| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 12578.3467133000 + 940.617859768512X[t] -9273.41189991766M1[t] -8171.45512129261M2[t] -3304.95713235452M3[t] + 1066.79085658356M4[t] -9907.20142016934M5[t] -6338.00379283771M6[t] -2779.3081961687M7[t] + 669.666289876279M8[t] -10768.7734064769M9[t] -9459.79795468256M10[t] -3727.14219083930M11[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) | 12578.3467133000 | 6086.449334 | 2.0666 | 0.042132 | 0.021066 |
| X | 940.617859768512 | 30.685034 | 30.654 | 0 | 0 |
| M1 | -9273.41189991766 | 4718.068005 | -1.9655 | 0.052961 | 0.026481 |
| M2 | -8171.45512129261 | 4714.746288 | -1.7332 | 0.087069 | 0.043534 |
| M3 | -3304.95713235452 | 4714.031264 | -0.7011 | 0.485361 | 0.24268 |
| M4 | 1066.79085658356 | 4713.448009 | 0.2263 | 0.821545 | 0.410773 |
| M5 | -9907.20142016934 | 4713.455984 | -2.1019 | 0.038832 | 0.019416 |
| M6 | -6338.00379283771 | 4712.480309 | -1.3449 | 0.182593 | 0.091296 |
| M7 | -2779.3081961687 | 4871.583131 | -0.5705 | 0.56999 | 0.284995 |
| M8 | 669.666289876279 | 4869.874883 | 0.1375 | 0.890985 | 0.445493 |
| M9 | -10768.7734064769 | 4868.963309 | -2.2117 | 0.029952 | 0.014976 |
| M10 | -9459.79795468256 | 4867.264228 | -1.9436 | 0.055603 | 0.027802 |
| M11 | -3727.14219083930 | 4867.109485 | -0.7658 | 0.446147 | 0.223074 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.962400410778208 |
| R-squared | 0.926214550666064 |
| Adjusted R-squared | 0.914715519601035 |
| F-TEST (value) | 80.5471822302383 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 77 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 9105.2857716034 |
| Sum Squared Residuals | 6383779631.65739 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 106370 | 97648.9061481644 | 8721.09385183561 |
| 2 | 109375 | 100255.851502419 | 9119.14849758123 |
| 3 | 116476 | 105310.473063311 | 11165.5269366895 |
| 4 | 123297 | 110716.900697994 | 12580.099302006 |
| 5 | 114813 | 100213.217351125 | 14599.7826488746 |
| 6 | 117925 | 106133.959627878 | 11791.0403721217 |
| 7 | 126466 | 111103.5820142 | 15362.4179857999 |
| 8 | 131235 | 116621.915791736 | 14613.0842082642 |
| 9 | 120546 | 106876.588242966 | 13669.4117570341 |
| 10 | 123791 | 111195.540846019 | 12595.4591539805 |
| 11 | 129813 | 117962.876255608 | 11850.1237443919 |
| 12 | 133463 | 123853.439523915 | 9609.56047608502 |
| 13 | 122987 | 116555.325129511 | 6431.6748704888 |
| 14 | 125418 | 122924.74192284 | 2493.25807716008 |
| 15 | 130199 | 129766.537417292 | 432.462582708131 |
| 16 | 133016 | 136019.521125767 | -3003.52112576698 |
| 17 | 121454 | 125703.961350852 | -4249.96135085205 |
| 18 | 122044 | 131906.888985535 | -9862.88898553549 |
| 19 | 128313 | 136029.955298066 | -7716.95529806561 |
| 20 | 131556 | 140701.733001810 | -9145.73300180967 |
| 21 | 120027 | 129921.725807294 | -9894.72580729445 |
| 22 | 123001 | 133958.493052417 | -10957.4930524175 |
| 23 | 130111 | 139597.087030284 | -9486.08703028389 |
| 24 | 132524 | 143888.599936984 | -11364.5999369843 |
| 25 | 123742 | 133768.631963275 | -10026.6319632750 |
| 26 | 124931 | 136939.948033391 | -12008.9480333907 |
| 27 | 133646 | 142182.693166236 | -8536.69316623624 |
| 28 | 136557 | 147024.750085059 | -10467.7500850586 |
| 29 | 127509 | 136238.881380259 | -8729.88138025937 |
| 30 | 128945 | 142159.623657012 | -13214.6236570123 |
| 31 | 137191 | 145812.381039658 | -8621.38103965815 |
| 32 | 139716 | 150107.911599495 | -10391.9115994948 |
| 33 | 129083 | 139892.275120841 | -10809.2751208407 |
| 34 | 131604 | 143740.91879401 | -12136.91879401 |
| 35 | 139413 | 149849.821701761 | -10436.8217017607 |
