| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = + 3171.06815055654 + 1.96330144662449X_1t[t] + 1411.54206862072X_2t[t] -1151.72798629381X_3t[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) | 3171.06815055654 | 1151.101818 | 2.7548 | 0.006653 | 0.003327 |
| X_1t | 1.96330144662449 | 0.388238 | 5.057 | 1e-06 | 1e-06 |
| X_2t | 1411.54206862072 | 596.769257 | 2.3653 | 0.019387 | 0.009693 |
| X_3t | -1151.72798629381 | 606.987429 | -1.8974 | 0.059828 | 0.029914 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.762271548187973 |
| R-squared | 0.581057913176889 |
| Adjusted R-squared | 0.572080582744965 |
| F-TEST (value) | 64.7250223864568 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 140 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7943.0584651562 |
| Sum Squared Residuals | 8832904889.32454 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 10345 | 12458.1885751461 | -2113.18857514607 |
| 2 | 17607 | 22169.8138164013 | -4562.8138164013 |
| 3 | 1423 | 4354.93892287111 | -2931.93892287111 |
| 4 | 20050 | 26118.9326221257 | -6068.93262212572 |
| 5 | 21212 | 29853.7185934757 | -8641.71859347569 |
| 6 | 93979 | 59319.6815335292 | 34659.3184664708 |
| 7 | 15524 | 16715.9658395145 | -1191.96583951454 |
| 8 | 16182 | 19939.7531055552 | -3757.75310555518 |
| 9 | 19238 | 25852.4986725842 | -6614.49867258418 |
| 10 | 28909 | 35966.5775650558 | -7057.5775650558 |
| 11 | 22357 | 23167.4206838058 | -810.420683805837 |
| 12 | 25560 | 34689.4364460265 | -9129.43644602651 |
| 13 | 9954 | 16245.4202110263 | -6291.42021102633 |
| 14 | 18490 | 24239.9930388746 | -5749.9930388746 |
| 15 | 17777 | 16702.8810207606 | 1074.11897923935 |
| 16 | 25268 | 13996.1234718963 | 11271.8765281037 |
| 17 | 37525 | 37260.7030497321 | 264.29695026788 |
| 18 | 6023 | 3173.03145200317 | 2849.96854799683 |
| 19 | 25042 | 29837.4024166909 | -4795.4024166909 |
| 20 | 35713 | 12201.6775223524 | 23511.3224776476 |
| 21 | 7039 | 9305.11487919635 | -2266.11487919635 |
| 22 | 40841 | 31895.0349141198 | 8945.9650858802 |
| 23 | 9214 | 6224.02504539924 | 2989.97495460076 |
| 24 | 17446 | 9839.8143093923 | 7606.1856906077 |
| 25 | 10295 | 18687.1667826088 | -8392.16678260876 |
| 26 | 13206 | 17921.4792184252 | -4715.4792184252 |
| 27 | 26093 | 24764.8897699857 | 1328.11023001431 |
| 28 | 20744 | 27753.6327642892 | -7009.63276428916 |
| 29 | 68013 | 36653.0031084996 | 31359.9968915004 |
| 30 | 12840 | 20113.1356335474 | -7273.13563354739 |
| 31 | 12672 | 11962.789891895 | 709.21010810496 |
| 32 | 10872 | 16144.633545876 | -5272.63354587601 |
| 33 | 21325 | 17793.7582348799 | 3531.2417651201 |
| 34 | 24542 | 5103.63821074913 | 19438.3617892509 |
| 35 | 16401 | 22103.8979196056 | -5702.89791960555 |
| 36 | 0 | 3171.06815055654 | -3171.06815055654 |
| 37 | 12821 | 22144.5930669337 | -9323.59306693367 |
| 38 | 14662 | 20978.9862895212 | -6316.9862895212 |
| 39 | 22190 | 10064.2542476675 | 12125.7457523325 |
| 40 | 37929 | 45841.8151177533 | -7912.81511775333 |
