| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 15515.9166666667 -2132.8410218254M1[t] -2859.02430555556M2[t] -1507.77901785714M3[t] -2251.39087301587M4[t] -1687.43129960317M5[t] -2357.90029761905M6[t] -2422.36929563492M7[t] -2104.69543650794M8[t] -2896.45014880952M9[t] -2143.91914682540M10[t] -2478.67385912698M11[t] + 77.7547123015873t + 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) | 15515.9166666667 | 129.27789 | 120.0199 | 0 | 0 |
| M1 | -2132.8410218254 | 159.023856 | -13.4121 | 0 | 0 |
| M2 | -2859.02430555556 | 158.904073 | -17.9921 | 0 | 0 |
| M3 | -1507.77901785714 | 158.79562 | -9.4951 | 0 | 0 |
| M4 | -2251.39087301587 | 158.69852 | -14.1866 | 0 | 0 |
| M5 | -1687.43129960317 | 158.612794 | -10.6387 | 0 | 0 |
| M6 | -2357.90029761905 | 158.538461 | -14.8727 | 0 | 0 |
| M7 | -2422.36929563492 | 158.475536 | -15.2854 | 0 | 0 |
| M8 | -2104.69543650794 | 158.424034 | -13.2852 | 0 | 0 |
| M9 | -2896.45014880952 | 158.383965 | -18.2875 | 0 | 0 |
| M10 | -2143.91914682540 | 158.355338 | -13.5387 | 0 | 0 |
| M11 | -2478.67385912698 | 158.338159 | -15.6543 | 0 | 0 |
| t | 77.7547123015873 | 1.346645 | 57.7396 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.99130582514897 |
| R-squared | 0.98268723897428 |
| Adjusted R-squared | 0.979761138519229 |
| F-TEST (value) | 335.83510001438 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 71 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 296.212858097258 |
| Sum Squared Residuals | 6229686.06845238 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 13328 | 13460.8303571429 | -132.830357142866 |
| 2 | 12873 | 12812.4017857143 | 60.5982142857136 |
| 3 | 14000 | 14241.4017857143 | -241.401785714286 |
| 4 | 13477 | 13575.5446428571 | -98.5446428571411 |
| 5 | 14237 | 14217.2589285714 | 19.7410714285714 |
| 6 | 13674 | 13624.5446428571 | 49.4553571428563 |
| 7 | 13529 | 13637.8303571429 | -108.830357142856 |
| 8 | 14058 | 14033.2589285714 | 24.7410714285723 |
| 9 | 12975 | 13319.2589285714 | -344.258928571428 |
| 10 | 14326 | 14149.5446428571 | 176.455357142858 |
| 11 | 14008 | 13892.5446428571 | 115.455357142857 |
| 12 | 16193 | 16448.9732142857 | -255.973214285714 |
| 13 | 14483 | 14393.8869047619 | 89.113095238095 |
| 14 | 14011 | 13745.4583333333 | 265.541666666668 |
| 15 | 15057 | 15174.4583333333 | -117.458333333333 |
| 16 | 14884 | 14508.6011904762 | 375.39880952381 |
| 17 | 15414 | 15150.3154761905 | 263.684523809524 |
| 18 | 14440 | 14557.6011904762 | -117.60119047619 |
| 19 | 14900 | 14570.8869047619 | 329.113095238095 |
| 20 | 15074 | 14966.3154761905 | 107.684523809524 |
| 21 | 14442 | 14252.3154761905 | 189.684523809524 |
| 22 | 15307 | 15082.6011904762 | 224.39880952381 |
| 23 | 14938 | 14825.6011904762 | 112.398809523810 |
| 24 | 17193 | 17382.0297619048 | -189.029761904762 |
| 25 | 15528 | 15326.9434523810 | 201.056547619049 |
| 26 | 14765 | 14678.5148809524 | 86.4851190476186 |
| 27 | 15838 | 16107.5148809524 | -269.514880952381 |
| 28 | 15723 | 15441.6577380952 | 281.342261904762 |
| 29 | 16150 | 16083.3720238095 | 66.6279761904768 |
| 30 | 15486 | 15490.6577380952 | -4.65773809523794 |
| 31 | 15986 | 15503.9434523810 | 482.056547619047 |
| 32 | 15983 | 15899.3720238095 | 83.6279761904762 |
| 33 | 15692 | 15185.3720238095 | 506.627976190476 |
