| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = -2688.8440155727 + 147.081501518406X_1t[t] + 513.088896305589X_2t[t] + 469.109240027626X_3t[t] + 0.674676542089624X_4t[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) | -2688.8440155727 | 3246.199589 | -0.8283 | 0.408918 | 0.204459 |
| X_1t | 147.081501518406 | 14.663575 | 10.0304 | 0 | 0 |
| X_2t | 513.088896305589 | 145.296 | 3.5313 | 0.000561 | 0.000281 |
| X_3t | 469.109240027626 | 347.642275 | 1.3494 | 0.179402 | 0.089701 |
| X_4t | 0.674676542089624 | 0.156009 | 4.3246 | 2.9e-05 | 1.4e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.90351747176738 |
| R-squared | 0.816343821788917 |
| Adjusted R-squared | 0.811058751912339 |
| F-TEST (value) | 154.462257047299 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 139 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 16465.8827443598 |
| Sum Squared Residuals | 37686415942.5896 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 63031 | 50959.251053167 | 12071.7489468329 |
| 2 | 66751 | 49347.302088083 | 17403.6979119171 |
| 3 | 7176 | 8566.92581010925 | -1390.92581010925 |
| 4 | 78306 | 88401.3612435886 | -10095.3612435886 |
| 5 | 137944 | 148819.97411678 | -10875.9741167799 |
| 6 | 261308 | 247231.890702622 | 14076.1092973784 |
| 7 | 69266 | 66401.4032623579 | 2864.5967376421 |
| 8 | 80226 | 54713.5359021244 | 25512.4640978756 |
| 9 | 73226 | 81027.6802444816 | -7801.68024448162 |
| 10 | 178519 | 134186.642549135 | 44332.3574508648 |
| 11 | 66476 | 71703.0196446086 | -5227.01964460865 |
| 12 | 98606 | 102290.103555323 | -3684.10355532334 |
| 13 | 50001 | 71845.5029509842 | -21844.5029509842 |
| 14 | 91093 | 109800.8474866 | -18707.8474866004 |
| 15 | 73884 | 55633.4833972586 | 18250.5166027414 |
| 16 | 72377 | 72782.818670069 | -405.818670068965 |
| 17 | 69388 | 88444.0719371656 | -19056.0719371656 |
| 18 | 15629 | 16663.4511311909 | -1034.45113119094 |
| 19 | 71693 | 115744.230561693 | -44051.2305616929 |
| 20 | 19920 | 53644.3435032874 | -33724.3435032874 |
| 21 | 39403 | 47706.5846029181 | -8303.5846029181 |
| 22 | 99933 | 110227.996519998 | -10294.9965199982 |
| 23 | 56088 | 51923.0032939209 | 4164.9967060791 |
| 24 | 62006 | 74301.6566118979 | -12295.6566118979 |
| 25 | 81665 | 84555.3179153915 | -2890.31791539151 |
| 26 | 65223 | 52640.8889539405 | 12582.1110460595 |
| 27 | 88794 | 91059.2303338482 | -2265.23033384815 |
| 28 | 90642 | 64681.3405016614 | 25960.6594983386 |
| 29 | 203699 | 143145.125198103 | 60553.8748018967 |
| 30 | 99340 | 93648.6221564397 | 5691.37784356035 |
| 31 | 56695 | 55783.3022539268 | 911.697746073187 |
| 32 | 108143 | 84674.9152945952 | 23468.0847054048 |
| 33 | 58313 | 76601.064286293 | -18288.064286293 |
| 34 | 29101 | 42772.8783602592 | -13671.8783602592 |
| 35 | 113060 | 94186.2087805872 | 18873.7912194128 |
| 36 | 0 | -2688.84401557269 | 2688.84401557269 |
| 37 | 65773 | 61731.7159565955 | 4041.28404340446 |
| 38 | 67047 | 82746.0782911984 | -15699.0782911984 |