| 41 | 18009 | 28662.6622439405 | -10653.6622439405 |
| 42 | 11076 | 15268.2479924651 | -4192.24799246511 |
| 43 | 24981 | 16799.51449584 | 8181.48550415995 |
| 44 | 30691 | 15738.9347284804 | 14952.0652715196 |
| 45 | 29164 | 25626.800014918 | 3537.199985082 |
| 46 | 13985 | 18415.5381735897 | -4430.53817358968 |
| 47 | 7588 | 9496.2249835622 | -1908.22498356221 |
| 48 | 20023 | 20461.9080461842 | -438.908046184195 |
| 49 | 25524 | 18181.8821560997 | 7342.11784390025 |
| 50 | 14717 | 16678.6746846995 | -1961.67468469948 |
| 51 | 6832 | 9564.92896152326 | -2732.92896152326 |
| 52 | 9624 | 14816.1251852129 | -5192.1251852129 |
| 53 | 24300 | 23624.715005194 | 675.284994806043 |
| 54 | 21790 | 24217.068567546 | -2427.06856754598 |
| 55 | 16493 | 20543.1565137122 | -4050.15651371218 |
| 56 | 9269 | 16074.6361305116 | -6805.63613051162 |
| 57 | 20105 | 19166.2007629143 | 938.799237085678 |
| 58 | 11216 | 11538.6219625802 | -322.621962580248 |
| 59 | 15569 | 18369.7008036032 | -2800.70080360322 |
| 60 | 21799 | 4296.05145214318 | 17502.9485478568 |
| 61 | 3772 | 7796.60635880384 | -4024.60635880384 |
| 62 | 6057 | 8622.06403678802 | -2565.06403678802 |
| 63 | 20828 | 7987.08131713884 | 12840.9186828612 |
| 64 | 9976 | 18924.3817082871 | -8948.38170828712 |
| 65 | 14055 | 9449.0710308308 | 4605.9289691692 |
| 66 | 17455 | 19979.5594636746 | -2524.55946367463 |
| 67 | 39553 | 26187.5671640619 | 13365.4328359381 |
| 68 | 14818 | 24984.8605407033 | -10166.8605407033 |
| 69 | 17065 | 18054.2907074108 | -989.290707410772 |
| 70 | 1536 | 4184.13169701478 | -2648.13169701478 |
| 71 | 11938 | 22762.3200589513 | -10824.3200589513 |
| 72 | 24589 | 12173.5561560688 | 12415.4438439312 |
| 73 | 21332 | 26218.2339807075 | -4886.23398070746 |
| 74 | 13229 | 21711.3555924662 | -8482.35559246617 |
| 75 | 11331 | 11655.2098561475 | -324.209856147473 |
| 76 | 853 | 3842.51724530212 | -2989.51724530212 |
| 77 | 19821 | 22983.4939211832 | -3162.49392118319 |
| 78 | 34666 | 21427.8639305942 | 13238.1360694058 |
| 79 | 15051 | 12348.9019855076 | 2702.09801449241 |
| 80 | 27969 | 23995.778978606 | 3973.22102139401 |
| 81 | 17897 | 19942.9150275612 | -2045.91502756124 |
| 82 | 6031 | 11924.182154335 | -5893.18215433503 |
| 83 | 7153 | 11690.5608548575 | -4537.56085485752 |
| 84 | 13365 | 19321.2900045269 | -5956.29000452685 |
| 85 | 11197 | 12398.6775310581 | -1201.6775310581 |
| 86 | 25291 | 11560.3015226662 | 13730.6984773338 |
| 87 | 28994 | 32464.3460429577 | -3470.34604295768 |
| 88 | 10461 | 11437.2718229013 | -976.271822901348 |
| 89 | 16415 | 17370.3919399422 | -955.391939942166 |
| 90 | 8495 | 15172.8224751385 | -6677.8224751385 |
| 91 | 18318 | 17251.9702797846 | 1066.02972021536 |
| 92 | 25143 | 18735.5678820603 | 6407.43211793972 |
| 93 | 20471 | 11027.6001119293 | 9443.3998880707 |
| 94 | 14561 | 13697.7363700218 | 863.26362997816 |
| 95 | 16902 | 12754.0003748847 | 4147.99962511529 |
| 96 | 12994 | 23533.816518779 | -10539.816518779 |
