| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -30.9802710985411 + 115.500191970367X[t] + 17.2956251455641t + 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) | -30.9802710985411 | 338.976556 | -0.0914 | 0.927449 | 0.463724 |
| X | 115.500191970367 | 10.741034 | 10.7532 | 0 | 0 |
| t | 17.2956251455641 | 3.585723 | 4.8235 | 8e-06 | 4e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.795247840667979 |
| R-squared | 0.632419128087083 |
| Adjusted R-squared | 0.621607925971997 |
| F-TEST (value) | 58.4966520239793 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 68 |
| p-value | 1.66533453693773e-15 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 521.185047863245 |
| Sum Squared Residuals | 18471102.0799025 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2350.44 | 3104.82053724692 | -754.380537246918 |
| 2 | 2440.25 | 3353.11654633322 | -912.866546333219 |
| 3 | 2408.64 | 3139.41178753805 | -730.77178753805 |
| 4 | 2472.81 | 3041.20722071325 | -568.397220713247 |
| 5 | 2407.6 | 2827.50246191808 | -419.902461918078 |
| 6 | 2454.62 | 3537.79923888584 | -1083.17923888584 |
| 7 | 2448.05 | 3093.09409614994 | -645.04409614994 |
| 8 | 2497.84 | 3341.39010523624 | -843.550105236237 |
| 9 | 2645.64 | 3358.6857303818 | -713.045730381801 |
| 10 | 2756.76 | 2913.9805876459 | -157.220587645898 |
| 11 | 2849.27 | 2815.77602082110 | 33.493979178904 |
| 12 | 2921.44 | 2948.57183793703 | -27.1318379370266 |
| 13 | 2981.85 | 2965.86746308259 | 15.9825369174092 |
| 14 | 3080.58 | 3329.66366413925 | -249.083664139255 |
| 15 | 3106.22 | 3462.45948125519 | -356.239481255186 |
| 16 | 3119.31 | 3133.25453048965 | -13.9445304896497 |
| 17 | 3061.26 | 2457.54900381301 | 603.710996186987 |
| 18 | 3097.31 | 2474.84462895858 | 622.465371041422 |
| 19 | 3161.69 | 2492.14025410414 | 669.549745895858 |
| 20 | 3257.16 | 2624.93607122007 | 632.223928779927 |
| 21 | 3277.01 | 2180.23092848417 | 1096.77907151583 |
| 22 | 3295.32 | 2890.52770545193 | 404.792294548066 |
| 23 | 3363.99 | 2792.32313862713 | 571.666861372868 |
| 24 | 3494.17 | 3271.61953165416 | 222.550468345838 |
| 25 | 3667.03 | 3750.91592468119 | -83.8859246811926 |
| 26 | 3813.06 | 3652.71135785639 | 160.348642143610 |
| 27 | 3917.96 | 3323.50640709085 | 594.453592909146 |
| 28 | 3895.51 | 3456.30222420679 | 439.207775793215 |
| 29 | 3801.06 | 3242.59746541162 | 558.462534588384 |
| 30 | 3570.12 | 3721.89385843865 | -151.773858438647 |
| 31 | 3701.61 | 3739.18948358421 | -37.5794835842104 |
| 32 | 3862.27 | 3756.48510872977 | 105.784891270225 |
| 33 | 3970.1 | 3773.78073387534 | 196.319266124661 |
| 34 | 4138.52 | 4253.07712690237 | -114.557126902369 |
| 35 | 4199.75 | 4154.87256007757 | 44.8774399224332 |
| 36 | 4290.89 | 3132.66645748983 | 1158.22354251017 |
| 37 | 4443.91 | 3958.46342642796 | 485.446573572038 |
| 38 | 4502.64 | 4206.75943551426 | 295.880564485741 |
| 39 | 4356.98 | 3993.05467671909 | 363.92532328091 |
| 40 | 4591.27 | 4356.85087777575 | 234.419122224247 |
| 41 | 4696.96 | 4374.14650292132 | 322.813497078682 |