| 36 | 143125 | 153765.087464554 | -10640.0874645537 |
| 37 | 133948 | 145244.169852451 | -11296.1698524508 |
| 38 | 137116 | 148133.300564636 | -11017.3005646361 |
| 39 | 144864 | 153281.983911505 | -8417.98391150467 |
| 40 | 149277 | 158500.287974234 | -9223.28797423442 |
| 41 | 138796 | 148372.851771273 | -9576.8517712732 |
| 42 | 143258 | 153823.285118142 | -10565.2851181418 |
| 43 | 150034 | 158792.907504464 | -8758.90750446362 |
| 44 | 154708 | 163464.685208208 | -8756.68520820764 |
| 45 | 144888 | 152496.554441739 | -7608.55444173874 |
| 46 | 148762 | 156627.383472839 | -7865.3834728386 |
| 47 | 156500 | 162830.348166566 | -6330.34816656612 |
| 48 | 161088 | 167215.922859243 | -6127.92285924339 |
| 49 | 152772 | 157284.078457488 | -4512.07845748775 |
| 50 | 158011 | 160079.147383696 | -2068.14738369614 |
| 51 | 163318 | 165039.707158611 | -1721.70715861107 |
| 52 | 169969 | 170540.196579271 | -571.196579271382 |
| 53 | 162269 | 160224.636804356 | 2044.36319564357 |
| 54 | 165765 | 166709.749796970 | -944.749796970428 |
| 55 | 170600 | 170550.63075157 | 49.3692484299818 |
| 56 | 174681 | 175034.284883360 | -353.284883360355 |
| 57 | 166364 | 163407.721615054 | 2956.2783849465 |
| 58 | 170240 | 166691.994572362 | 3548.00542763831 |
| 59 | 176150 | 172518.712122182 | 3631.28787781819 |
| 60 | 182056 | 176057.730741067 | 5998.26925893259 |
| 61 | 172218 | 166878.380627127 | 5339.6193728734 |
| 62 | 177856 | 169955.634911266 | 7900.36508873449 |
| 63 | 182253 | 175386.503616065 | 6866.4963839353 |
| 64 | 188090 | 181263.240180632 | 6826.75981936761 |
| 65 | 176863 | 171229.865763648 | 5633.13423635199 |
| 66 | 183273 | 176774.360896494 | 6498.63910350648 |
| 67 | 187969 | 180803.365423047 | 7165.6345769532 |
| 68 | 194650 | 185287.019554837 | 9362.98044516286 |
| 69 | 183036 | 174695.135932276 | 8340.86406772436 |
| 70 | 189516 | 178355.656033491 | 11160.3439665087 |
| 71 | 193805 | 185122.99144308 | 8682.00855692013 |
| 72 | 200499 | 190543.245781502 | 9955.75421849753 |
| 73 | 188142 | 181740.142811469 | 6401.85718853093 |
| 74 | 193732 | 184911.458881585 | 8820.54111841515 |
| 75 | 197126 | 190436.389372361 | 6689.61062763911 |
| 76 | 205140 | 195842.817007044 | 9297.18299295567 |
| 77 | 191751 | 185339.133660176 | 6411.86633982431 |
| 78 | 196700 | 192106.432010720 | 4593.56798927975 |
| 79 | 199784 | 197264.177968996 | 2519.82203100424 |
| 80 | 207360 | 202688.449960555 | 4671.55003944539 |
| 81 | 196101 | 192754.998839831 | 3346.00116016894 |
| 82 | 200824 | 197168.013228861 | 3655.98677113851 |
| 83 | 205743 | 203653.163280520 | 2089.83671948046 |
| 84 | 212489 | 209919.973692734 | 2569.02630726617 |
| 85 | 200810 | 201869.365010515 | -1059.36501051522 |
| 86 | 203683 | 206921.916800168 | -3238.91680016804 |
| 87 | 207286 | 213763.71229462 | -6477.71229461999 |
| 88 | 210910 | 216348.286349998 | -5438.28634999790 |
| 89 | 194915 | 201047.45191831 | -6132.45191830986 |
| 90 | 217920 | 206215.699907248 | 11704.3000927521 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.179096516737757 | 0.358193033475514 | 0.820903483262243 |
| 17 | 0.214837659747152 | 0.429675319494305 | 0.785162340252848 |
| 18 | 0.249279035611104 | 0.498558071222208 | 0.750720964388896 |
| 19 | 0.276457763287381 | 0.552915526574762 | 0.723542236712619 |
| 20 | 0.288868523378219 | 0.577737046756437 | 0.711131476621781 |
| 21 | 0.282237803957177 | 0.564475607914355 | 0.717762196042823 |
| 22 | 0.262387503785132 | 0.524775007570264 | 0.737612496214868 |
| 23 | 0.213807800985515 | 0.427615601971031 | 0.786192199014485 |
| 24 | 0.179303352774691 | 0.358606705549382 | 0.820696647225309 |
