| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1.92944665325443 + 0.272322364476941X[t] + 0.416145636793173M1[t] + 0.482812303459842M2[t] + 0.332812303459842M3[t] + 0.535194753289615M4[t] + 0.301861419956282M5[t] + 0.151861419956281M6[t] -0.227159400887366M7[t] -0.193826067554032M8[t] -0.260492734220699M9[t] -0.12M10[t] -0.22M11[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) | 1.92944665325443 | 0.378276 | 5.1006 | 4e-06 | 2e-06 |
| X | 0.272322364476941 | 0.018697 | 14.5649 | 0 | 0 |
| M1 | 0.416145636793173 | 0.186726 | 2.2286 | 0.029869 | 0.014934 |
| M2 | 0.482812303459842 | 0.186726 | 2.5857 | 0.012348 | 0.006174 |
| M3 | 0.332812303459842 | 0.186726 | 1.7824 | 0.080112 | 0.040056 |
| M4 | 0.535194753289615 | 0.188485 | 2.8395 | 0.006287 | 0.003143 |
| M5 | 0.301861419956282 | 0.188485 | 1.6015 | 0.114889 | 0.057445 |
| M6 | 0.151861419956281 | 0.188485 | 0.8057 | 0.423826 | 0.211913 |
| M7 | -0.227159400887366 | 0.189617 | -1.198 | 0.235966 | 0.117983 |
| M8 | -0.193826067554032 | 0.189617 | -1.0222 | 0.311083 | 0.155541 |
| M9 | -0.260492734220699 | 0.189617 | -1.3738 | 0.174983 | 0.087491 |
| M10 | -0.12 | 0.194985 | -0.6154 | 0.540764 | 0.270382 |
| M11 | -0.22 | 0.194985 | -1.1283 | 0.264009 | 0.132004 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.906667996552816 |
| R-squared | 0.822046855973097 |
| Adjusted R-squared | 0.783914039395903 |
| F-TEST (value) | 21.5574649281151 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 56 |
| p-value | 1.11022302462516e-16 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.308299121025296 |
| Sum Squared Residuals | 5.32270748939832 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8.2 | 7.87373628892952 | 0.326263711070480 |
| 2 | 8 | 7.94040295559618 | 0.0595970444038233 |
| 3 | 7.5 | 7.79040295559617 | -0.290402955596175 |
| 4 | 6.8 | 6.76733476527971 | 0.032665234720286 |
| 5 | 6.5 | 6.53400143194638 | -0.0340014319463803 |
| 6 | 6.6 | 6.38400143194638 | 0.215998568053620 |
| 7 | 7.6 | 8.0201661082321 | -0.420166108232099 |
| 8 | 8 | 8.05349944156543 | -0.0534994415654309 |
| 9 | 8.1 | 7.98683277489876 | 0.113167225101235 |
| 10 | 7.7 | 7.5009840708225 | 0.199015929177501 |
| 11 | 7.5 | 7.4009840708225 | 0.0990159291775013 |
| 12 | 7.6 | 7.6209840708225 | -0.0209840708224989 |
| 13 | 7.8 | 7.73757510669104 | 0.0624248933089629 |
| 14 | 7.8 | 7.8042417733577 | -0.00424177335770586 |
| 15 | 7.8 | 7.6542417733577 | 0.145758226642294 |
| 16 | 7.5 | 8.07448211476903 | -0.574482114769032 |
| 17 | 7.5 | 7.8411487814357 | -0.341148781435699 |
| 18 | 7.1 | 7.6911487814357 | -0.591148781435699 |
| 19 | 7.5 | 7.44828914283052 | 0.0517108571694780 |
| 20 | 7.5 | 7.48162247616385 | 0.0183775238361449 |
| 21 | 7.6 | 7.41495580949719 | 0.185044190502811 |
| 22 | 7.7 | 7.90946761753791 | -0.20946761753791 |
| 23 | 7.7 | 7.80946761753791 | -0.109467617537910 |
| 24 | 7.9 | 8.02946761753791 | -0.12946761753791 |
| 25 | 8.1 | 7.9282007618249 | 0.171799238175104 |
| 26 | 8.2 | 7.99486742849156 | 0.205132571508435 |
| 27 | 8.2 | 7.84486742849156 | 0.355132571508434 |
| 28 | 8.2 | 7.47537291291976 | 0.724627087080239 |
| 29 | 7.9 | 7.24203957958643 | 0.657960420413573 |
| 30 | 7.3 | 7.09203957958643 | 0.207960420413573 |
| 31 | 6.9 | 6.49516086716123 | 0.404839132838772 |
| 32 | 6.6 | 6.52849420049456 | 0.0715057995054387 |
| 33 | 6.7 | 6.4618275338279 | 0.238172466172106 |
| 34 | 6.9 | 6.84741039607784 | 0.0525896039221603 |
| 35 | 7 | 6.74741039607784 | 0.25258960392216 |
| 36 | 7.1 | 6.96741039607784 | 0.132589603922160 |
| 37 | 7.2 | 7.05676919549868 | 0.143230804501316 |
| 38 | 7.1 | 7.12343586216535 | -0.0234358621653530 |
| 39 | 6.9 | 6.97343586216535 | -0.0734358621653529 |
| 40 | 7 | 6.87626371107049 | 0.123736288929510 |
| 41 | 6.8 | 6.64293037773716 | 0.157069622262843 |
| 42 | 6.4 | 6.49293037773716 | -0.092930377737156 |
| 43 | 6.7 | 6.74025099519047 | -0.0402509951904743 |
| 44 | 6.6 | 6.77358432852381 | -0.173584328523808 |
| 45 | 6.4 | 6.70691766185714 | -0.306917661857141 |