| 39 | 41953 | 57326.5882951354 | -15373.5882951354 |
| 40 | 109835 | 112674.811086864 | -2839.81108686436 |
| 41 | 82577 | 85240.8331522606 | -2663.8331522606 |
| 42 | 59588 | 63473.1350641764 | -3885.13506417638 |
| 43 | 40064 | 43171.3145381943 | -3107.31453819425 |
| 44 | 70227 | 99083.5342982163 | -28856.5342982163 |
| 45 | 60437 | 69241.4438416435 | -8804.44384164354 |
| 46 | 47000 | 35586.8308103179 | 11413.1691896821 |
| 47 | 40295 | 31843.8590471697 | 8451.14095283026 |
| 48 | 103397 | 83822.0467692677 | 19574.9532307323 |
| 49 | 78982 | 69925.9465219199 | 9056.05347808013 |
| 50 | 60206 | 85606.4474346182 | -25400.4474346182 |
| 51 | 39887 | 37971.0064003804 | 1915.99359961959 |
| 52 | 49791 | 43476.983761031 | 6314.016238969 |
| 53 | 129283 | 96190.1547799784 | 33092.8452200215 |
| 54 | 104816 | 79734.408697162 | 25081.591302838 |
| 55 | 101395 | 90915.9201830595 | 10479.0798169405 |
| 56 | 72824 | 63115.527981132 | 9708.47201886794 |
| 57 | 76018 | 63045.9548404364 | 12972.0451595636 |
| 58 | 33891 | 34762.5158393023 | -871.515839302316 |
| 59 | 62164 | 56300.8266834014 | 5863.17331659863 |
| 60 | 28266 | 50943.889619875 | -22677.889619875 |
| 61 | 35093 | 29746.0367079014 | 5346.96329209856 |
| 62 | 35252 | 58879.9964219123 | -23627.9964219123 |
| 63 | 36977 | 45357.4317077339 | -8380.43170773395 |
| 64 | 42406 | 38826.1301822314 | 3579.86981776857 |
| 65 | 56353 | 35787.0764365351 | 20565.9235634649 |
| 66 | 58817 | 68150.4125483197 | -9333.41254831972 |
| 67 | 76053 | 85009.5171846809 | -8956.5171846809 |
| 68 | 70872 | 107105.23232211 | -36233.2323221096 |
| 69 | 42372 | 45679.8030250293 | -3307.80302502931 |
| 70 | 19144 | 8921.81161408946 | 10222.1883859105 |
| 71 | 114177 | 103138.645419263 | 11038.3545807374 |
| 72 | 53544 | 54839.1019262264 | -1295.10192622643 |
| 73 | 51379 | 67805.9682209309 | -16426.9682209309 |
| 74 | 40756 | 62819.3239825803 | -22063.3239825803 |
| 75 | 46357 | 67826.6975232358 | -21469.6975232358 |
| 76 | 17799 | 22847.1299491736 | -5048.12994917358 |
| 77 | 71154 | 64759.6207861869 | 6394.3792138131 |
| 78 | 58305 | 84089.5496927453 | -25784.5496927453 |
| 79 | 27454 | 37490.1964436991 | -10036.1964436991 |
| 80 | 34323 | 65774.4168712344 | -31451.4168712344 |
| 81 | 44761 | 51564.655689514 | -6803.655689514 |
| 82 | 113862 | 66818.1773890926 | 47043.8226109074 |
| 83 | 35027 | 41289.9836931866 | -6262.98369318663 |
| 84 | 62396 | 74494.8960526298 | -12098.8960526298 |
| 85 | 29613 | 42626.1904419987 | -13013.1904419987 |
| 86 | 65559 | 67490.6799730865 | -1931.67997308653 |
| 87 | 109788 | 78423.1684905169 | 31364.8315094831 |
| 88 | 27883 | 36862.5591878306 | -8979.55918783055 |
| 89 | 40181 | 43057.9411067359 | -2876.94110673585 |
| 90 | 53398 | 48024.5018630762 | 5373.49813692382 |
| 91 | 56435 | 69905.3184257798 | -13470.3184257798 |
| 92 | 77283 | 91856.9965112742 | -14573.9965112742 |
| 93 | 71738 | 48917.7908648456 | 22820.2091351544 |
| 94 | 48096 | 48577.204973687 | -481.204973687041 |