| 42 | 4621.4 | 4275.94193609651 | 345.458063903484 |
| 43 | 4562.84 | 4062.23717730135 | 500.602822698654 |
| 44 | 4202.52 | 3964.03261047654 | 238.487389523457 |
| 45 | 4296.49 | 3981.32823562211 | 315.161764377892 |
| 46 | 4435.23 | 4114.12405273804 | 321.105947261961 |
| 47 | 4105.18 | 3322.91833409104 | 782.261665908965 |
| 48 | 4116.68 | 3802.21472711807 | 314.465272881934 |
| 49 | 3844.49 | 3588.5099683229 | 255.980031677102 |
| 50 | 3720.98 | 3952.30616937956 | -231.326169379561 |
| 51 | 3674.4 | 3969.60179452513 | -295.201794525125 |
| 52 | 3857.62 | 3524.89665178922 | 332.723348210777 |
| 53 | 3801.06 | 3311.19189299405 | 489.868107005946 |
| 54 | 3504.37 | 3097.48713419888 | 406.882865801115 |
| 55 | 3032.6 | 2883.78237540372 | 148.817624596285 |
| 56 | 3047.03 | 3132.07838449001 | -85.0483844900124 |
| 57 | 2962.34 | 3380.37439357631 | -418.03439357631 |
| 58 | 2197.82 | 2473.66848295894 | -275.848482958941 |
| 59 | 2014.45 | 1913.46314825267 | 100.986851747328 |
| 60 | 1862.83 | 1584.25819748714 | 278.571802512864 |
| 61 | 1905.41 | 2179.05478248453 | -273.644782484533 |
| 62 | 1810.99 | 1734.34963974863 | 76.6403602513692 |
| 63 | 1670.07 | 1751.64526489419 | -81.575264894195 |
| 64 | 1864.44 | 1999.94127398049 | -135.501273980492 |
| 65 | 2052.02 | 2363.73747503716 | -311.717475037156 |
| 66 | 2029.6 | 2496.53329215309 | -466.933292153087 |
| 67 | 2070.83 | 2629.32910926902 | -558.499109269018 |
| 68 | 2293.41 | 3339.62588623678 | -1046.21588623678 |
| 69 | 2443.27 | 3356.92151138235 | -913.651511382345 |
| 70 | 2513.17 | 3258.71694455754 | -745.546944557543 |
| 71 | 2466.92 | 3507.01295364384 | -1040.09295364384 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.00102668144419874 | 0.00205336288839748 | 0.998973318555801 |
| 7 | 9.12010137824352e-05 | 0.000182402027564870 | 0.999908798986218 |
| 8 | 9.19373795798606e-06 | 1.83874759159721e-05 | 0.999990806262042 |
| 9 | 2.98002280332412e-05 | 5.96004560664823e-05 | 0.999970199771967 |
| 10 | 7.1261832432127e-05 | 0.000142523664864254 | 0.999928738167568 |
| 11 | 4.57827162826245e-05 | 9.15654325652489e-05 | 0.999954217283717 |
| 12 | 2.67812251226739e-05 | 5.35624502453479e-05 | 0.999973218774877 |
| 13 | 1.24133821541939e-05 | 2.48267643083878e-05 | 0.999987586617846 |
| 14 | 1.47910185554862e-05 | 2.95820371109723e-05 | 0.999985208981444 |
| 15 | 1.07837206629824e-05 | 2.15674413259648e-05 | 0.999989216279337 |
| 16 | 4.60184083977071e-06 | 9.20368167954142e-06 | 0.99999539815916 |
| 17 | 1.92709806946177e-06 | 3.85419613892355e-06 | 0.99999807290193 |
| 18 | 6.68576701161044e-07 | 1.33715340232209e-06 | 0.9999993314233 |
| 19 | 1.87044193950222e-07 | 3.74088387900444e-07 | 0.999999812955806 |
| 20 | 4.60602315516615e-08 | 9.2120463103323e-08 | 0.999999953939768 |
| 21 | 1.18953009013329e-08 | 2.37906018026658e-08 | 0.9999999881047 |
| 22 | 4.8473220705328e-09 | 9.6946441410656e-09 | 0.999999995152678 |
| 23 | 1.29785872319355e-09 | 2.59571744638709e-09 | 0.99999999870214 |
| 24 | 4.02779256391995e-10 | 8.0555851278399e-10 | 0.99999999959722 |
