| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 93124.3064063537 + 0.595245145625902X[t] + 1460.64625979357M1[t] + 2625.50165379033M2[t] + 2063.61079494683M3[t] + 2144.30079128605M4[t] -474.914587784631M5[t] -4747.33433857108M6[t] -1131.23893509993M7[t] -6743.02998141279M8[t] -2789.33139941479M9[t] -2464.15797519326M10[t] -2133.01676893371M11[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) | 93124.3064063537 | 16338.164757 | 5.6998 | 1e-06 | 0 |
| X | 0.595245145625902 | 0.054336 | 10.955 | 0 | 0 |
| M1 | 1460.64625979357 | 5794.131653 | 0.2521 | 0.801928 | 0.400964 |
| M2 | 2625.50165379033 | 5795.421135 | 0.453 | 0.652342 | 0.326171 |
| M3 | 2063.61079494683 | 5807.031147 | 0.3554 | 0.723701 | 0.361851 |
| M4 | 2144.30079128605 | 5824.907886 | 0.3681 | 0.714218 | 0.357109 |
| M5 | -474.914587784631 | 5858.378469 | -0.0811 | 0.935689 | 0.467845 |
| M6 | -4747.33433857108 | 5827.960201 | -0.8146 | 0.418891 | 0.209446 |
| M7 | -1131.23893509993 | 5878.16325 | -0.1924 | 0.848113 | 0.424057 |
| M8 | -6743.02998141279 | 6229.689339 | -1.0824 | 0.283884 | 0.141942 |
| M9 | -2789.33139941479 | 6141.928098 | -0.4541 | 0.651544 | 0.325772 |
| M10 | -2464.15797519326 | 6073.938233 | -0.4057 | 0.686571 | 0.343285 |
| M11 | -2133.01676893371 | 6051.646679 | -0.3525 | 0.725859 | 0.362929 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.860025172821497 |
| R-squared | 0.739643297886646 |
| Adjusted R-squared | 0.681786252972568 |
| F-TEST (value) | 12.7839798763498 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 54 |
| p-value | 7.89301957127009e-12 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 9568.45326181193 |
| Sum Squared Residuals | 4943986082.46788 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 267413 | 270129.889052973 | -2716.88905297294 |
| 2 | 267366 | 270447.115359599 | -3081.11535959852 |
| 3 | 264777 | 268139.370488634 | -3362.37048863429 |
| 4 | 258863 | 264756.328982576 | -5893.32898257637 |
| 5 | 254844 | 260400.188268569 | -5556.18826856933 |
| 6 | 254868 | 259720.668216781 | -4852.66821678082 |
| 7 | 277267 | 280247.082962338 | -2980.08296233820 |
| 8 | 285351 | 280081.189753357 | 5269.81024664329 |
| 9 | 286602 | 284391.440177585 | 2210.55982241537 |
| 10 | 283042 | 286068.415327523 | -3026.41532752258 |
| 11 | 276687 | 279969.718470731 | -3282.71847073114 |
| 12 | 277915 | 282137.854703257 | -4222.85470325678 |
| 13 | 277128 | 281335.378919381 | -4207.37891938067 |
| 14 | 277103 | 281630.581155618 | -4527.58115561799 |
| 15 | 275037 | 279351.408051644 | -4314.40805164376 |
| 16 | 270150 | 275598.124065007 | -5448.12406500655 |
| 17 | 267140 | 271411.032972357 | -4271.03297235725 |
| 18 | 264993 | 269352.329918154 | -4359.32991815353 |
| 19 | 287259 | 290493.037653997 | -3234.03765399685 |
| 20 | 291186 | 287394.371612517 | 3791.62838748346 |
| 21 | 292300 | 290296.867267339 | 2003.1327326608 |
| 22 | 288186 | 283478.503698904 | 4707.49630109572 |
| 23 | 281477 | 277854.812468322 | 3622.18753167769 |
| 24 | 282656 | 280319.976028515 | 2336.02397148472 |
| 25 | 280190 | 281026.446688801 | -836.446688800826 |
| 26 | 280408 | 280075.800835243 | 332.199164756861 |
| 27 | 276836 | 275525.172255560 | 1310.82774443953 |
| 28 | 275216 | 273240.358043182 | 1975.64195681765 |
| 29 | 274352 | 270284.233911687 | 4067.76608831259 |
| 30 | 271311 | 267921.360588069 | 3389.63941193114 |
| 31 | 289802 | 288284.082918579 | 1517.91708142087 |
| 32 | 290726 | 285837.805556705 | 4888.19444329519 |
| 33 | 292300 | 285346.808636314 | 6953.1913636858 |
| 34 | 278506 | 274661.732601893 | 3844.26739810657 |
| 35 | 269826 | 267133.852150454 | 2692.1478495458 |
| 36 | 265861 | 266586.480028634 | -725.480028634476 |
| 37 | 269034 | 268123.912912214 | 910.087087786215 |
| 38 | 264176 | 265203.005626634 | -1027.00562663437 |
| 39 | 255198 | 259758.318838222 | -4560.31883822159 |
| 40 | 253353 | 257512.195560309 | -4159.19556030916 |
| 41 | 246057 | 250378.045751666 | -4321.04575166602 |
| 42 | 235372 | 245099.066459626 | -9727.06645962618 |
| 43 | 258556 | 268665.398163895 | -10109.3981638950 |
| 44 | 260993 | 267096.512146673 | -6103.5121466733 |