| 97 | 29697 | 20931.2203361005 | 8765.77966389946 |
| 98 | 3895 | 8351.62024018013 | -4456.62024018013 |
| 99 | 9807 | 13894.0086513303 | -4087.00865133025 |
| 100 | 10711 | 12713.9928104066 | -2002.99281040665 |
| 101 | 2325 | 6413.81856702015 | -4088.81856702015 |
| 102 | 19000 | 13704.9197117651 | 5295.08028823495 |
| 103 | 22418 | 15413.5322995153 | 7004.46770048468 |
| 104 | 7872 | 10337.1415760775 | -2465.14157607755 |
| 105 | 5650 | 9063.62880126154 | -3413.62880126154 |
| 106 | 3979 | 5485.72888462453 | -1506.72888462453 |
| 107 | 14956 | 22299.5582002247 | -7343.55820022472 |
| 108 | 3738 | 6431.47670736896 | -2693.47670736896 |
| 109 | 0 | 3171.06815055654 | -3171.06815055654 |
| 110 | 10586 | 20651.0548491034 | -10065.0548491034 |
| 111 | 18122 | 8055.8200131123 | 10066.1799868877 |
| 112 | 17899 | 21885.8997875279 | -3986.89978752794 |
| 113 | 10913 | 15644.756357874 | -4731.75635787395 |
| 114 | 18060 | 15135.5660383359 | 2924.43396166414 |
| 115 | 0 | 3171.06815055654 | -3171.06815055654 |
| 116 | 0 | 3171.06815055654 | -3171.06815055654 |
| 117 | 15452 | 24209.2638879202 | -8757.26388792016 |
| 118 | 33996 | 14154.5041703713 | 19841.4958296287 |
| 119 | 8877 | 11128.3151055773 | -2251.31510557734 |
| 120 | 18708 | 13623.7429157394 | 5084.25708426064 |
| 121 | 2781 | 3438.73543866995 | -657.735438669953 |
| 122 | 20854 | 19289.9118993933 | 1564.08810060672 |
| 123 | 8179 | 11767.1411839467 | -3588.14118394668 |
| 124 | 7139 | 7828.73533667634 | -689.735336676344 |
| 125 | 13798 | 4263.32204625224 | 9534.67795374776 |
| 126 | 5619 | 10430.0866081122 | -4811.08660811218 |
| 127 | 13050 | 18134.1624933623 | -5084.16249336232 |
| 128 | 11297 | 14089.7267953035 | -2792.72679530345 |
| 129 | 16170 | 15451.5280363861 | 718.47196361392 |
| 130 | 0 | 3171.06815055654 | -3171.06815055654 |
| 131 | 0 | 3171.06815055654 | -3171.06815055654 |
| 132 | 20539 | 6670.36433782628 | 13868.6356621737 |
| 133 | 0 | 3171.06815055654 | -3171.06815055654 |
| 134 | 10056 | 6587.24738569558 | 3468.75261430442 |
| 135 | 0 | 3171.06815055654 | -3171.06815055654 |
| 136 | 2418 | 3575.50824856119 | -1157.50824856119 |
| 137 | 0 | 3171.06815055654 | -3171.06815055654 |
| 138 | 11806 | 10653.8914003566 | 1152.10859964343 |
| 139 | 15924 | 5720.75001102009 | 10203.2499889799 |
| 140 | 0 | 3171.06815055654 | -3171.06815055654 |
| 141 | 0 | 3171.06815055654 | -3171.06815055654 |
| 142 | 7084 | 12350.2185682525 | -5266.21856825254 |
| 143 | 14831 | 19651.7713662614 | -4820.77136626144 |
| 144 | 6585 | 7462.8682582193 | -877.868258219294 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.204611084835847 | 0.409222169671695 | 0.795388915164153 |
| 8 | 0.755184659575641 | 0.489630680848717 | 0.244815340424359 |
| 9 | 0.708367275140486 | 0.583265449719028 | 0.291632724859514 |
| 10 | 0.602711481901087 | 0.794577036197827 | 0.397288518098913 |
| 11 | 0.486532560029129 | 0.973065120058258 | 0.513467439970871 |
| 12 | 0.382847744453218 | 0.765695488906436 | 0.617152255546782 |
