| Multiple Linear Regression - Estimated Regression Equation |
| X[t] = + 12600.7142857143 + 17016.7857142857M1[t] + 14685.2857142857M2[t] + 18977.7857142857M3[t] + 15879.2857142857M4[t] + 11504.9107142857M5[t] + 12881.1607142857M6[t] + 7005.03571428572M7[t] + 5734.91071428572M8[t] + 7345.78571428573M9[t] + 10263.4107142857M10[t] + 5520.71428571429M11[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) | 12600.7142857143 | 814.601465 | 15.4686 | 0 | 0 |
| M1 | 17016.7857142857 | 1115.438995 | 15.2557 | 0 | 0 |
| M2 | 14685.2857142857 | 1115.438995 | 13.1655 | 0 | 0 |
| M3 | 18977.7857142857 | 1115.438995 | 17.0137 | 0 | 0 |
| M4 | 15879.2857142857 | 1115.438995 | 14.2359 | 0 | 0 |
| M5 | 11504.9107142857 | 1115.438995 | 10.3142 | 0 | 0 |
| M6 | 12881.1607142857 | 1115.438995 | 11.5481 | 0 | 0 |
| M7 | 7005.03571428572 | 1115.438995 | 6.2801 | 0 | 0 |
| M8 | 5734.91071428572 | 1115.438995 | 5.1414 | 2e-06 | 1e-06 |
| M9 | 7345.78571428573 | 1115.438995 | 6.5856 | 0 | 0 |
| M10 | 10263.4107142857 | 1115.438995 | 9.2012 | 0 | 0 |
| M11 | 5520.71428571429 | 1152.02044 | 4.7922 | 7e-06 | 4e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.9348192921154 |
| R-squared | 0.873887108911139 |
| Adjusted R-squared | 0.856969525960194 |
| F-TEST (value) | 51.655553363924 |
| F-TEST (DF numerator) | 11 |
| F-TEST (DF denominator) | 82 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 2155.23289484233 |
| Sum Squared Residuals | 380892364.142857 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 31514 | 29617.4999999999 | 1896.50000000005 |
| 2 | 27071 | 27286 | -214.999999999987 |
| 3 | 29462 | 31578.4999999999 | -2116.49999999993 |
| 4 | 26105 | 28479.9999999999 | -2374.99999999994 |
| 5 | 22397 | 24105.625 | -1708.62499999999 |
| 6 | 23843 | 25481.8750000001 | -1638.87500000005 |
| 7 | 21705 | 19605.75 | 2099.25000000001 |
| 8 | 18089 | 18335.625 | -246.624999999996 |
| 9 | 20764 | 19946.5 | 817.500000000001 |
| 10 | 25316 | 22864.125 | 2451.87499999999 |
| 11 | 17704 | 18121.4285714286 | -417.428571428592 |
| 12 | 15548 | 12600.7142857143 | 2947.28571428571 |
| 13 | 28029 | 29617.5 | -1588.50000000001 |
| 14 | 29383 | 27286 | 2097.00000000000 |
| 15 | 36438 | 31578.5 | 4859.49999999999 |
| 16 | 32034 | 28480 | 3553.99999999999 |
| 17 | 22679 | 24105.625 | -1426.625 |
| 18 | 24319 | 25481.875 | -1162.87499999999 |
| 19 | 18004 | 19605.75 | -1601.75 |
| 20 | 17537 | 18335.625 | -798.625000000001 |
| 21 | 20366 | 19946.5 | 419.5 |
| 22 | 22782 | 22864.125 | -82.1249999999986 |
| 23 | 19169 | 18121.4285714286 | 1047.57142857143 |
| 24 | 13807 | 12600.7142857143 | 1206.28571428572 |
| 25 | 29743 | 29617.5 | 125.499999999993 |
| 26 | 25591 | 27286 | -1695.00000000000 |
| 27 | 29096 | 31578.5 | -2482.50000000001 |
| 28 | 26482 | 28480 | -1998.00000000001 |
| 29 | 22405 | 24105.625 | -1700.625 |
| 30 | 27044 | 25481.875 | 1562.12500000001 |
| 31 | 17970 | 19605.75 | -1635.75 |
| 32 | 18730 | 18335.625 | 394.374999999999 |
| 33 | 19684 | 19946.5 | -262.5 |
| 34 | 19785 | 22864.125 | -3079.125 |
| 35 | 18479 | 18121.4285714286 | 357.571428571432 |
| 36 | 10698 | 12600.7142857143 | -1902.71428571428 |
| 37 | 31956 | 29617.5 | 2338.49999999999 |
| 38 | 29506 | 27286 | 2220.00000000000 |
| 39 | 34506 | 31578.5 | 2927.49999999999 |
| 40 | 27165 | 28480 | -1315.00000000001 |
| 41 | 26736 | 24105.625 | 2630.375 |
| 42 | 23691 | 25481.875 | -1790.87499999999 |