| 45 | 254663 | 261166.760330699 | -6503.76033069883 |
| 46 | 250643 | 255201.978301091 | -4558.97830109146 |
| 47 | 243422 | 249578.882315655 | -6156.88231565511 |
| 48 | 247105 | 252145.83279575 | -5040.8327957501 |
| 49 | 248541 | 254337.440094372 | -5796.44009437228 |
| 50 | 245039 | 252014.754180147 | -6975.75418014688 |
| 51 | 237080 | 247298.052204835 | -10218.0522048346 |
| 52 | 237085 | 245959.677774002 | -8874.67777400166 |
| 53 | 225554 | 237771.944057601 | -12217.9440576007 |
| 54 | 226839 | 237629.335127167 | -10790.3351271667 |
| 55 | 247934 | 258926.592336310 | -10992.5923363097 |
| 56 | 248333 | 256179.120930749 | -7846.12093074864 |
| 57 | 246969 | 251632.123588063 | -4663.12358806314 |
| 58 | 245098 | 246064.370070588 | -966.370070588245 |
| 59 | 246263 | 243137.734594837 | 3125.26540516277 |
| 60 | 255765 | 248111.856443843 | 7653.14355615663 |
| 61 | 264319 | 251671.932332259 | 12647.0676677405 |
| 62 | 268347 | 253067.742842759 | 15279.2571572409 |
| 63 | 273046 | 251901.678161105 | 21144.3218388947 |
| 64 | 273963 | 251563.315574924 | 22399.6844250761 |
| 65 | 267430 | 245131.555038119 | 22298.4449618807 |
| 66 | 271993 | 245653.239690204 | 26339.7603097961 |
| 67 | 292710 | 266911.805964881 | 25798.1940351189 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.000272740306682288 | 0.000545480613364576 | 0.999727259693318 |
| 17 | 8.40239482044959e-05 | 0.000168047896408992 | 0.999915976051795 |
| 18 | 7.49170597548235e-06 | 1.49834119509647e-05 | 0.999992508294025 |
| 19 | 4.92950080567018e-07 | 9.85900161134036e-07 | 0.99999950704992 |
| 20 | 5.98715748209359e-08 | 1.19743149641872e-07 | 0.999999940128425 |
| 21 | 3.62299972378704e-09 | 7.24599944757409e-09 | 0.999999996377 |
| 22 | 2.10110891749833e-06 | 4.20221783499666e-06 | 0.999997898891082 |
| 23 | 3.95714747858896e-06 | 7.91429495717792e-06 | 0.999996042852521 |
| 24 | 3.70853660413269e-06 | 7.41707320826538e-06 | 0.999996291463396 |
| 25 | 1.19816370468405e-06 | 2.39632740936809e-06 | 0.999998801836295 |
| 26 | 5.85719310664065e-07 | 1.17143862132813e-06 | 0.99999941428069 |
| 27 | 3.79400249429956e-07 | 7.58800498859913e-07 | 0.99999962059975 |
| 28 | 6.51165243118333e-07 | 1.30233048623667e-06 | 0.999999348834757 |
| 29 | 1.29136350023109e-06 | 2.58272700046217e-06 | 0.9999987086365 |
| 30 | 1.29952461265898e-06 | 2.59904922531795e-06 | 0.999998700475387 |
| 31 | 5.39656413898947e-07 | 1.07931282779789e-06 | 0.999999460343586 |
| 32 | 1.45978497106152e-07 | 2.91956994212303e-07 | 0.999999854021503 |
| 33 | 6.76760033735602e-08 | 1.35352006747120e-07 | 0.999999932323997 |
| 34 | 2.27338012034522e-08 | 4.54676024069044e-08 | 0.999999977266199 |
| 35 | 6.51820861675371e-09 | 1.30364172335074e-08 | 0.999999993481791 |
| 36 | 1.53816005183794e-09 | 3.07632010367588e-09 | 0.99999999846184 |
| 37 | 4.89495386889852e-10 | 9.78990773779704e-10 | 0.999999999510505 |
| 38 | 1.24912743062200e-10 | 2.49825486124401e-10 | 0.999999999875087 |
| 39 | 4.88148937542593e-11 | 9.76297875085186e-11 | 0.999999999951185 |
| 40 | 1.89791477030563e-11 | 3.79582954061126e-11 | 0.99999999998102 |
| 41 | 9.34239246869916e-12 | 1.86847849373983e-11 | 0.999999999990658 |
| 42 | 2.21511899107560e-11 | 4.43023798215119e-11 | 0.999999999977849 |
| 43 | 1.08375414951116e-10 | 2.16750829902233e-10 | 0.999999999891625 |
| 44 | 2.56484865842372e-10 | 5.12969731684744e-10 | 0.999999999743515 |
| 45 | 4.75735421326044e-10 | 9.51470842652088e-10 | 0.999999999524265 |
| 46 | 2.34334157908895e-09 | 4.68668315817789e-09 | 0.999999997656658 |
| 47 | 7.47462107226761e-08 | 1.49492421445352e-07 | 0.99999992525379 |
| 48 | 5.70879206197699e-06 | 1.14175841239540e-05 | 0.999994291207938 |
| 49 | 0.0181150133568992 | 0.0362300267137984 | 0.9818849866431 |
| 50 | 0.382683330595654 | 0.765366661191308 | 0.617316669404346 |
| 51 | 0.798556772882816 | 0.402886454234369 | 0.201443227117184 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 33 | 0.916666666666667 | NOK |
| 5% type I error level | 34 | 0.944444444444444 | NOK |
| 10% type I error level | 34 | 0.944444444444444 | NOK |
