| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 317487.905437682 -5289.50501950168X[t] + 4994.36570923069M1[t] + 6573.16604386424M2[t] + 7132.07362427232M3[t] + 3824.18911972193M4[t] + 2881.13794850487M5[t] + 2923.21219557962M6[t] + 5193.80628833877M7[t] + 6833.78978898882M8[t] + 414.960401560134M9[t] -1019.94060234020M10[t] -352.491104290366M11[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) | 317487.905437682 | 28089.187605 | 11.3029 | 0 | 0 |
| X | -5289.50501950168 | 3793.843694 | -1.3942 | 0.168854 | 0.084427 |
| M1 | 4994.36570923069 | 11596.336277 | 0.4307 | 0.668381 | 0.33419 |
| M2 | 6573.16604386424 | 11638.185385 | 0.5648 | 0.574511 | 0.287256 |
| M3 | 7132.07362427232 | 11551.60165 | 0.6174 | 0.539512 | 0.269756 |
| M4 | 3824.18911972193 | 11471.859556 | 0.3334 | 0.740135 | 0.370067 |
| M5 | 2881.13794850487 | 11460.143441 | 0.2514 | 0.802438 | 0.401219 |
| M6 | 2923.21219557962 | 11488.68054 | 0.2544 | 0.800102 | 0.400051 |
| M7 | 5193.80628833877 | 11497.759898 | 0.4517 | 0.653245 | 0.326622 |
| M8 | 6833.78978898882 | 11509.159816 | 0.5938 | 0.555101 | 0.27755 |
| M9 | 414.960401560134 | 11969.722155 | 0.0347 | 0.97247 | 0.486235 |
| M10 | -1019.94060234020 | 11974.531075 | -0.0852 | 0.932431 | 0.466215 |
| M11 | -352.491104290366 | 11994.947476 | -0.0294 | 0.976663 | 0.488331 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.213187085790247 |
| R-squared | 0.0454487335477382 |
| Adjusted R-squared | -0.162816997314573 |
| F-TEST (value) | 0.218224733178908 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 55 |
| p-value | 0.996878762606105 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 18919.7074278135 |
| Sum Squared Residuals | 19687543103.4735 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 269285 | 279108.329986999 | -9823.32998699944 |
| 2 | 269829 | 281745.031325533 | -11916.0313255327 |
| 3 | 270911 | 284948.691415692 | -14037.6914156916 |
| 4 | 266844 | 285343.460424792 | -18499.4604247924 |
| 5 | 271244 | 285987.260759426 | -14743.2607594258 |
| 6 | 269907 | 285500.384504550 | -15593.3845045504 |
| 7 | 271296 | 282481.473577808 | -11185.4735778079 |
| 8 | 270157 | 282005.655070657 | -11848.6550706572 |
| 9 | 271322 | 275057.875181278 | -3735.87518127840 |
| 10 | 267179 | 275738.776185179 | -8559.77618517873 |
| 11 | 264101 | 277464.126687129 | -13363.1266871289 |
| 12 | 265518 | 277287.667289469 | -11769.6672894691 |
| 13 | 269419 | 281224.131994799 | -11805.1319947995 |
| 14 | 268714 | 282802.932329433 | -14088.932329433 |
| 15 | 272482 | 283361.839909841 | -10879.8399098411 |
| 16 | 268351 | 281640.806911141 | -13289.8069111412 |
| 17 | 268175 | 280697.755739924 | -12522.7557399241 |
| 18 | 270674 | 282855.631994800 | -12181.6319947996 |
| 19 | 272764 | 283010.424079758 | -10246.4240797580 |
| 20 | 272599 | 284650.407580408 | -12051.4075804081 |
| 21 | 270333 | 277702.627691029 | -7369.62769102923 |
| 22 | 270846 | 275738.776185179 | -4892.77618517873 |
| 23 | 270491 | 276406.225683229 | -5915.22568322856 |
| 24 | 269160 | 275700.815783619 | -6540.81578361859 |
| 25 | 274027 | 279637.280488949 | -5610.28048894894 |
| 26 | 273784 | 280687.130321632 | -6903.13032163233 |
| 27 | 276663 | 281246.037902040 | -4583.03790204042 |
| 28 | 274525 | 277938.15339749 | -3413.15339749002 |
| 29 | 271344 | 278581.953732123 | -7237.95373212347 |
| 30 | 271115 | 281797.730990899 | -10682.7309908992 |
| 31 | 270798 | 286184.127091459 | -15386.1270914590 |
| 32 | 273911 | 289410.962097960 | -15499.9620979596 |
| 33 | 273985 | 282463.182208581 | -8478.18220858074 |
| 34 | 271917 | 279970.38020078 | -8053.38020078007 |
| 35 | 273338 | 280108.87919688 | -6770.87919687974 |
| 36 | 270601 | 279932.41979922 | -9331.41979921994 |
| 37 | 273547 | 284397.835006500 | -10850.8350065005 |
| 38 | 275363 | 286505.585843084 | -11142.5858430842 |
| 39 | 281229 | 288122.394427393 | -6893.39442739259 |
| 40 | 277793 | 284285.559420892 | -6492.55942089202 |
| 41 | 279913 | 284400.409253575 | -4487.40925357531 |
| 42 | 282500 | 286558.285508451 | -4058.28550845072 |
| 43 | 280041 | 287242.028095359 | -7201.02809535937 |
| 44 | 282166 | 289410.962097960 | -7244.96209795959 |
