | 7.93357643758766 | -0.0335764375876577 |
| 41 | 8 | 8.1118793828892 | -0.111879382889200 |
| 42 | 7.9 | 8.25272791023843 | -0.352727910238429 |
| 43 | 7.6 | 8.11527349228611 | -0.515273492286115 |
| 44 | 7.1 | 7.60206171107994 | -0.502061711079944 |
| 45 | 6.8 | 7.18545582047686 | -0.385455820476858 |
| 46 | 6.5 | 6.82715287517532 | -0.327152875175315 |
| 47 | 6.9 | 7.33654628330996 | -0.436546283309958 |
| 48 | 8.2 | 8.86127279102384 | -0.661272791023844 |
| 49 | 8.7 | 9.73787868162693 | -1.03787868162693 |
| 50 | 8.3 | 9.14509116409537 | -0.845091164095371 |
| 51 | 7.9 | 8.1178190743338 | -0.217819074333801 |
| 52 | 7.5 | 7.54206171107994 | -0.0420617110799438 |
| 53 | 7.8 | 7.81824333800841 | -0.0182433380084153 |
| 54 | 8.3 | 8.54636395511922 | -0.246363955119214 |
| 55 | 8.4 | 8.99618162692847 | -0.596181626928471 |
| 56 | 8.2 | 9.07024193548387 | -0.870241935483872 |
| 57 | 7.7 | 8.75151472650771 | -1.05151472650771 |
| 58 | 7.2 | 8.39321178120617 | -1.19321178120617 |
| 59 | 7.3 | 8.70684782608696 | -1.40684782608696 |
| 60 | 8.1 | 9.64430224403927 | -1.54430224403927 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0223180733084264 | 0.0446361466168528 | 0.977681926691574 |
| 17 | 0.00797515577441008 | 0.0159503115488202 | 0.99202484422559 |
| 18 | 0.00495186245676104 | 0.00990372491352208 | 0.995048137543239 |
| 19 | 0.00431093396964533 | 0.00862186793929065 | 0.995689066030355 |
| 20 | 0.00322039837362435 | 0.00644079674724871 | 0.996779601626376 |
| 21 | 0.00148859620689248 | 0.00297719241378496 | 0.998511403793108 |
| 22 | 0.00047365650794482 | 0.00094731301588964 | 0.999526343492055 |
| 23 | 0.000168473080606498 | 0.000336946161212997 | 0.999831526919393 |
| 24 | 9.48392211469318e-05 | 0.000189678442293864 | 0.999905160778853 |
| 25 | 7.60179189020013e-05 | 0.000152035837804003 | 0.999923982081098 |
| 26 | 6.69114849297619e-05 | 0.000133822969859524 | 0.99993308851507 |
| 27 | 2.87649992461353e-05 | 5.75299984922706e-05 | 0.999971235000754 |
| 28 | 1.12762543146486e-05 | 2.25525086292971e-05 | 0.999988723745685 |
| 29 | 4.17865511147363e-06 | 8.35731022294727e-06 | 0.999995821344889 |
| 30 | 1.67117340492875e-06 | 3.3423468098575e-06 | 0.999998328826595 |
| 31 | 9.68147344373713e-07 | 1.93629468874743e-06 | 0.999999031852656 |
| 32 | 2.41655043075104e-06 | 4.83310086150207e-06 | 0.99999758344957 |
| 33 | 0.00010597357759822 | 0.00021194715519644 | 0.999894026422402 |
| 34 | 0.0071557671240856 | 0.0143115342481712 | 0.992844232875914 |
| 35 | 0.283811152910054 | 0.567622305820107 | 0.716188847089946 |
| 36 | 0.937833041187647 | 0.124333917624705 | 0.0621669588123527 |
| 37 | 0.994658259907706 | 0.0106834801845872 | 0.00534174009229360 |
| 38 | 0.998312342743936 | 0.00337531451212886 | 0.00168765725606443 |
| 39 | 0.996153622103638 | 0.00769275579272377 | 0.00384637789636188 |
| 40 | 0.990915548817743 | 0.0181689023645131 | 0.00908445118225655 |
| 41 | 0.976277210042818 | 0.0474455799143632 | 0.0237227899571816 |
| 42 | 0.955275064984645 | 0.0894498700307102 | 0.0447249350153551 |
| 43 | 0.93679429005019 | 0.126411419899620 | 0.0632057099498102 |
| 44 | 0.930010696347068 | 0.139978607305864 | 0.0699893036529321 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 18 | 0.620689655172414 | NOK |
| 5% type I error level | 24 | 0.827586206896552 | NOK |
| 10% type I error level | 25 | 0.862068965517241 | NOK |