| 13 | 0.29532852083457 | 0.590657041669141 | 0.70467147916543 |
| 14 | 0.590553458922273 | 0.818893082155454 | 0.409446541077727 |
| 15 | 0.556322878777846 | 0.887354242444307 | 0.443677121222153 |
| 16 | 0.801032334745538 | 0.397935330508923 | 0.198967665254462 |
| 17 | 0.784370870774257 | 0.431258258451486 | 0.215629129225743 |
| 18 | 0.79664885555842 | 0.40670228888316 | 0.20335114444158 |
| 19 | 0.761607713196674 | 0.476784573606651 | 0.238392286803326 |
| 20 | 0.95353452501888 | 0.0929309499622418 | 0.0464654749811209 |
| 21 | 0.934184822989645 | 0.13163035402071 | 0.065815177010355 |
| 22 | 0.92323815293347 | 0.15352369413306 | 0.0767618470665301 |
| 23 | 0.902085919504336 | 0.195828160991329 | 0.0979140804956643 |
| 24 | 0.877908211900729 | 0.244183576198542 | 0.122091788099271 |
| 25 | 0.940221987835125 | 0.119556024329751 | 0.0597780121648755 |
| 26 | 0.950944779768134 | 0.0981104404637316 | 0.0490552202318658 |
| 27 | 0.935549086877444 | 0.128901826245112 | 0.064450913122556 |
| 28 | 0.92685099951268 | 0.14629800097464 | 0.07314900048732 |
| 29 | 0.999014156109286 | 0.00197168778142804 | 0.000985843890714022 |
| 30 | 0.998626969350533 | 0.00274606129893327 | 0.00137303064946664 |
| 31 | 0.997875143302466 | 0.0042497133950676 | 0.0021248566975338 |
| 32 | 0.996964001610185 | 0.00607199677962918 | 0.00303599838981459 |
| 33 | 0.995610609425031 | 0.00877878114993707 | 0.00438939057496853 |
| 34 | 0.999388484412723 | 0.00122303117455388 | 0.000611515587276941 |
| 35 | 0.999490857661197 | 0.00101828467760639 | 0.000509142338803194 |
| 36 | 0.99924110102982 | 0.00151779794035983 | 0.000758898970179916 |
| 37 | 0.999641191433843 | 0.000717617132313618 | 0.000358808566156809 |
| 38 | 0.999582991157198 | 0.000834017685604927 | 0.000417008842802463 |
| 39 | 0.99983454209771 | 0.000330915804581622 | 0.000165457902290811 |
| 40 | 0.999882423363065 | 0.000235153273869937 | 0.000117576636934969 |
| 41 | 0.999977773688082 | 4.44526238365927e-05 | 2.22263119182963e-05 |
| 42 | 0.999965078910447 | 6.98421791060513e-05 | 3.49210895530256e-05 |
| 43 | 0.999967292602743 | 6.54147945149833e-05 | 3.27073972574917e-05 |
| 44 | 0.999989456758666 | 2.10864826678604e-05 | 1.05432413339302e-05 |
| 45 | 0.999987898177743 | 2.42036445138185e-05 | 1.21018222569093e-05 |
| 46 | 0.999981834731267 | 3.63305374651922e-05 | 1.81652687325961e-05 |
| 47 | 0.99997002929558 | 5.99414088403962e-05 | 2.99707044201981e-05 |
| 48 | 0.999950569541456 | 9.88609170884175e-05 | 4.94304585442087e-05 |
| 49 | 0.999951099988325 | 9.7800023350346e-05 | 4.8900011675173e-05 |
| 50 | 0.999921204486355 | 0.000157591027289574 | 7.8795513644787e-05 |
| 51 | 0.999878783054988 | 0.000242433890024773 | 0.000121216945012387 |
| 52 | 0.999838479664077 | 0.000323040671846317 | 0.000161520335923158 |
| 53 | 0.99975379334185 | 0.00049241331630167 | 0.000246206658150835 |
| 54 | 0.999628248974997 | 0.000743502050006034 | 0.000371751025003017 |
| 55 | 0.999498487344275 | 0.00100302531145077 | 0.000501512655725387 |