| 43 | 18157 | 19605.75 | -1448.75 |
| 44 | 17328 | 18335.625 | -1007.625 |
| 45 | 18205 | 19946.5 | -1741.5 |
| 46 | 20995 | 22864.125 | -1869.125 |
| 47 | 17382 | 18121.4285714286 | -739.428571428568 |
| 48 | 9367 | 12600.7142857143 | -3233.71428571428 |
| 49 | 31124 | 29617.5 | 1506.49999999999 |
| 50 | 26551 | 27286 | -735.000000000004 |
| 51 | 30651 | 31578.5 | -927.50000000001 |
| 52 | 25859 | 28480 | -2621.00000000001 |
| 53 | 25100 | 24105.625 | 994.375 |
| 54 | 25778 | 25481.875 | 296.125000000007 |
| 55 | 20418 | 19605.75 | 812.25 |
| 56 | 18688 | 18335.625 | 352.374999999999 |
| 57 | 20424 | 19946.5 | 477.5 |
| 58 | 24776 | 22864.125 | 1911.875 |
| 59 | 19814 | 18121.4285714286 | 1692.57142857143 |
| 60 | 12738 | 12600.7142857143 | 137.285714285717 |
| 61 | 31566 | 29617.5 | 1948.49999999999 |
| 62 | 30111 | 27286 | 2825.00000000000 |
| 63 | 30019 | 31578.5 | -1559.50000000001 |
| 64 | 31934 | 28480 | 3453.99999999999 |
| 65 | 25826 | 24105.625 | 1720.375 |
| 66 | 26835 | 25481.875 | 1353.12500000001 |
| 67 | 20205 | 19605.75 | 599.25 |
| 68 | 17789 | 18335.625 | -546.625000000001 |
| 69 | 20520 | 19946.5 | 573.5 |
| 70 | 22518 | 22864.125 | -346.124999999999 |
| 71 | 15572 | 18121.4285714286 | -2549.42857142857 |
| 72 | 11509 | 12600.7142857143 | -1091.71428571428 |
| 73 | 25447 | 29617.5 | -4170.50000000001 |
| 74 | 24090 | 27286 | -3196.00000000000 |
| 75 | 27786 | 31578.5 | -3792.50000000001 |
| 76 | 26195 | 28480 | -2285.00000000001 |
| 77 | 20516 | 24105.625 | -3589.625 |
| 78 | 22759 | 25481.875 | -2722.87499999999 |
| 79 | 19028 | 19605.75 | -577.75 |
| 80 | 16971 | 18335.625 | -1364.625 |
| 81 | 20036 | 19946.5 | 89.5 |
| 82 | 22485 | 22864.125 | -379.124999999999 |
| 83 | 18730 | 18121.4285714286 | 608.571428571432 |
| 84 | 14538 | 12600.7142857143 | 1937.28571428572 |
| 85 | 27561 | 29617.5 | -2056.50000000001 |
| 86 | 25985 | 27286 | -1301.00000000000 |
| 87 | 34670 | 31578.5 | 3091.49999999999 |
| 88 | 32066 | 28480 | 3585.99999999999 |
| 89 | 27186 | 24105.625 | 3080.375 |
| 90 | 29586 | 25481.875 | 4104.12500000001 |
| 91 | 21359 | 19605.75 | 1753.25 |
| 92 | 21553 | 18335.625 | 3217.375 |
| 93 | 19573 | 19946.5 | -373.5 |
| 94 | 24256 | 22864.125 | 1391.875 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 15 | 0.92685977834978 | 0.146280443300441 | 0.0731402216502204 |
| 16 | 0.969866970380733 | 0.0602660592385346 | 0.0301330296192673 |
| 17 | 0.94316472896118 | 0.113670542077639 | 0.0568352710388195 |
| 18 | 0.903745452779862 | 0.192509094440275 | 0.0962545472201376 |
| 19 | 0.901396220182334 | 0.197207559635333 | 0.0986037798176665 |
| 20 | 0.84989373911244 | 0.30021252177512 | 0.15010626088756 |
| 21 | 0.784217021850576 | 0.431565956298848 | 0.215782978149424 |
| 22 | 0.744546347065226 | 0.510907305869548 | 0.255453652934774 |
| 23 | 0.679789439825982 | 0.640421120348037 | 0.320210560174018 |
| 24 | 0.624731103703467 | 0.750537792593066 | 0.375268896296533 |
| 25 | 0.537269294154575 | 0.92546141169085 | 0.462730705845425 |
| 26 | 0.522215215400212 | 0.955569569199576 | 0.477784784599788 |
| 27 | 0.582779987636198 | 0.834440024727604 | 0.417220012363802 |
| 28 | 0.569136423642726 | 0.861727152714548 | 0.430863576357274 |
| 29 | 0.511102937383103 | 0.977794125233794 | 0.488897062616897 |
| 30 | 0.506440199254642 | 0.987119601490716 | 0.493559800745358 |
| 31 | 0.467057897220519 | 0.934115794441038 | 0.532942102779481 |
