| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 7378.28355988144 + 3.95381014494266X[t] + 6461.74593137428M1[t] + 4918.47723861162M2[t] + 3506.72080584833M3[t] + 4679.62057135073M4[t] + 5504.75273192363M5[t] + 6198.70800814803M6[t] + 7252.52025307776M7[t] + 5491.07357394325M8[t] + 4915.84217683649M9[t] + 3132.54862030323M10[t] + 2278.21743653034M11[t] -215.719989563514t + 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) | 7378.28355988144 | 2945.752256 | 2.5047 | 0.015861 | 0.00793 |
| X | 3.95381014494266 | 0.812262 | 4.8677 | 1.4e-05 | 7e-06 |
| M1 | 6461.74593137428 | 3219.306232 | 2.0072 | 0.050627 | 0.025313 |
| M2 | 4918.47723861162 | 2925.344267 | 1.6813 | 0.099477 | 0.049738 |
| M3 | 3506.72080584833 | 2629.965705 | 1.3334 | 0.188976 | 0.094488 |
| M4 | 4679.62057135073 | 2527.999725 | 1.8511 | 0.070579 | 0.03529 |
| M5 | 5504.75273192363 | 2368.659055 | 2.324 | 0.024597 | 0.012299 |
| M6 | 6198.70800814803 | 2210.59078 | 2.8041 | 0.007366 | 0.003683 |
| M7 | 7252.52025307776 | 2327.574203 | 3.1159 | 0.003156 | 0.001578 |
| M8 | 5491.07357394325 | 2266.580054 | 2.4226 | 0.019405 | 0.009702 |
| M9 | 4915.84217683649 | 2177.697695 | 2.2574 | 0.028777 | 0.014389 |
| M10 | 3132.54862030323 | 1991.630336 | 1.5729 | 0.122606 | 0.061303 |
| M11 | 2278.21743653034 | 1959.230055 | 1.1628 | 0.250903 | 0.125451 |
| t | -215.719989563514 | 28.521856 | -7.5633 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.813060614890317 |
| R-squared | 0.661067563485821 |
| Adjusted R-squared | 0.565282309688335 |
| F-TEST (value) | 6.90155882327656 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 3.96688436321568e-07 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3046.67568215229 |
| Sum Squared Residuals | 426982704.762034 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10144 | 14067.1362379258 | -3923.13623792581 |
| 2 | 10751 | 13067.2791034286 | -2316.2791034286 |
| 3 | 11752 | 13377.1696521237 | -1625.16965212370 |
| 4 | 13808 | 14757.4071135715 | -949.407113571461 |
| 5 | 16203 | 16675.5304425569 | -472.530442556864 |
| 6 | 17432 | 17185.3962103773 | 246.603789622711 |
| 7 | 18014 | 17201.0959555954 | 812.904044404558 |
| 8 | 16956 | 15670.7098332759 | 1285.29016672406 |
| 9 | 17982 | 16631.2963408153 | 1350.70365918475 |
| 10 | 19435 | 17305.0584526997 | 2129.94154730029 |
| 11 | 19990 | 16017.5477213915 | 3972.45227860853 |
| 12 | 20154 | 16322.9078779170 | 3831.09212208298 |
| 13 | 10327 | 11996.4454921511 | -1669.44549215111 |
| 14 | 9807 | 11482.9070054819 | -1675.90700548187 |
| 15 | 10862 | 12544.0214817161 | -1682.02148171608 |
| 16 | 13743 | 14545.0071359198 | -802.00713591983 |
| 17 | 16458 | 17123.4167591107 | -665.416759110656 |
| 18 | 18466 | 18178.9083269332 | 287.091673066823 |
| 19 | 18810 | 18700.6957707040 | 109.304229296019 |
| 20 | 17361 | 16644.4528991071 | 716.547100892892 |
| 21 | 17411 | 15481.8433588122 | 1929.15664118778 |
| 22 | 18517 | 16721.0003214235 | 1795.99967857652 |
| 23 | 18525 | 17655.530891573 | 869.469108426989 |
| 24 | 17859 | 18016.2443901278 | -157.244390127759 |
| 25 | 9499 | 10068.0919115944 | -569.091911594363 |
| 26 | 9490 | 11064.9089002932 | -1574.90890029323 |
| 27 | 9255 | 11473.6447026119 | -2218.64470261189 |
| 28 | 10758 | 13870.0113713099 | -3112.01137130991 |
| 29 | 12375 | 14677.1140495664 | -2302.11404956642 |
| 30 | 14617 | 16594.5362289864 | -1977.53622898645 |
| 31 | 15427 | 18761.1086930534 | -3334.1086930534 |
| 32 | 14136 | 17436.3206982709 | -3300.32069827092 |
| 33 | 14308 | 16574.2007289917 | -2266.20072899166 |
