| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 318115.398162939 -1319.53689420027X[t] + 194.849655232781M1[t] -1514.42482052588M2[t] -5277.09751585129M3[t] -10799.9026082240M4[t] -11679.6684389217M5[t] -14336.1172997772M6[t] + 10431.3901533681M7[t] + 13434.4813255061M8[t] + 11894.5216074274M9[t] + 1914.98881954373M10[t] -3644.97403732826M11[t] -527.851900808109t + 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) | 318115.398162939 | 9097.359536 | 34.9679 | 0 | 0 |
| X | -1319.53689420027 | 216.989243 | -6.0811 | 0 | 0 |
| M1 | 194.849655232781 | 7453.373696 | 0.0261 | 0.979238 | 0.489619 |
| M2 | -1514.42482052588 | 7453.866897 | -0.2032 | 0.83975 | 0.419875 |
| M3 | -5277.09751585129 | 7455.5949 | -0.7078 | 0.482056 | 0.241028 |
| M4 | -10799.9026082240 | 7505.211576 | -1.439 | 0.155821 | 0.077911 |
| M5 | -11679.6684389217 | 7447.882485 | -1.5682 | 0.122574 | 0.061287 |
| M6 | -14336.1172997772 | 7457.223342 | -1.9224 | 0.059735 | 0.029867 |
| M7 | 10431.3901533681 | 7444.595128 | 1.4012 | 0.166771 | 0.083385 |
| M8 | 13434.4813255061 | 7445.459617 | 1.8044 | 0.076647 | 0.038324 |
| M9 | 11894.5216074274 | 7448.727847 | 1.5969 | 0.116029 | 0.058014 |
| M10 | 1914.98881954373 | 7777.213697 | 0.2462 | 0.80642 | 0.40321 |
| M11 | -3644.97403732826 | 7777.061605 | -0.4687 | 0.641149 | 0.320574 |
| t | -527.851900808109 | 82.610068 | -6.3897 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.772218481857322 |
| R-squared | 0.596321383722027 |
| Adjusted R-squared | 0.500906438056324 |
| F-TEST (value) | 6.24976914844461 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 55 |
| p-value | 5.13881478925171e-07 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12293.2695635889 |
| Sum Squared Residuals | 8311846210.9683 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 267413 | 289544.306381479 | -22131.3063814788 |
| 2 | 267366 | 280709.495533909 | -13343.4955339095 |
| 3 | 264777 | 276418.970937776 | -11641.9709377760 |
| 4 | 258863 | 266409.703261994 | -7546.70326199439 |
| 5 | 254844 | 258404.401059487 | -3560.40105948723 |
| 6 | 254868 | 268415.469239826 | -13547.4692398262 |
| 7 | 277267 | 290016.051003763 | -12749.0510037630 |
| 8 | 285351 | 293810.827169293 | -8459.82716929313 |
| 9 | 286602 | 283825.794185205 | 2776.20581479537 |
| 10 | 283042 | 278596.557073314 | 4445.44292668605 |
| 11 | 276687 | 272508.742315634 | 4178.25768436615 |
| 12 | 277915 | 272986.790663753 | 4928.20933624652 |
| 13 | 277128 | 268695.177735577 | 8432.82226442265 |
| 14 | 277103 | 274375.272724212 | 2727.72727578787 |
| 15 | 275037 | 275362.895704880 | -325.895704879723 |
| 16 | 270150 | 273270.849394300 | -3120.84939429975 |
| 17 | 267140 | 269224.157874393 | -2084.15787439338 |
| 18 | 264993 | 263400.783324329 | 1592.21667567078 |
| 19 | 287259 | 287640.438876666 | -381.438876666466 |
| 20 | 291186 | 287476.604359596 | 3709.39564040421 |
| 21 | 292300 | 281450.182058108 | 10849.8179418919 |
| 22 | 288186 | 272262.334263617 | 15923.6657363833 |
| 23 | 281477 | 274091.740871138 | 7385.25912886184 |
| 24 | 282656 | 282487.010584459 | 168.989415540628 |
| 25 | 280190 | 272917.250079482 | 7272.74992051782 |
| 26 | 280408 | 268041.049914515 | 12366.9500854851 |
| 27 | 276836 | 269028.672895182 | 7807.32710481758 |
| 28 | 275216 | 273534.311055604 | 1681.68894439621 |
| 29 | 274352 | 266848.545747297 | 7503.45425270312 |
| 30 | 271311 | 254427.486726231 | 16883.5132737686 |
| 31 | 289802 | 273388.994701768 | 16413.0052982324 |
| 32 | 290726 | 279822.844655698 | 10903.1553443018 |
| 33 | 292300 | 277755.033036811 | 14544.9669631886 |
| 34 | 278506 | 275164.869713321 | 3341.13028667877 |
| 35 | 269826 | 261159.833590440 | 8666.16640956048 |
| 36 | 265861 | 260318.345044359 | 5542.65495564112 |
| 37 | 269034 | 254707.195221982 | 14326.8047780175 |
| 38 | 264176 | 253789.605739616 | 10386.3942603840 |
| 39 | 255198 | 245540.470460882 | 9657.52953911834 |
| 40 | 253353 | 240809.350361901 | 12543.6496380988 |
| 41 | 246057 | 236762.658841995 | 9294.3411580052 |
| 42 | 235372 | 238856.505657132 | -3484.50565713222 |
| 43 | 258556 | 260457.087421069 | -1901.08742106894 |
| 44 | 260993 | 266890.937375000 | -5897.93737499959 |