| 45 | 290304 | 284050.033714431 | 6253.96628556876 |
| 46 | 283519 | 283144.083212481 | 374.916787518922 |
| 47 | 287816 | 284340.483212481 | 3475.51678751892 |
| 48 | 285226 | 283106.122810921 | 2119.87718907906 |
| 49 | 287595 | 286513.637014301 | 1081.36298569888 |
| 50 | 289741 | 288092.437348935 | 1648.56265106533 |
| 51 | 289148 | 290767.146937143 | -1619.14693714342 |
| 52 | 288301 | 289046.113938444 | -745.113938443531 |
| 53 | 290155 | 289689.914273077 | 465.085726923015 |
| 54 | 289648 | 288145.137014301 | 1502.86298569877 |
| 55 | 288225 | 284597.275585609 | 3627.72441439147 |
| 56 | 289351 | 285708.308584308 | 3642.69141569158 |
| 57 | 294735 | 281405.28120468 | 13329.7187953196 |
| 58 | 305333 | 284201.984216381 | 21131.0157836186 |
| 59 | 309030 | 286456.285220282 | 22573.7147797182 |
| 60 | 310215 | 284692.974316771 | 25522.0256832286 |
| 61 | 321935 | 284926.785508451 | 37008.2144915494 |
| 62 | 325734 | 283331.882831383 | 42402.1171686168 |
| 63 | 320846 | 282832.889407891 | 38013.1105921091 |
| 64 | 323023 | 280582.905907241 | 42440.0940927591 |
| 65 | 319753 | 281226.706241874 | 38526.2937581257 |
| 66 | 321753 | 280739.829986999 | 41013.1700130011 |
| 67 | 320757 | 280365.671570007 | 40391.3284299928 |
| 68 | 324479 | 281476.704568707 | 43002.2954312929 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 4.04726383938087e-05 | 8.09452767876174e-05 | 0.999959527361606 |
| 17 | 3.9635164909055e-05 | 7.927032981811e-05 | 0.99996036483509 |
| 18 | 2.7899084026308e-06 | 5.5798168052616e-06 | 0.999997210091597 |
| 19 | 2.1997906532819e-07 | 4.3995813065638e-07 | 0.999999780020935 |
| 20 | 2.5628955899716e-08 | 5.1257911799432e-08 | 0.999999974371044 |
| 21 | 2.06248990383508e-09 | 4.12497980767016e-09 | 0.99999999793751 |
| 22 | 8.60435482866107e-10 | 1.72087096573221e-09 | 0.999999999139564 |
| 23 | 2.56441790436846e-09 | 5.12883580873693e-09 | 0.999999997435582 |
| 24 | 5.96786655598481e-10 | 1.19357331119696e-09 | 0.999999999403213 |
| 25 | 3.21063236347167e-10 | 6.42126472694335e-10 | 0.999999999678937 |
| 26 | 1.37950811913018e-10 | 2.75901623826036e-10 | 0.99999999986205 |
| 27 | 5.37675037074263e-11 | 1.07535007414853e-10 | 0.999999999946233 |
| 28 | 2.35299604439305e-11 | 4.7059920887861e-11 | 0.99999999997647 |
| 29 | 7.35448261911208e-12 | 1.47089652382242e-11 | 0.999999999992645 |
| 30 | 2.07098427221814e-12 | 4.14196854443628e-12 | 0.999999999997929 |
| 31 | 3.27682319596922e-13 | 6.55364639193843e-13 | 0.999999999999672 |
| 32 | 2.24942649977273e-13 | 4.49885299954545e-13 | 0.999999999999775 |
| 33 | 1.22913332100359e-13 | 2.45826664200718e-13 | 0.999999999999877 |
| 34 | 7.51178128900476e-14 | 1.50235625780095e-13 | 0.999999999999925 |
| 35 | 4.03046746371523e-13 | 8.06093492743047e-13 | 0.999999999999597 |
| 36 | 9.98760480636597e-13 | 1.99752096127319e-12 | 0.999999999999001 |
| 37 | 1.93846373570703e-12 | 3.87692747141405e-12 | 0.999999999998062 |
| 38 | 3.78648413945245e-12 | 7.57296827890491e-12 | 0.999999999996213 |
| 39 | 1.08072496182894e-11 | 2.16144992365788e-11 | 0.999999999989193 |
| 40 | 1.35726153600103e-10 | 2.71452307200205e-10 | 0.999999999864274 |
| 41 | 4.67434826407799e-09 | 9.34869652815598e-09 | 0.999999995325652 |
| 42 | 3.31522028514376e-08 | 6.63044057028753e-08 | 0.999999966847797 |
| 43 | 2.34034184644552e-08 | 4.68068369289105e-08 | 0.999999976596581 |
| 44 | 1.81622521119419e-08 | 3.63245042238839e-08 | 0.999999981837748 |
| 45 | 1.31141761759197e-07 | 2.62283523518394e-07 | 0.999999868858238 |
| 46 | 6.70895848320283e-07 | 1.34179169664057e-06 | 0.999999329104152 |
| 47 | 2.3674338603258e-05 | 4.7348677206516e-05 | 0.999976325661397 |
| 48 | 0.00165179409963221 | 0.00330358819926441 | 0.998348205900368 |
| 49 | 0.0443011645309187 | 0.0886023290618375 | 0.955698835469081 |
| 50 | 0.102251011352816 | 0.204502022705633 | 0.897748988647184 |
| 51 | 0.062598301759448 | 0.125196603518896 | 0.937401698240552 |
| 52 | 0.0364844893224037 | 0.0729689786448073 | 0.963515510677596 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 33 | 0.891891891891892 | NOK |
| 5% type I error level | 33 | 0.891891891891892 | NOK |
| 10% type I error level | 35 | 0.945945945945946 | NOK |