| 95 | 25214 | 44896.338875564 | -19682.338875564 |
| 96 | 119332 | 88358.478434529 | 30973.5215654711 |
| 97 | 79201 | 77359.8947901413 | 1841.10520985872 |
| 98 | 19349 | 16932.7466095998 | 2416.25339040015 |
| 99 | 78760 | 62660.9501885426 | 16099.0498114574 |
| 100 | 54133 | 63822.9619565437 | -9689.96195654366 |
| 101 | 21623 | 20515.0535313931 | 1107.94646860693 |
| 102 | 25497 | 44971.1131571141 | -19474.1131571141 |
| 103 | 69535 | 59959.844491946 | 9575.15550805403 |
| 104 | 30709 | 24849.8023069483 | 5859.19769305167 |
| 105 | 37043 | 26795.2118030459 | 10247.7881969541 |
| 106 | 24716 | 29007.5708491423 | -4291.57084914226 |
| 107 | 54865 | 49465.5803193211 | 5399.41968067888 |
| 108 | 27246 | 17603.6655076269 | 9642.33449237314 |
| 109 | 0 | -2688.84401557269 | 2688.84401557269 |
| 110 | 38814 | 49919.626004136 | -11105.626004136 |
| 111 | 27646 | 41481.945448352 | -13835.945448352 |
| 112 | 65373 | 65232.834869143 | 140.165130856957 |
| 113 | 43021 | 53402.9306141556 | -10381.9306141556 |
| 114 | 43116 | 47445.1363782595 | -4329.13637825954 |
| 115 | 3058 | -2541.76251405429 | 5599.76251405429 |
| 116 | 0 | -2688.84401557269 | 2688.84401557269 |
| 117 | 96347 | 57029.1414273193 | 39317.8585726807 |
| 118 | 48626 | 75114.1740300059 | -26488.1740300059 |
| 119 | 73073 | 60268.5229861784 | 12804.4770138216 |
| 120 | 45266 | 49661.474940318 | -4395.47494031797 |
| 121 | 43410 | 46195.9614055197 | -2785.96140551973 |
| 122 | 83842 | 75846.7621122552 | 7995.2378877448 |
| 123 | 39296 | 37157.3493988566 | 2138.65060114336 |
| 124 | 35223 | 49452.7663422442 | -14229.7663422442 |
| 125 | 39841 | 29859.8194245809 | 9981.18057541914 |
| 126 | 19764 | 18202.3835314205 | 1561.61646857954 |
| 127 | 59975 | 71922.2834815417 | -11947.2834815417 |
| 128 | 64589 | 44158.5363446392 | 20430.4636553608 |
| 129 | 63339 | 65928.4622245788 | -2589.46222457883 |
| 130 | 11796 | 10381.9019807422 | 1414.09801925781 |
| 131 | 7627 | 988.19352238745 | 6638.80647761255 |
| 132 | 68998 | 53464.0732278158 | 15533.9267721842 |
| 133 | 6836 | -601.838258842602 | 7437.8382588426 |
| 134 | 28834 | 44965.5760663052 | -16131.5760663052 |
| 135 | 5118 | 759.089475065685 | 4358.91052493431 |
| 136 | 20898 | 18847.4706030943 | 2050.52939690573 |
| 137 | 0 | -2688.84401557269 | 2688.84401557269 |
| 138 | 42690 | 38546.8422520762 | 4143.15774792382 |
| 139 | 14507 | 25653.3472149297 | -11146.3472149297 |
| 140 | 7131 | 1282.35652542426 | 5848.64347457574 |
| 141 | 4194 | -629.702994315011 | 4823.70299431501 |
| 142 | 21416 | 25783.1591590515 | -4367.15915905147 |
| 143 | 30591 | 24573.7911046004 | 6017.20889539957 |
| 144 | 42419 | 46136.6425162273 | -3717.64251622728 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.388269350026812 | 0.776538700053623 | 0.611730649973188 |
| 9 | 0.350749852910054 | 0.701499705820108 | 0.649250147089946 |
| 10 | 0.919937651494701 | 0.160124697010598 | 0.080062348505299 |
| 11 | 0.885312459580028 | 0.229375080839943 | 0.114687540419972 |