| 34 | 16490 | 16015.6577380952 | 474.342261904762 |
| 35 | 15686 | 15758.6577380952 | -72.6577380952378 |
| 36 | 18897 | 18315.0863095238 | 581.91369047619 |
| 37 | 16316 | 16260 | 56.000000000002 |
| 38 | 15636 | 15611.5714285714 | 24.4285714285714 |
| 39 | 17163 | 17040.5714285714 | 122.428571428571 |
| 40 | 16534 | 16374.7142857143 | 159.285714285714 |
| 41 | 16518 | 17016.4285714286 | -498.428571428571 |
| 42 | 16375 | 16423.7142857143 | -48.7142857142856 |
| 43 | 16290 | 16437 | -147.000000000000 |
| 44 | 16352 | 16832.4285714286 | -480.428571428571 |
| 45 | 15943 | 16118.4285714286 | -175.428571428572 |
| 46 | 16362 | 16948.7142857143 | -586.714285714286 |
| 47 | 16393 | 16691.7142857143 | -298.714285714286 |
| 48 | 19051 | 19248.1428571429 | -197.142857142858 |
| 49 | 16747 | 17193.0565476190 | -446.056547619046 |
| 50 | 16320 | 16544.6279761905 | -224.627976190477 |
| 51 | 17910 | 17973.6279761905 | -63.6279761904764 |
| 52 | 16961 | 17307.7708333333 | -346.770833333334 |
| 53 | 17480 | 17949.4851190476 | -469.485119047619 |
| 54 | 17049 | 17356.7708333333 | -307.770833333333 |
| 55 | 16879 | 17370.0565476190 | -491.056547619048 |
| 56 | 17473 | 17765.4851190476 | -292.485119047619 |
| 57 | 16998 | 17051.4851190476 | -53.4851190476192 |
| 58 | 17307 | 17881.7708333333 | -574.770833333333 |
| 59 | 17418 | 17624.7708333333 | -206.770833333333 |
| 60 | 20169 | 20181.1994047619 | -12.1994047619036 |
| 61 | 17871 | 18126.1130952381 | -255.113095238093 |
| 62 | 17226 | 17477.6845238095 | -251.684523809524 |
| 63 | 19062 | 18906.6845238095 | 155.315476190476 |
| 64 | 17804 | 18240.8273809524 | -436.827380952381 |
| 65 | 19100 | 18882.5416666667 | 217.458333333332 |
| 66 | 18522 | 18289.8273809524 | 232.172619047619 |
| 67 | 18060 | 18303.1130952381 | -243.113095238095 |
| 68 | 18869 | 18698.5416666667 | 170.458333333332 |
| 69 | 18127 | 17984.5416666667 | 142.458333333333 |
| 70 | 18871 | 18814.8273809524 | 56.1726190476174 |
| 71 | 18890 | 18557.8273809524 | 332.172619047619 |
| 72 | 21263 | 21114.2559523810 | 148.744047619047 |
| 73 | 19547 | 19059.1696428571 | 487.830357142859 |
| 74 | 18450 | 18410.7410714286 | 39.2589285714294 |
| 75 | 20254 | 19839.7410714286 | 414.258928571429 |
| 76 | 19240 | 19173.8839285714 | 66.1160714285708 |
| 77 | 20216 | 19815.5982142857 | 400.401785714286 |
| 78 | 19420 | 19222.8839285714 | 197.116071428572 |
| 79 | 19415 | 19236.1696428571 | 178.830357142856 |
| 80 | 20018 | 19631.5982142857 | 386.401785714286 |
| 81 | 18652 | 18917.5982142857 | -265.598214285714 |
| 82 | 19978 | 19747.8839285714 | 230.116071428571 |
| 83 | 19509 | 19490.8839285714 | 18.1160714285713 |
| 84 | 21971 | 22047.3125 | -76.3125000000006 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0480796323752216 | 0.0961592647504431 | 0.951920367624778 |
| 17 | 0.0132432466795159 | 0.0264864933590317 | 0.986756753320484 |
| 18 | 0.0432107824099888 | 0.0864215648199775 | 0.956789217590011 |
| 19 | 0.0315084969136554 | 0.0630169938273108 | 0.968491503086345 |
| 20 | 0.0152933905266357 | 0.0305867810532714 | 0.984706609473364 |
| 21 | 0.0158812131725255 | 0.0317624263450509 | 0.984118786827475 |
| 22 | 0.00966682614310173 | 0.0193336522862035 | 0.990333173856898 |
| 23 | 0.00630198435563809 | 0.0126039687112762 | 0.993698015644362 |
