| Multiple Linear Regression - Estimated Regression Equation |
| y[t] = + 11299.1094197952 + 7.00716723549491x[t] + 1046.03710466439M1[t] -927.165312855518M2[t] -2065.70663822526M3[t] + 654.692036405005M4[t] + 965.910711035267M5[t] + 597.789385665529M6[t] -935.93193970421M7[t] -56.9346985210472M8[t] -47.3160238907847M9[t] + 1621.50265073948M10[t] + 426.641325369738M11[t] + 82.1613253697383t + 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) | 11299.1094197952 | 406.218187 | 27.8154 | 0 | 0 |
| x | 7.00716723549491 | 349.337996 | 0.0201 | 0.984082 | 0.492041 |
| M1 | 1046.03710466439 | 454.500279 | 2.3015 | 0.025843 | 0.012921 |
| M2 | -927.165312855518 | 476.877883 | -1.9442 | 0.057866 | 0.028933 |
| M3 | -2065.70663822526 | 476.307928 | -4.3369 | 7.6e-05 | 3.8e-05 |
| M4 | 654.692036405005 | 475.906784 | 1.3757 | 0.175444 | 0.087722 |
| M5 | 965.910711035267 | 475.674878 | 2.0306 | 0.047974 | 0.023987 |
| M6 | 597.789385665529 | 475.612459 | 1.2569 | 0.215006 | 0.107503 |
| M7 | -935.93193970421 | 475.719592 | -1.9674 | 0.055054 | 0.027527 |
| M8 | -56.9346985210472 | 475.023262 | -0.1199 | 0.905108 | 0.452554 |
| M9 | -47.3160238907847 | 474.428663 | -0.0997 | 0.920981 | 0.46049 |
| M10 | 1621.50265073948 | 474.003492 | 3.4209 | 0.001301 | 0.000651 |
| M11 | 426.641325369738 | 473.748207 | 0.9006 | 0.372411 | 0.186205 |
| t | 82.1613253697383 | 8.98048 | 9.1489 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.93959849877296 |
| R-squared | 0.8828453388964 |
| Adjusted R-squared | 0.850440858165617 |
| F-TEST (value) | 27.2445451674136 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 47 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 748.92709043569 |
| Sum Squared Residuals | 26361913.979058 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 12192.5 | 12427.3078498293 | -234.807849829343 |
| 2 | 11268.8 | 10536.2667576792 | 732.533242320818 |
| 3 | 9097.4 | 9479.88675767918 | -382.486757679182 |
| 4 | 12639.8 | 12282.4467576792 | 357.353242320818 |
| 5 | 13040.1 | 12675.8267576792 | 364.273242320819 |
| 6 | 11687.3 | 12389.8667576792 | -702.566757679182 |
| 7 | 11191.7 | 10938.3067576792 | 253.393242320819 |
| 8 | 11391.9 | 11899.4653242321 | -507.565324232083 |
| 9 | 11793.1 | 11991.2453242321 | -198.145324232082 |
| 10 | 13933.2 | 13742.2253242321 | 190.974675767919 |
| 11 | 12778.1 | 12629.5253242321 | 148.574675767918 |
| 12 | 11810.3 | 12285.0453242321 | -474.745324232083 |
| 13 | 13698.4 | 13413.2437542662 | 285.156245733786 |
| 14 | 11956.6 | 11522.2026621160 | 434.39733788396 |
| 15 | 10723.8 | 10465.8226621160 | 257.977337883958 |
| 16 | 13938.9 | 13268.3826621160 | 670.517337883959 |
| 17 | 13979.8 | 13661.7626621160 | 318.037337883959 |
| 18 | 13807.4 | 13375.8026621160 | 431.597337883959 |
| 19 | 12973.9 | 11924.2426621160 | 1049.65733788396 |
| 20 | 12509.8 | 12885.4012286689 | -375.601228668943 |
| 21 | 12934.1 | 12977.1812286689 | -43.0812286689418 |
| 22 | 14908.3 | 14728.1612286689 | 180.138771331057 |
| 23 | 13772.1 | 13615.4612286689 | 156.638771331059 |
| 24 | 13012.6 | 13270.9812286689 | -258.381228668942 |
| 25 | 14049.9 | 14399.1796587031 | -349.279658703074 |
| 26 | 11816.5 | 12508.1385665529 | -691.638566552901 |
| 27 | 11593.2 | 11451.7585665529 | 141.441433447099 |
| 28 | 14466.2 | 14254.3185665529 | 211.8814334471 |
| 29 | 13615.9 | 14647.6985665529 | -1031.7985665529 |
| 30 | 14733.9 | 14361.7385665529 | 372.161433447099 |
| 31 | 13880.7 | 12910.1785665529 | 970.5214334471 |
| 32 | 13527.5 | 13871.3371331058 | -343.837133105801 |
| 33 | 13584 | 13963.1171331058 | -379.117133105802 |
| 34 | 16170.2 | 15714.0971331058 | 456.102866894198 |