| 25 | 0.127845629551121 | 0.255691259102241 | 0.87215437044888 |
| 26 | 0.0860656584281957 | 0.172131316856391 | 0.913934341571804 |
| 27 | 0.0629281556994619 | 0.125856311398924 | 0.937071844300538 |
| 28 | 0.0407958782087462 | 0.0815917564174923 | 0.959204121791254 |
| 29 | 0.0268181700675395 | 0.053636340135079 | 0.97318182993246 |
| 30 | 0.0185729383867189 | 0.0371458767734378 | 0.981427061613281 |
| 31 | 0.0122605301803665 | 0.0245210603607330 | 0.987739469819633 |
| 32 | 0.00759849237448418 | 0.0151969847489684 | 0.992401507625516 |
| 33 | 0.00489516129177526 | 0.00979032258355052 | 0.995104838708225 |
| 34 | 0.00334445000665756 | 0.00668890001331512 | 0.996655549993342 |
| 35 | 0.00226820103975865 | 0.0045364020795173 | 0.997731798960241 |
| 36 | 0.00180517318125498 | 0.00361034636250996 | 0.998194826818745 |
| 37 | 0.00232535053639351 | 0.00465070107278703 | 0.997674649463607 |
| 38 | 0.00369525931652762 | 0.00739051863305524 | 0.996304740683472 |
| 39 | 0.00519914622892752 | 0.0103982924578550 | 0.994800853771072 |
| 40 | 0.00741851847911453 | 0.0148370369582291 | 0.992581481520886 |
| 41 | 0.0085436635462132 | 0.0170873270924264 | 0.991456336453787 |
| 42 | 0.0203566047581421 | 0.0407132095162842 | 0.979643395241858 |
| 43 | 0.0286969661936851 | 0.0573939323873703 | 0.971303033806315 |
| 44 | 0.0494651361280466 | 0.0989302722560932 | 0.950534863871953 |
| 45 | 0.0882984257538932 | 0.176596851507786 | 0.911701574246107 |
| 46 | 0.178567857565682 | 0.357135715131365 | 0.821432142434318 |
| 47 | 0.282814913988089 | 0.565629827976177 | 0.717185086011911 |
| 48 | 0.474005198301033 | 0.948010396602067 | 0.525994801698967 |
| 49 | 0.639751976793555 | 0.720496046412889 | 0.360248023206445 |
| 50 | 0.794523233399651 | 0.410953533200698 | 0.205476766600349 |
| 51 | 0.852369291665272 | 0.295261416669456 | 0.147630708334728 |
| 52 | 0.9070615684156 | 0.1858768631688 | 0.0929384315844 |
| 53 | 0.930884648393887 | 0.138230703212227 | 0.0691153516061135 |
| 54 | 0.979582983454615 | 0.0408340330907705 | 0.0204170165453852 |
| 55 | 0.986478122411442 | 0.0270437551771163 | 0.0135218775885581 |
| 56 | 0.994988462138652 | 0.0100230757226951 | 0.00501153786134757 |
| 57 | 0.99697233170981 | 0.00605533658038139 | 0.00302766829019069 |
| 58 | 0.998720291268001 | 0.00255941746399735 | 0.00127970873199867 |
| 59 | 0.999198635753966 | 0.00160272849206780 | 0.000801364246033898 |
| 60 | 0.99952408130738 | 0.000951837385239332 | 0.000475918692619666 |
| 61 | 0.999493702866974 | 0.00101259426605152 | 0.000506297133025762 |
| 62 | 0.999350810583523 | 0.00129837883295375 | 0.000649189416476873 |
| 63 | 0.998902959622795 | 0.00219408075441095 | 0.00109704037720548 |
| 64 | 0.998332572786345 | 0.00333485442730923 | 0.00166742721365462 |
| 65 | 0.99690586588754 | 0.00618826822491937 | 0.00309413411245968 |
| 66 | 0.999066307144005 | 0.00186738571199006 | 0.000933692855995032 |
| 67 | 0.998020080908615 | 0.00395983818277063 | 0.00197991909138532 |
| 68 | 0.996153980147324 | 0.00769203970535174 | 0.00384601985267587 |
| 69 | 0.9922713572074 | 0.0154572855852004 | 0.00772864279260018 |
| 70 | 0.983638557903345 | 0.0327228841933102 | 0.0163614420966551 |
| 71 | 0.965281280964996 | 0.0694374380700084 | 0.0347187190350042 |
| 72 | 0.929051973803094 | 0.141896052393812 | 0.0709480261969062 |
| 73 | 0.859148523435805 | 0.281702953128389 | 0.140851476564195 |
| 74 | 0.730610403454114 | 0.538779193091773 | 0.269389596545886 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 18 | 0.305084745762712 | NOK |
| 5% type I error level | 30 | 0.508474576271186 | NOK |
| 10% type I error level | 35 | 0.593220338983051 | NOK |