| 32 | 0.397848685294001 | 0.795697370588003 | 0.602151314705999 |
| 33 | 0.331867023914892 | 0.663734047829784 | 0.668132976085108 |
| 34 | 0.419718430430460 | 0.839436860860921 | 0.580281569569540 |
| 35 | 0.350343456516012 | 0.700686913032024 | 0.649656543483988 |
| 36 | 0.386705430100845 | 0.77341086020169 | 0.613294569899155 |
| 37 | 0.382315351336166 | 0.764630702672332 | 0.617684648663834 |
| 38 | 0.373728944188797 | 0.747457888377593 | 0.626271055811203 |
| 39 | 0.410984374588245 | 0.821968749176491 | 0.589015625411754 |
| 40 | 0.364007006628667 | 0.728014013257333 | 0.635992993371333 |
| 41 | 0.424201267392250 | 0.848402534784499 | 0.57579873260775 |
| 42 | 0.395162737691529 | 0.790325475383058 | 0.604837262308471 |
| 43 | 0.354560299917814 | 0.709120599835628 | 0.645439700082186 |
| 44 | 0.303839708132058 | 0.607679416264116 | 0.696160291867942 |
| 45 | 0.28121384720459 | 0.56242769440918 | 0.71878615279541 |
| 46 | 0.261693059701925 | 0.52338611940385 | 0.738306940298075 |
| 47 | 0.215315238071449 | 0.430630476142898 | 0.784684761928551 |
| 48 | 0.276823856891296 | 0.553647713782592 | 0.723176143108704 |
| 49 | 0.257387140539078 | 0.514774281078156 | 0.742612859460922 |
| 50 | 0.212815105279205 | 0.42563021055841 | 0.787184894720795 |
| 51 | 0.177307960536416 | 0.354615921072833 | 0.822692039463584 |
| 52 | 0.207765531467573 | 0.415531062935146 | 0.792234468532427 |
| 53 | 0.171245630204443 | 0.342491260408886 | 0.828754369795557 |
| 54 | 0.135226659600937 | 0.270453319201873 | 0.864773340399063 |
| 55 | 0.106353233291295 | 0.212706466582590 | 0.893646766708705 |
| 56 | 0.0789401066654212 | 0.157880213330842 | 0.921059893334579 |
| 57 | 0.0571496760405953 | 0.114299352081191 | 0.942850323959405 |
| 58 | 0.0513007507943522 | 0.102601501588704 | 0.948699249205648 |
| 59 | 0.0453748377678132 | 0.0907496755356263 | 0.954625162232187 |
| 60 | 0.0309669405770236 | 0.0619338811540471 | 0.969033059422976 |
| 61 | 0.0438101862245342 | 0.0876203724490683 | 0.956189813775466 |
| 62 | 0.0734131266238489 | 0.146826253247698 | 0.926586873376151 |
| 63 | 0.0588397237849542 | 0.117679447569908 | 0.941160276215046 |
| 64 | 0.0791802272371751 | 0.158360454474350 | 0.920819772762825 |
| 65 | 0.0668388675428477 | 0.133677735085695 | 0.933161132457152 |
| 66 | 0.0496454888573111 | 0.0992909777146221 | 0.95035451114269 |
| 67 | 0.0332434306226999 | 0.0664868612453997 | 0.9667565693773 |
| 68 | 0.0227272792780502 | 0.0454545585561005 | 0.97727272072195 |
| 69 | 0.0142134542080186 | 0.0284269084160372 | 0.985786545791981 |
| 70 | 0.00850634210206705 | 0.0170126842041341 | 0.991493657897933 |
| 71 | 0.0082557442349064 | 0.0165114884698128 | 0.991744255765094 |
| 72 | 0.00624462468786345 | 0.0124892493757269 | 0.993755375312137 |
| 73 | 0.00769282602583937 | 0.0153856520516787 | 0.99230717397416 |
| 74 | 0.00643358637559222 | 0.0128671727511844 | 0.993566413624408 |
| 75 | 0.0223779769817871 | 0.0447559539635741 | 0.977622023018213 |
| 76 | 0.0433737612902434 | 0.0867475225804868 | 0.956626238709757 |
| 77 | 0.143545352431646 | 0.287090704863293 | 0.856454647568354 |
| 78 | 0.508753287340274 | 0.982493425319452 | 0.491246712659726 |
| 79 | 0.435123010688006 | 0.870246021376011 | 0.564876989311994 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 8 | 0.123076923076923 | NOK |
| 10% type I error level | 15 | 0.230769230769231 | NOK |