| 56 | 0.999434751127216 | 0.00113049774556794 | 0.000565248872783968 |
| 57 | 0.999145571192569 | 0.00170885761486296 | 0.00085442880743148 |
| 58 | 0.998711957471967 | 0.00257608505606528 | 0.00128804252803264 |
| 59 | 0.998192096566979 | 0.00361580686604212 | 0.00180790343302106 |
| 60 | 0.999648198113834 | 0.000703603772331288 | 0.000351801886165644 |
| 61 | 0.999535534779678 | 0.000928930440644409 | 0.000464465220322205 |
| 62 | 0.999358459177978 | 0.00128308164404298 | 0.000641540822021491 |
| 63 | 0.999691612441027 | 0.000616775117945831 | 0.000308387558972916 |
| 64 | 0.999680326194914 | 0.000639347610171573 | 0.000319673805085786 |
| 65 | 0.999570103284419 | 0.000859793431162202 | 0.000429896715581101 |
| 66 | 0.99935947998439 | 0.00128104003122152 | 0.000640520015610761 |
| 67 | 0.999750450384565 | 0.000499099230869248 | 0.000249549615434624 |
| 68 | 0.999806288679375 | 0.000387422641249279 | 0.00019371132062464 |
| 69 | 0.999694526619947 | 0.000610946760106892 | 0.000305473380053446 |
| 70 | 0.99955407440365 | 0.000891851192698976 | 0.000445925596349488 |
| 71 | 0.999683247526321 | 0.000633504947357275 | 0.000316752473678637 |
| 72 | 0.999852573386581 | 0.000294853226837317 | 0.000147426613418658 |
| 73 | 0.999790468852898 | 0.00041906229420454 | 0.00020953114710227 |
| 74 | 0.999813016429675 | 0.000373967140649952 | 0.000186983570324976 |
| 75 | 0.999701987423456 | 0.000596025153089045 | 0.000298012576544523 |
| 76 | 0.99956421695432 | 0.000871566091359417 | 0.000435783045679709 |
| 77 | 0.999351204736713 | 0.00129759052657328 | 0.000648795263286638 |
| 78 | 0.999789509759705 | 0.000420980480589885 | 0.000210490240294942 |
| 79 | 0.99968675122876 | 0.000626497542480054 | 0.000313248771240027 |
| 80 | 0.99966607557856 | 0.000667848842881852 | 0.000333924421440926 |
| 81 | 0.999481438688077 | 0.00103712262384501 | 0.000518561311922503 |
| 82 | 0.999384066725665 | 0.0012318665486693 | 0.000615933274334649 |
| 83 | 0.999195040992003 | 0.00160991801599336 | 0.000804959007996678 |
| 84 | 0.999023362793995 | 0.00195327441200939 | 0.000976637206004693 |
| 85 | 0.998533262631425 | 0.00293347473715088 | 0.00146673736857544 |
| 86 | 0.999531154938094 | 0.000937690123812908 | 0.000468845061906454 |
| 87 | 0.999286724844992 | 0.00142655031001496 | 0.000713275155007482 |
| 88 | 0.99889370049725 | 0.00221259900549872 | 0.00110629950274936 |
| 89 | 0.998303102540395 | 0.00339379491921015 | 0.00169689745960507 |
| 90 | 0.998190584486181 | 0.00361883102763724 | 0.00180941551381862 |
| 91 | 0.997279390903951 | 0.00544121819209705 | 0.00272060909604852 |
| 92 | 0.99715425886656 | 0.00569148226687947 | 0.00284574113343974 |
| 93 | 0.997907545360253 | 0.00418490927949359 | 0.0020924546397468 |
| 94 | 0.99682898968899 | 0.00634202062201966 | 0.00317101031100983 |
| 95 | 0.996008042386066 | 0.0079839152278676 | 0.0039919576139338 |
| 96 | 0.996374799524809 | 0.00725040095038286 | 0.00362520047519143 |
| 97 | 0.997444474622837 | 0.00511105075432567 | 0.00255552537716284 |