| 24 | 0.00319094541650986 | 0.00638189083301973 | 0.99680905458349 |
| 25 | 0.00143352618919697 | 0.00286705237839393 | 0.998566473810803 |
| 26 | 0.00212110096484134 | 0.00424220192968269 | 0.997878899035159 |
| 27 | 0.00238615697092997 | 0.00477231394185995 | 0.99761384302907 |
| 28 | 0.00131420023077466 | 0.00262840046154932 | 0.998685799769225 |
| 29 | 0.00104463247716716 | 0.00208926495433431 | 0.998955367522833 |
| 30 | 0.000514169460455934 | 0.00102833892091187 | 0.999485830539544 |
| 31 | 0.000776122767264041 | 0.00155224553452808 | 0.999223877232736 |
| 32 | 0.00045201418687845 | 0.0009040283737569 | 0.999547985813122 |
| 33 | 0.00239104900531053 | 0.00478209801062106 | 0.99760895099469 |
| 34 | 0.00481588271422675 | 0.0096317654284535 | 0.995184117285773 |
| 35 | 0.00686617241902948 | 0.0137323448380590 | 0.99313382758097 |
| 36 | 0.102272467142470 | 0.204544934284941 | 0.89772753285753 |
| 37 | 0.113338559214983 | 0.226677118429967 | 0.886661440785017 |
| 38 | 0.159719499815921 | 0.319438999631842 | 0.840280500184079 |
| 39 | 0.139186574074133 | 0.278373148148267 | 0.860813425925867 |
| 40 | 0.291585373792779 | 0.583170747585559 | 0.708414626207221 |
| 41 | 0.584474474166782 | 0.831051051666435 | 0.415525525833218 |
| 42 | 0.564639796808957 | 0.870720406382086 | 0.435360203191043 |
| 43 | 0.702621746976873 | 0.594756506046253 | 0.297378253023127 |
| 44 | 0.782353228856723 | 0.435293542286554 | 0.217646771143277 |
| 45 | 0.797662920721426 | 0.404674158557147 | 0.202337079278574 |
| 46 | 0.898354404500992 | 0.203291190998017 | 0.101645595499008 |
| 47 | 0.876890356415658 | 0.246219287168683 | 0.123109643584342 |
| 48 | 0.858653848981126 | 0.282692302037748 | 0.141346151018874 |
| 49 | 0.85715539592608 | 0.285689208147840 | 0.142844604073920 |
| 50 | 0.83488474687285 | 0.330230506254301 | 0.165115253127151 |
| 51 | 0.785695729980791 | 0.428608540038418 | 0.214304270019209 |
| 52 | 0.772954826807269 | 0.454090346385462 | 0.227045173192731 |
| 53 | 0.809578338257672 | 0.380843323484657 | 0.190421661742328 |
| 54 | 0.77083114707481 | 0.458337705850379 | 0.229168852925189 |
| 55 | 0.753727922744182 | 0.492544154511635 | 0.246272077255818 |
| 56 | 0.730345718803364 | 0.539308562393272 | 0.269654281196636 |
| 57 | 0.701912347381594 | 0.596175305236811 | 0.298087652618406 |
| 58 | 0.7867422343356 | 0.426515531328799 | 0.213257765664400 |
| 59 | 0.731444268566857 | 0.537111462866286 | 0.268555731433143 |
| 60 | 0.669796407678462 | 0.660407184643076 | 0.330203592321538 |
| 61 | 0.800781167812383 | 0.398437664375234 | 0.199218832187617 |
| 62 | 0.744179576169955 | 0.51164084766009 | 0.255820423830045 |
| 63 | 0.704109506968414 | 0.591780986063172 | 0.295890493031586 |
| 64 | 0.776403232124102 | 0.447193535751795 | 0.223596767875898 |
| 65 | 0.730615425479784 | 0.538769149040433 | 0.269384574520216 |
| 66 | 0.628788517161007 | 0.742422965677986 | 0.371211482838993 |
| 67 | 0.72463104934399 | 0.550737901312021 | 0.275368950656010 |
| 68 | 0.752852786618917 | 0.494294426762166 | 0.247147213381083 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 11 | 0.207547169811321 | NOK |
| 5% type I error level | 17 | 0.320754716981132 | NOK |
| 10% type I error level | 20 | 0.377358490566038 | NOK |