| 46 | 6.3 | 6.24830119422857 | 0.0516988057714302 |
| 47 | 6.2 | 6.14830119422857 | 0.0516988057714306 |
| 48 | 6.5 | 6.36830119422857 | 0.131698805771430 |
| 49 | 6.8 | 6.92060801326021 | -0.120608013260214 |
| 50 | 6.8 | 6.98727467992688 | -0.187274679926882 |
| 51 | 6.4 | 6.83727467992688 | -0.437274679926882 |
| 52 | 6.1 | 6.49501240080277 | -0.395012400802773 |
| 53 | 5.8 | 6.26167906746944 | -0.46167906746944 |
| 54 | 6.1 | 6.11167906746944 | -0.0116790674694396 |
| 55 | 7.2 | 7.5299858521736 | -0.329985852173603 |
| 56 | 7.3 | 7.56331918550694 | -0.263319185506937 |
| 57 | 6.9 | 7.49665251884027 | -0.59665251884027 |
| 58 | 6.1 | 6.19383672133318 | -0.0938367213331819 |
| 59 | 5.8 | 6.09383672133318 | -0.293836721333182 |
| 60 | 6.2 | 6.31383672133318 | -0.113836721333181 |
| 61 | 7.1 | 7.68311063379565 | -0.583110633795649 |
| 62 | 7.7 | 7.74977730046232 | -0.0497773004623174 |
| 63 | 7.9 | 7.59977730046232 | 0.300222699537682 |
| 64 | 7.7 | 7.61153409515823 | 0.0884659048417694 |
| 65 | 7.4 | 7.3782007618249 | 0.0217992381751027 |
| 66 | 7.5 | 7.22820076182490 | 0.271799238175102 |
| 67 | 8 | 7.66614703441207 | 0.333852965587926 |
| 68 | 8.1 | 7.69948036774541 | 0.400519632254592 |
| 69 | 8 | 7.63281370107874 | 0.367186298921259 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.252397425058284 | 0.504794850116569 | 0.747602574941716 |
| 17 | 0.167602367470976 | 0.335204734941952 | 0.832397632529024 |
| 18 | 0.160427153477088 | 0.320854306954177 | 0.839572846522912 |
| 19 | 0.107889408810491 | 0.215778817620982 | 0.892110591189509 |
| 20 | 0.0673327443564569 | 0.134665488712914 | 0.932667255643543 |
| 21 | 0.0416646709640778 | 0.0833293419281556 | 0.958335329035922 |
| 22 | 0.0315816442847724 | 0.0631632885695448 | 0.968418355715228 |
| 23 | 0.0170252199983618 | 0.0340504399967236 | 0.982974780001638 |
| 24 | 0.0102899764712728 | 0.0205799529425456 | 0.989710023528727 |
| 25 | 0.00490511864212974 | 0.0098102372842595 | 0.99509488135787 |
| 26 | 0.00389271904886006 | 0.00778543809772011 | 0.99610728095114 |
| 27 | 0.0132876977113068 | 0.0265753954226137 | 0.986712302288693 |
| 28 | 0.332089052361926 | 0.664178104723853 | 0.667910947638074 |
| 29 | 0.664902851893582 | 0.670194296212836 | 0.335097148106418 |
| 30 | 0.640076689422226 | 0.719846621155548 | 0.359923310577774 |
| 31 | 0.641576995748877 | 0.716846008502246 | 0.358423004251123 |
| 32 | 0.620531371363334 | 0.758937257273332 | 0.379468628636666 |
| 33 | 0.687936205801165 | 0.624127588397671 | 0.312063794198835 |
| 34 | 0.620911918508259 | 0.758176162983482 | 0.379088081491741 |
| 35 | 0.549463119292864 | 0.901073761414272 | 0.450536880707136 |
| 36 | 0.462781865975869 | 0.925563731951738 | 0.537218134024131 |
| 37 | 0.512536825617775 | 0.97492634876445 | 0.487463174382225 |
| 38 | 0.466625046734767 | 0.933250093469534 | 0.533374953265233 |
| 39 | 0.41389408635338 | 0.82778817270676 | 0.58610591364662 |
| 40 | 0.369684636476538 | 0.739369272953075 | 0.630315363523462 |
| 41 | 0.358403191764531 | 0.716806383529062 | 0.641596808235469 |
| 42 | 0.293231784004110 | 0.586463568008219 | 0.70676821599589 |
| 43 | 0.243622693566717 | 0.487245387133434 | 0.756377306433283 |
| 44 | 0.193600979099377 | 0.387201958198754 | 0.806399020900623 |
| 45 | 0.194039123387632 | 0.388078246775265 | 0.805960876612368 |
| 46 | 0.138828103401638 | 0.277656206803276 | 0.861171896598362 |
| 47 | 0.109496207083002 | 0.218992414166004 | 0.890503792916998 |
| 48 | 0.0735510812466132 | 0.147102162493226 | 0.926448918753387 |
| 49 | 0.144617870352999 | 0.289235740705997 | 0.855382129647001 |
| 50 | 0.108643846946100 | 0.217287693892201 | 0.8913561530539 |
| 51 | 0.103813388750168 | 0.207626777500337 | 0.896186611249832 |
| 52 | 0.0697966778280855 | 0.139593355656171 | 0.930203322171915 |
| 53 | 0.0438786204299421 | 0.0877572408598843 | 0.956121379570058 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 2 | 0.0526315789473684 | NOK |
| 5% type I error level | 5 | 0.131578947368421 | NOK |
| 10% type I error level | 8 | 0.210526315789474 | NOK |