| 12 | 0.837358401467018 | 0.325283197065963 | 0.162641598532982 |
| 13 | 0.873100834342341 | 0.253798331315318 | 0.126899165657659 |
| 14 | 0.870068288233309 | 0.259863423533382 | 0.129931711766691 |
| 15 | 0.840810745888354 | 0.318378508223293 | 0.159189254111646 |
| 16 | 0.794656634309645 | 0.410686731380711 | 0.205343365690355 |
| 17 | 0.867066158474948 | 0.265867683050104 | 0.132933841525052 |
| 18 | 0.819819845853724 | 0.360360308292552 | 0.180180154146276 |
| 19 | 0.922438520336812 | 0.155122959326377 | 0.0775614796631883 |
| 20 | 0.961492435959308 | 0.0770151280813848 | 0.0385075640406924 |
| 21 | 0.950166483468692 | 0.0996670330626157 | 0.0498335165313078 |
| 22 | 0.940666527160422 | 0.118666945679156 | 0.059333472839578 |
| 23 | 0.93621483523091 | 0.127570329538179 | 0.0637851647690897 |
| 24 | 0.924051626545539 | 0.151896746908923 | 0.0759483734544613 |
| 25 | 0.901752916834138 | 0.196494166331724 | 0.0982470831658621 |
| 26 | 0.88558404209057 | 0.228831915818861 | 0.114415957909431 |
| 27 | 0.854724839684638 | 0.290550320630724 | 0.145275160315362 |
| 28 | 0.908508155789864 | 0.182983688420272 | 0.0914918442101359 |
| 29 | 0.99819828076994 | 0.00360343846011992 | 0.00180171923005996 |
| 30 | 0.997309144505947 | 0.00538171098810507 | 0.00269085549405254 |
| 31 | 0.996009936995313 | 0.00798012600937444 | 0.00399006300468722 |
| 32 | 0.997292519903178 | 0.00541496019364457 | 0.00270748009682229 |
| 33 | 0.997892220136668 | 0.00421555972666446 | 0.00210777986333223 |
| 34 | 0.997380111257484 | 0.00523977748503151 | 0.00261988874251575 |
| 35 | 0.997723102498971 | 0.00455379500205728 | 0.00227689750102864 |
| 36 | 0.996538650878964 | 0.00692269824207225 | 0.00346134912103612 |
| 37 | 0.99516198923509 | 0.00967602152981788 | 0.00483801076490894 |
| 38 | 0.994854253134703 | 0.0102914937305939 | 0.00514574686529694 |
| 39 | 0.993833412396242 | 0.0123331752075162 | 0.0061665876037581 |
| 40 | 0.991325696790467 | 0.0173486064190657 | 0.00867430320953287 |
| 41 | 0.987895987720735 | 0.0242080245585295 | 0.0121040122792647 |
| 42 | 0.983549351471485 | 0.0329012970570302 | 0.0164506485285151 |
| 43 | 0.977705792615825 | 0.0445884147683496 | 0.0222942073841748 |
| 44 | 0.986242280331137 | 0.0275154393377251 | 0.0137577196688626 |
| 45 | 0.98218724678712 | 0.0356255064257588 | 0.0178127532128794 |
| 46 | 0.980350009698577 | 0.0392999806028459 | 0.0196499903014229 |
| 47 | 0.976287178898092 | 0.047425642203815 | 0.0237128211019075 |
| 48 | 0.979430578441467 | 0.0411388431170652 | 0.0205694215585326 |
| 49 | 0.97548642787315 | 0.0490271442536989 | 0.0245135721268494 |
| 50 | 0.982555229485502 | 0.0348895410289951 | 0.0174447705144975 |
| 51 | 0.977570114706016 | 0.0448597705879677 | 0.0224298852939838 |
| 52 | 0.971246895383203 | 0.0575062092335949 | 0.0287531046167974 |
| 53 | 0.990211684425133 | 0.0195766311497336 | 0.00978831557486679 |
| 54 | 0.994500366054854 | 0.0109992678902916 | 0.00549963394514578 |