| 35 | 13260.6 | 14601.3971331058 | -1340.79713310580 |
| 36 | 14741.9 | 14256.9171331058 | 484.982866894197 |
| 37 | 15486.5 | 15385.1155631399 | 101.384436860067 |
| 38 | 13154.5 | 13494.0744709898 | -339.574470989761 |
| 39 | 12621.2 | 12437.6944709898 | 183.505529010240 |
| 40 | 15031.6 | 15240.2544709898 | -208.654470989760 |
| 41 | 15452.4 | 15633.6344709898 | -181.234470989760 |
| 42 | 15428 | 15347.6744709898 | 80.3255290102399 |
| 43 | 13105.9 | 13896.1144709898 | -790.214470989761 |
| 44 | 14716.8 | 14864.2802047782 | -147.480204778157 |
| 45 | 14180 | 14956.0602047782 | -776.060204778158 |
| 46 | 16202.2 | 16707.0402047782 | -504.840204778156 |
| 47 | 14392.4 | 15594.3402047782 | -1201.94020477816 |
| 48 | 15140.6 | 15249.8602047782 | -109.260204778157 |
| 49 | 15960.1 | 16378.0586348123 | -417.958634812288 |
| 50 | 14351.3 | 14487.0175426621 | -135.717542662116 |
| 51 | 13230.2 | 13430.6375426621 | -200.437542662115 |
| 52 | 15202.1 | 16233.1975426621 | -1031.09754266212 |
| 53 | 17157.3 | 16626.5775426621 | 530.722457337883 |
| 54 | 16159.1 | 16340.6175426621 | -181.517542662115 |
| 55 | 13405.7 | 14889.0575426621 | -1483.35754266212 |
| 56 | 17224.7 | 15850.2161092150 | 1374.48389078498 |
| 57 | 17338.4 | 15941.9961092150 | 1396.40389078498 |
| 58 | 17370.6 | 17692.9761092150 | -322.376109215018 |
| 59 | 18817.8 | 16580.2761092150 | 2237.52389078498 |
| 60 | 16593.2 | 16235.7961092150 | 357.403890784984 |
| 61 | 17979.5 | 17363.9945392491 | 615.505460750852 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0662761513527165 | 0.132552302705433 | 0.933723848647284 |
| 18 | 0.076178075808031 | 0.152356151616062 | 0.923821924191969 |
| 19 | 0.0504963420663837 | 0.100992684132767 | 0.949503657933616 |
| 20 | 0.0229111196721132 | 0.0458222393442264 | 0.977088880327887 |
| 21 | 0.00949749618991345 | 0.0189949923798269 | 0.990502503810087 |
| 22 | 0.00475177993650222 | 0.00950355987300444 | 0.995248220063498 |
| 23 | 0.00223821910311672 | 0.00447643820623343 | 0.997761780896883 |
| 24 | 0.00075702873566451 | 0.00151405747132902 | 0.999242971264335 |
| 25 | 0.00112193537305074 | 0.00224387074610148 | 0.99887806462695 |
| 26 | 0.0110842989969933 | 0.0221685979939866 | 0.988915701003007 |
| 27 | 0.00569316812682057 | 0.0113863362536411 | 0.99430683187318 |
| 28 | 0.00442644519293138 | 0.00885289038586277 | 0.995573554807069 |
| 29 | 0.0116953622870498 | 0.0233907245740995 | 0.98830463771295 |
| 30 | 0.0105982307726674 | 0.0211964615453349 | 0.989401769227333 |
| 31 | 0.0893876040153979 | 0.178775208030796 | 0.910612395984602 |
| 32 | 0.0617823272664603 | 0.123564654532921 | 0.93821767273354 |
| 33 | 0.039244899752331 | 0.078489799504662 | 0.960755100247669 |
| 34 | 0.0479995596918256 | 0.0959991193836511 | 0.952000440308174 |
| 35 | 0.190030213120053 | 0.380060426240107 | 0.809969786879946 |
| 36 | 0.210299681561760 | 0.420599363123519 | 0.78970031843824 |
| 37 | 0.160733038120358 | 0.321466076240716 | 0.839266961879642 |
| 38 | 0.119286192726631 | 0.238572385453262 | 0.88071380727337 |
| 39 | 0.0751012439432984 | 0.150202487886597 | 0.924898756056702 |
| 40 | 0.0575824135885074 | 0.115164827177015 | 0.942417586411493 |
| 41 | 0.0492823560427836 | 0.0985647120855671 | 0.950717643957216 |
| 42 | 0.0263139011772264 | 0.0526278023544529 | 0.973686098822774 |
| 43 | 0.0266388490337116 | 0.0532776980674232 | 0.973361150966288 |
| 44 | 0.0107824422619315 | 0.0215648845238630 | 0.989217557738069 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 5 | 0.178571428571429 | NOK |
| 5% type I error level | 12 | 0.428571428571429 | NOK |
| 10% type I error level | 17 | 0.607142857142857 | NOK |