| 98 | 0.996716462692631 | 0.00656707461473778 | 0.00328353730736889 |
| 99 | 0.995316921549668 | 0.00936615690066394 | 0.00468307845033197 |
| 100 | 0.993043206892543 | 0.0139135862149144 | 0.00695679310745718 |
| 101 | 0.991051418023472 | 0.0178971639530564 | 0.00894858197652821 |
| 102 | 0.989699615891852 | 0.0206007682162966 | 0.0103003841081483 |
| 103 | 0.993036083484978 | 0.0139278330300439 | 0.00696391651502197 |
| 104 | 0.989721741078335 | 0.0205565178433304 | 0.0102782589216652 |
| 105 | 0.985846870774836 | 0.0283062584503271 | 0.0141531292251636 |
| 106 | 0.979601058654179 | 0.0407978826916427 | 0.0203989413458214 |
| 107 | 0.97395692314944 | 0.052086153701122 | 0.026043076850561 |
| 108 | 0.964834446415128 | 0.0703311071697435 | 0.0351655535848718 |
| 109 | 0.955049052178117 | 0.0899018956437654 | 0.0449509478218827 |
| 110 | 0.960118157799562 | 0.0797636844008753 | 0.0398818422004376 |
| 111 | 0.967548996120742 | 0.0649020077585168 | 0.0324510038792584 |
| 112 | 0.957892511518528 | 0.0842149769629445 | 0.0421074884814723 |
| 113 | 0.947620726376813 | 0.104758547246374 | 0.0523792736231868 |
| 114 | 0.928601695201561 | 0.142796609596878 | 0.0713983047984388 |
| 115 | 0.909187834750075 | 0.181624330499849 | 0.0908121652499247 |
| 116 | 0.88658870248139 | 0.22682259503722 | 0.11341129751861 |
| 117 | 0.894920276987903 | 0.210159446024195 | 0.105079723012097 |
| 118 | 0.993523366374912 | 0.012953267250176 | 0.00647663362508802 |
| 119 | 0.98992115210408 | 0.0201576957918398 | 0.0100788478959199 |
| 120 | 0.989814951923156 | 0.020370096153688 | 0.010185048076844 |
| 121 | 0.98335657368741 | 0.0332868526251812 | 0.0166434263125906 |
| 122 | 0.97727747636709 | 0.0454450472658182 | 0.0227225236329091 |
| 123 | 0.966034887850595 | 0.0679302242988102 | 0.0339651121494051 |
| 124 | 0.947927154767416 | 0.104145690465169 | 0.0520728452325843 |
| 125 | 0.96719763096691 | 0.0656047380661784 | 0.0328023690330892 |
| 126 | 0.951657170399909 | 0.0966856592001825 | 0.0483428296000913 |
| 127 | 0.937734978744194 | 0.124530042511613 | 0.0622650212558063 |
| 128 | 0.918236772238536 | 0.163526455522929 | 0.0817632277614644 |
| 129 | 0.874685195746007 | 0.250629608507985 | 0.125314804253993 |
| 130 | 0.826425141924515 | 0.34714971615097 | 0.173574858075485 |
| 131 | 0.767785338123278 | 0.464429323753445 | 0.232214661876722 |
| 132 | 0.943410199769663 | 0.113179600460673 | 0.0565898002303367 |
| 133 | 0.907111568589995 | 0.18577686282001 | 0.0928884314100049 |
| 134 | 0.951734086684308 | 0.0965318266313836 | 0.0482659133156918 |
| 135 | 0.90478284257165 | 0.190434314856702 | 0.095217157428351 |
| 136 | 0.815185620253243 | 0.369628759493515 | 0.184814379746757 |
| 137 | 0.68664945883257 | 0.626701082334859 | 0.313350541167429 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 71 | 0.541984732824427 | NOK |
| 5% type I error level | 83 | 0.633587786259542 | NOK |
| 10% type I error level | 95 | 0.725190839694656 | NOK |