| 55 | 0.993365909609234 | 0.0132681807815327 | 0.00663409039076633 |
| 56 | 0.991912749982723 | 0.0161745000345544 | 0.0080872500172772 |
| 57 | 0.991688912796076 | 0.016622174407849 | 0.0083110872039245 |
| 58 | 0.988561701740702 | 0.0228765965185969 | 0.0114382982592984 |
| 59 | 0.984935655436729 | 0.0301286891265427 | 0.0150643445632714 |
| 60 | 0.988417162063441 | 0.0231656758731181 | 0.011582837936559 |
| 61 | 0.986033599765346 | 0.0279328004693087 | 0.0139664002346544 |
| 62 | 0.990509363935972 | 0.0189812721280554 | 0.0094906360640277 |
| 63 | 0.987710023982454 | 0.0245799520350914 | 0.0122899760175457 |
| 64 | 0.983367884884524 | 0.033264230230953 | 0.0166321151154765 |
| 65 | 0.986034942986095 | 0.0279301140278094 | 0.0139650570139047 |
| 66 | 0.982817228995244 | 0.0343655420095111 | 0.0171827710047555 |
| 67 | 0.977846765376066 | 0.0443064692478683 | 0.0221532346239342 |
| 68 | 0.99370765278178 | 0.012584694436439 | 0.00629234721821952 |
| 69 | 0.991259728208964 | 0.0174805435820722 | 0.0087402717910361 |
| 70 | 0.988777727425575 | 0.0224445451488493 | 0.0112222725744246 |
| 71 | 0.986843702434985 | 0.0263125951300302 | 0.0131562975650151 |
| 72 | 0.98429281868057 | 0.03141436263886 | 0.01570718131943 |
| 73 | 0.98344891836321 | 0.0331021632735797 | 0.0165510816367899 |
| 74 | 0.987004736362367 | 0.0259905272752662 | 0.0129952636376331 |
| 75 | 0.993310329835611 | 0.0133793403287775 | 0.00668967016438876 |
| 76 | 0.992918794177486 | 0.0141624116450271 | 0.00708120582251357 |
| 77 | 0.991924249721588 | 0.0161515005568238 | 0.00807575027841188 |
| 78 | 0.99302417856609 | 0.013951642867819 | 0.0069758214339095 |
| 79 | 0.991977890491013 | 0.0160442190179736 | 0.00802210950898679 |
| 80 | 0.995116129863993 | 0.00976774027201438 | 0.00488387013600719 |
| 81 | 0.993380706388405 | 0.0132385872231905 | 0.00661929361159525 |
| 82 | 0.999477181817042 | 0.00104563636591639 | 0.000522818182958194 |
| 83 | 0.99929525801379 | 0.00140948397242051 | 0.000704741986210257 |
| 84 | 0.999216878310575 | 0.00156624337885056 | 0.00078312168942528 |
| 85 | 0.999232672593202 | 0.00153465481359657 | 0.000767327406798285 |
| 86 | 0.99882160016585 | 0.00235679966830131 | 0.00117839983415066 |
| 87 | 0.999759990164838 | 0.000480019670323154 | 0.000240009835161577 |
| 88 | 0.999720260604232 | 0.00055947879153669 | 0.000279739395768345 |
| 89 | 0.99955381462787 | 0.000892370744260405 | 0.000446185372130202 |
| 90 | 0.999297956080874 | 0.00140408783825189 | 0.000702043919125945 |
| 91 | 0.999098870820982 | 0.00180225835803555 | 0.000901129179017775 |
| 92 | 0.99886620640801 | 0.0022675871839824 | 0.0011337935919912 |
| 93 | 0.999457663195582 | 0.00108467360883616 | 0.000542336804418081 |
| 94 | 0.99913142470478 | 0.00173715059043933 | 0.000868575295219663 |
| 95 | 0.999284174322965 | 0.00143165135407032 | 0.000715825677035158 |
| 96 | 0.99981617370055 | 0.000367652598900676 | 0.000183826299450338 |
| 97 | 0.999740153804038 | 0.000519692391924047 | 0.000259846195962023 |