| 34 | 15293 | 17991.2791481253 | -2698.27914812535 |
| 35 | 15679 | 18218.0777023301 | -2539.07770233015 |
| 36 | 16319 | 19365.5994197285 | -3046.59941972848 |
| 37 | 11196 | 8131.83071074773 | 3064.16928925227 |
| 38 | 11169 | 8049.25752987725 | 3119.74247012275 |
| 39 | 12158 | 8050.75088726682 | 4107.24911273318 |
| 40 | 14251 | 9332.14309509101 | 4918.85690490899 |
| 41 | 16237 | 11337.2502472651 | 4899.74975273485 |
| 42 | 19706 | 15978.8476165507 | 3727.15238344933 |
| 43 | 18960 | 14733.2819255321 | 4226.7180744679 |
| 44 | 18537 | 14669.7593669863 | 3867.24063301367 |
| 45 | 19103 | 16298.5397890210 | 2804.46021097905 |
| 46 | 19691 | 17166.0385980076 | 2524.96140199239 |
| 47 | 19464 | 17072.5785304720 | 2391.42146952795 |
| 48 | 17264 | 13574.3733275628 | 3689.62667243724 |
| 49 | 8957 | 5859.49564758098 | 3097.50435241902 |
| 50 | 9703 | 7255.64746091905 | 2447.35253908095 |
| 51 | 9166 | 7747.41327628151 | 1418.58672371849 |
| 52 | 9519 | 9574.43128410779 | -55.4312841077877 |
| 53 | 10535 | 11994.6885015009 | -1459.68850150091 |
| 54 | 11526 | 13809.3116171524 | -2283.31161715242 |
| 55 | 9630 | 11444.8176551151 | -1814.81765511508 |
| 56 | 7061 | 9629.75720235971 | -2568.75720235971 |
| 57 | 6021 | 9839.11978235992 | -3818.11978235992 |
| 58 | 4728 | 8480.62347974385 | -3752.62347974385 |
| 59 | 2657 | 7351.26515423332 | -4694.26515423332 |
| 60 | 1264 | 5580.87498466397 | -4316.87498466397 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00356809153681226 | 0.00713618307362452 | 0.996431908463188 |
| 18 | 0.00075022431047229 | 0.00150044862094458 | 0.999249775689528 |
| 19 | 8.56748506512946e-05 | 0.000171349701302589 | 0.999914325149349 |
| 20 | 9.2675548917958e-06 | 1.85351097835916e-05 | 0.999990732445108 |
| 21 | 1.12815764249729e-06 | 2.25631528499459e-06 | 0.999998871842358 |
| 22 | 3.74303397903608e-07 | 7.48606795807215e-07 | 0.999999625696602 |
| 23 | 2.74098465785763e-06 | 5.48196931571526e-06 | 0.999997259015342 |
| 24 | 7.34818240664762e-06 | 1.46963648132952e-05 | 0.999992651817593 |
| 25 | 1.48352498926296e-06 | 2.96704997852593e-06 | 0.99999851647501 |
| 26 | 3.11337802941747e-07 | 6.22675605883494e-07 | 0.999999688662197 |
| 27 | 2.25773476370176e-07 | 4.51546952740352e-07 | 0.999999774226524 |
| 28 | 7.62023095888406e-07 | 1.52404619177681e-06 | 0.999999237976904 |
| 29 | 2.7765244417018e-06 | 5.5530488834036e-06 | 0.999997223475558 |
| 30 | 2.22377507220397e-06 | 4.44755014440795e-06 | 0.999997776224928 |
| 31 | 3.16853245085323e-06 | 6.33706490170646e-06 | 0.99999683146755 |
| 32 | 4.59469066445211e-06 | 9.18938132890421e-06 | 0.999995405309336 |
| 33 | 4.51110223721642e-06 | 9.02220447443284e-06 | 0.999995488897763 |
| 34 | 9.63390611245494e-06 | 1.92678122249099e-05 | 0.999990366093888 |
| 35 | 3.00676300578268e-05 | 6.01352601156536e-05 | 0.999969932369942 |
| 36 | 0.0383677813774291 | 0.0767355627548582 | 0.96163221862257 |
| 37 | 0.335151964786386 | 0.670303929572773 | 0.664848035213614 |
| 38 | 0.861772785746588 | 0.276454428506825 | 0.138227214253412 |
| 39 | 0.9929569169324 | 0.0140861661351998 | 0.00704308306759989 |
| 40 | 0.991517976782284 | 0.0169640464354322 | 0.00848202321771608 |
| 41 | 0.98256033462206 | 0.0348793307558788 | 0.0174396653779394 |
| 42 | 0.971726372760808 | 0.056547254478384 | 0.028273627239192 |
| 43 | 0.918865441294573 | 0.162269117410854 | 0.081134558705427 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 19 | 0.703703703703704 | NOK |
| 5% type I error level | 22 | 0.814814814814815 | NOK |
| 10% type I error level | 24 | 0.888888888888889 | NOK |