| 45 | 254663 | 270101.273332914 | -15438.2733329138 |
| 46 | 250643 | 259593.888644222 | -8950.88864422206 |
| 47 | 243422 | 249547.463203941 | -6125.46320394116 |
| 48 | 247105 | 250025.511552061 | -2920.51155206077 |
| 49 | 248541 | 249692.509306485 | -1151.50930648545 |
| 50 | 245039 | 254053.06740092 | -9014.06740092001 |
| 51 | 237080 | 244484.395227985 | -7404.39522798543 |
| 52 | 237085 | 241072.812023205 | -3987.81202320519 |
| 53 | 225554 | 242304.2680801 | -16750.2680800999 |
| 54 | 226839 | 241759.041106837 | -14920.0411068368 |
| 55 | 247934 | 264679.159764974 | -16745.1597649738 |
| 56 | 248333 | 271113.009718904 | -22780.0097189044 |
| 57 | 246969 | 275642.882571019 | -28673.8825710189 |
| 58 | 245098 | 259857.350305526 | -14759.3503055261 |
| 59 | 246263 | 260367.220018847 | -14104.2200188473 |
| 60 | 255765 | 263484.342155367 | -7719.34215536748 |
| 61 | 264319 | 271068.561274994 | -6749.56127499374 |
| 62 | 268347 | 271470.508686827 | -3123.50868682751 |
| 63 | 273046 | 271138.594773295 | 1907.40522670521 |
| 64 | 273963 | 273532.973902996 | 430.02609700428 |
| 65 | 267430 | 261832.968396728 | 5597.0316032722 |
| 66 | 271993 | 258516.713945644 | 13476.2860543558 |
| 67 | 292710 | 277346.268231760 | 15363.7317682397 |
| 68 | 295881 | 273355.776721509 | 22525.2232784912 |
| 69 | 293299 | 277357.834815943 | 15941.1651840568 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 7.47843944043301e-05 | 0.000149568788808660 | 0.999925215605596 |
| 18 | 2.63406380100667e-06 | 5.26812760201334e-06 | 0.9999973659362 |
| 19 | 1.35071106191922e-07 | 2.70142212383843e-07 | 0.999999864928894 |
| 20 | 5.2095395548097e-06 | 1.04190791096194e-05 | 0.999994790460445 |
| 21 | 4.28294247068315e-06 | 8.5658849413663e-06 | 0.99999571705753 |
| 22 | 2.06593507308570e-06 | 4.13187014617140e-06 | 0.999997934064927 |
| 23 | 1.20956361379888e-06 | 2.41912722759776e-06 | 0.999998790436386 |
| 24 | 5.98639773421184e-07 | 1.19727954684237e-06 | 0.999999401360227 |
| 25 | 2.96352652829377e-07 | 5.92705305658754e-07 | 0.999999703647347 |
| 26 | 8.10486011580455e-08 | 1.62097202316091e-07 | 0.999999918951399 |
| 27 | 3.09777816844045e-08 | 6.1955563368809e-08 | 0.999999969022218 |
| 28 | 7.12420044664198e-09 | 1.42484008932840e-08 | 0.9999999928758 |
| 29 | 1.84553433437688e-09 | 3.69106866875375e-09 | 0.999999998154466 |
| 30 | 3.20955429555239e-10 | 6.41910859110477e-10 | 0.999999999679045 |
| 31 | 6.80088749581383e-11 | 1.36017749916277e-10 | 0.999999999931991 |
| 32 | 2.22432607875999e-10 | 4.44865215751997e-10 | 0.999999999777567 |
| 33 | 4.63296993283939e-10 | 9.26593986567878e-10 | 0.999999999536703 |
| 34 | 1.53892232041231e-07 | 3.07784464082462e-07 | 0.999999846107768 |
| 35 | 2.38665836057452e-06 | 4.77331672114905e-06 | 0.99999761334164 |
| 36 | 1.82018466656365e-05 | 3.64036933312730e-05 | 0.999981798153334 |
| 37 | 1.90571377646235e-05 | 3.81142755292471e-05 | 0.999980942862235 |
| 38 | 3.81477690367156e-05 | 7.62955380734312e-05 | 0.999961852230963 |
| 39 | 6.23706668748733e-05 | 0.000124741333749747 | 0.999937629333125 |
| 40 | 7.33823314770971e-05 | 0.000146764662954194 | 0.999926617668523 |
| 41 | 0.000218251845381548 | 0.000436503690763096 | 0.999781748154619 |
| 42 | 0.00104019193423560 | 0.00208038386847119 | 0.998959808065764 |
| 43 | 0.00218664766722636 | 0.00437329533445273 | 0.997813352332774 |
| 44 | 0.00553775721935601 | 0.0110755144387120 | 0.994462242780644 |
| 45 | 0.0443351251374992 | 0.0886702502749984 | 0.95566487486250 |
| 46 | 0.195935199010415 | 0.391870398020829 | 0.804064800989585 |
| 47 | 0.485459801699326 | 0.970919603398652 | 0.514540198300674 |
| 48 | 0.813392907517131 | 0.373214184965737 | 0.186607092482869 |
| 49 | 0.950197352722526 | 0.0996052945549473 | 0.0498026472774736 |
| 50 | 0.999866800355509 | 0.000266399288982584 | 0.000133199644491292 |
| 51 | 0.999809340425946 | 0.000381319148107593 | 0.000190659574053796 |
| 52 | 0.999186138913845 | 0.00162772217230963 | 0.000813861086154814 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 30 | 0.833333333333333 | NOK |
| 5% type I error level | 31 | 0.861111111111111 | NOK |
| 10% type I error level | 33 | 0.916666666666667 | NOK |