| 98 | 0.999569081808625 | 0.000861836382750629 | 0.000430918191375314 |
| 99 | 0.999565613212095 | 0.000868773575809398 | 0.000434386787904699 |
| 100 | 0.99940545336425 | 0.00118909327149798 | 0.000594546635748992 |
| 101 | 0.999022236452577 | 0.00195552709484505 | 0.000977763547422527 |
| 102 | 0.999158757872287 | 0.0016824842554269 | 0.00084124212771345 |
| 103 | 0.99900987874179 | 0.00198024251642229 | 0.000990121258211143 |
| 104 | 0.998419026952134 | 0.00316194609573222 | 0.00158097304786611 |
| 105 | 0.997754835880792 | 0.00449032823841609 | 0.00224516411920804 |
| 106 | 0.997071857864721 | 0.0058562842705576 | 0.0029281421352788 |
| 107 | 0.995880404465653 | 0.00823919106869427 | 0.00411959553434713 |
| 108 | 0.994364691541915 | 0.0112706169161692 | 0.00563530845808462 |
| 109 | 0.991322257818892 | 0.017355484362216 | 0.00867774218110799 |
| 110 | 0.989112277986728 | 0.0217754440265443 | 0.0108877220132721 |
| 111 | 0.98731752951744 | 0.0253649409651218 | 0.0126824704825609 |
| 112 | 0.981016856198879 | 0.0379662876022423 | 0.0189831438011211 |
| 113 | 0.980075502363087 | 0.0398489952738266 | 0.0199244976369133 |
| 114 | 0.970397033269231 | 0.0592059334615372 | 0.0296029667307686 |
| 115 | 0.957477657066855 | 0.0850446858662904 | 0.0425223429331452 |
| 116 | 0.939841371965405 | 0.12031725606919 | 0.0601586280345952 |
| 117 | 0.997602914737238 | 0.0047941705255244 | 0.0023970852627622 |
| 118 | 0.999682097191895 | 0.00063580561620896 | 0.00031790280810448 |
| 119 | 0.99974225588476 | 0.00051548823047794 | 0.00025774411523897 |
| 120 | 0.999612154571136 | 0.000775690857727684 | 0.000387845428863842 |
| 121 | 0.999244034683997 | 0.00151193063200692 | 0.000755965316003462 |
| 122 | 0.999622033925222 | 0.000755932149556222 | 0.000377966074778111 |
| 123 | 0.999493039931565 | 0.00101392013687004 | 0.000506960068435019 |
| 124 | 0.998904228164937 | 0.00219154367012671 | 0.00109577183506336 |
| 125 | 0.997700593247323 | 0.00459881350535493 | 0.00229940675267746 |
| 126 | 0.995347505283969 | 0.00930498943206277 | 0.00465249471603138 |
| 127 | 0.99104068005231 | 0.0179186398953797 | 0.00895931994768983 |
| 128 | 0.996670174075179 | 0.0066596518496418 | 0.0033298259248209 |
| 129 | 0.99532040691918 | 0.00935918616163923 | 0.00467959308081961 |
| 130 | 0.989750405710728 | 0.0204991885785432 | 0.0102495942892716 |
| 131 | 0.977743538492333 | 0.0445129230153335 | 0.0222564615076668 |
| 132 | 0.99625330549617 | 0.00749338900765792 | 0.00374669450382896 |
| 133 | 0.98926869095353 | 0.0214626180929395 | 0.0107313090464697 |
| 134 | 0.995672644800587 | 0.00865471039882526 | 0.00432735519941263 |
| 135 | 0.988098059539258 | 0.0238038809214838 | 0.0119019404607419 |
| 136 | 0.97374945975217 | 0.0525010804956605 | 0.0262505402478303 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 50 | 0.387596899224806 | NOK |
| 5% type I error level | 103 | 0.7984496124031 | NOK |
| 10% type I error level | 109 | 0.844961240310077 | NOK |