| 25 | 3.69342650349873e-10 | 7.38685300699745e-10 | 0.999999999630657 |
| 26 | 5.70709356733038e-10 | 1.14141871346608e-09 | 0.99999999942929 |
| 27 | 1.28448963018446e-09 | 2.56897926036891e-09 | 0.99999999871551 |
| 28 | 5.03902086140383e-10 | 1.00780417228077e-09 | 0.999999999496098 |
| 29 | 1.69088989558892e-10 | 3.38177979117785e-10 | 0.999999999830911 |
| 30 | 1.2353993465258e-07 | 2.4707986930516e-07 | 0.999999876460065 |
| 31 | 1.41738596497632e-06 | 2.83477192995265e-06 | 0.999998582614035 |
| 32 | 3.53074540526981e-06 | 7.06149081053963e-06 | 0.999996469254595 |
| 33 | 6.78814541456882e-06 | 1.35762908291376e-05 | 0.999993211854585 |
| 34 | 6.97300541571676e-05 | 0.000139460108314335 | 0.999930269945843 |
| 35 | 0.000659962238123255 | 0.00131992447624651 | 0.999340037761877 |
| 36 | 0.000626782898489448 | 0.00125356579697890 | 0.99937321710151 |
| 37 | 0.000969739659123436 | 0.00193947931824687 | 0.999030260340876 |
| 38 | 0.00163033196053022 | 0.00326066392106044 | 0.99836966803947 |
| 39 | 0.00185918981677770 | 0.00371837963355541 | 0.998140810183222 |
| 40 | 0.00235482604570854 | 0.00470965209141707 | 0.997645173954292 |
| 41 | 0.00221101430769277 | 0.00442202861538554 | 0.997788985692307 |
| 42 | 0.00139095149524300 | 0.00278190299048601 | 0.998609048504757 |
| 43 | 0.000881015551712103 | 0.00176203110342421 | 0.999118984448288 |
| 44 | 0.0144904202961532 | 0.0289808405923064 | 0.985509579703847 |
| 45 | 0.0349249667234579 | 0.0698499334469157 | 0.965075033276542 |
| 46 | 0.0401378699316444 | 0.0802757398632889 | 0.959862130068356 |
| 47 | 0.182076585365441 | 0.364153170730881 | 0.81792341463456 |
| 48 | 0.331786742044383 | 0.663573484088766 | 0.668213257955617 |
| 49 | 0.594081979422888 | 0.811836041154224 | 0.405918020577112 |
| 50 | 0.875712956374629 | 0.248574087250742 | 0.124287043625371 |
| 51 | 0.980369604037913 | 0.0392607919241736 | 0.0196303959620868 |
| 52 | 0.982272958549966 | 0.0354540829000683 | 0.0177270414500342 |
| 53 | 0.995353054318079 | 0.00929389136384191 | 0.00464694568192096 |
| 54 | 0.999740104787878 | 0.000519790424243005 | 0.000259895212121502 |
| 55 | 0.999941753008288 | 0.000116493983423989 | 5.82469917119945e-05 |
| 56 | 0.999987390346677 | 2.52193066461695e-05 | 1.26096533230848e-05 |
| 57 | 0.999995877554644 | 8.2448907114044e-06 | 4.1224453557022e-06 |
| 58 | 0.999990888002567 | 1.82239948653831e-05 | 9.11199743269157e-06 |
| 59 | 0.99998525356801 | 2.94928639815058e-05 | 1.47464319907529e-05 |
| 60 | 0.99999002657879 | 1.99468424198326e-05 | 9.9734212099163e-06 |
| 61 | 0.99995965927586 | 8.06814482811266e-05 | 4.03407241405633e-05 |
| 62 | 0.99991464514875 | 0.000170709702498171 | 8.53548512490857e-05 |
| 63 | 0.99965746433913 | 0.000685071321738711 | 0.000342535660869356 |
| 64 | 0.997862956800195 | 0.00427408639961012 | 0.00213704319980506 |
| 65 | 0.99295094297214 | 0.0140981140557201 | 0.00704905702786004 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 50 | 0.833333333333333 | NOK |
| 5% type I error level | 54 | 0.9 | NOK |
| 10% type I error level | 56 | 0.933333333333333 | NOK |
