| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -0.579523901807764 + 1.02934079084922X[t] -0.411228941058860M1[t] -0.95414467705487M2[t] -0.990635208661665M3[t] -1.21391964540537M4[t] -1.36022308765738M5[t] -1.31061465241099M6[t] -1.60787662081260M7[t] + 0.0232524650700799M8[t] -1.55744159337999M9[t] -1.31779819082949M10[t] -0.855700400480026M11[t] + 0.0206660927654979t + 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) | -0.579523901807764 | 0.528695 | -1.0961 | 0.277125 | 0.138562 |
| X | 1.02934079084922 | 0.034375 | 29.9447 | 0 | 0 |
| M1 | -0.411228941058860 | 0.256803 | -1.6013 | 0.114226 | 0.057113 |
| M2 | -0.95414467705487 | 0.257203 | -3.7097 | 0.000436 | 0.000218 |
| M3 | -0.990635208661665 | 0.270918 | -3.6566 | 0.000518 | 0.000259 |
| M4 | -1.21391964540537 | 0.259064 | -4.6858 | 1.5e-05 | 8e-06 |
| M5 | -1.36022308765738 | 0.258245 | -5.2672 | 2e-06 | 1e-06 |
| M6 | -1.31061465241099 | 0.268991 | -4.8723 | 8e-06 | 4e-06 |
| M7 | -1.60787662081260 | 0.26967 | -5.9624 | 0 | 0 |
| M8 | 0.0232524650700799 | 0.268731 | 0.0865 | 0.931318 | 0.465659 |
| M9 | -1.55744159337999 | 0.280128 | -5.5598 | 1e-06 | 0 |
| M10 | -1.31779819082949 | 0.281753 | -4.6771 | 1.6e-05 | 8e-06 |
| M11 | -0.855700400480026 | 0.270983 | -3.1578 | 0.002426 | 0.001213 |
| t | 0.0206660927654979 | 0.003247 | 6.3641 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.988100561390578 |
| R-squared | 0.976342719420376 |
| Adjusted R-squared | 0.97153733430264 |
| F-TEST (value) | 203.176789268527 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 64 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.46038124843887 |
| Sum Squared Residuals | 13.5648572105045 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14.5 | 14.2641569544673 | 0.235843045532726 |
| 2 | 14.3 | 13.6389732321519 | 0.661026767848087 |
| 3 | 15.3 | 14.9612918214146 | 0.338708178585409 |
| 4 | 14.4 | 14.1410690029268 | 0.258930997073150 |
| 5 | 13.7 | 13.6036953371007 | 0.0963046628993436 |
| 6 | 14.2 | 14.1886402605372 | 0.0113597394628484 |
| 7 | 13.5 | 13.5003080685613 | -0.000308068561344622 |
| 8 | 11.9 | 11.6523445583222 | 0.247655441677822 |
| 9 | 14.6 | 14.8272842305440 | -0.227284230544017 |
| 10 | 15.6 | 15.4993300421997 | 0.100669957800292 |
| 11 | 14.1 | 14.232214580871 | -0.132214580870997 |
| 12 | 14.9 | 15.0056469950316 | -0.105646995031598 |
| 13 | 14.2 | 14.3062819094835 | -0.106281909483471 |
| 14 | 14.6 | 14.5045708198474 | 0.0954291801525889 |
| 15 | 17.2 | 17.1650324372141 | 0.0349675627859135 |
| 16 | 15.4 | 15.4184029069620 | -0.0184029069620428 |
| 17 | 14.3 | 14.2634247666263 | 0.0365752333736828 |
| 18 | 17.5 | 16.9070512717613 | 0.59294872823875 |
| 19 | 14.5 | 14.5717738144267 | -0.0717738144266994 |
| 20 | 14.4 | 14.1648874113764 | 0.23511258862356 |
| 21 | 16.6 | 16.6192885300038 | -0.0192885300038222 |
| 22 | 16.7 | 16.9825321044047 | -0.282532104404747 |
| 23 | 16.6 | 16.9506255920951 | -0.350625592095097 |
| 24 | 16.9 | 17.1064535317462 | -0.206453531746169 |
| 25 | 15.7 | 15.9953521298584 | -0.295352129858354 |
| 26 | 16.4 | 16.0907069611374 | 0.309293038862626 |
| 27 | 18.4 | 18.6482344994191 | -0.248234499419129 |
| 28 | 16.9 | 17.1074731273369 | -0.207473127336930 |
| 29 | 16.5 | 16.3642313033409 | 0.135768696659112 |
| 30 | 18.3 | 17.8755829385417 | 0.424417061458319 |
| 31 | 15.1 | 15.2315032439524 | -0.131503243952363 |
| 32 | 15.7 | 15.6480894735815 | 0.0519105264185206 |
| 33 | 18.1 | 18.3083587503787 | -0.208358750378704 |
| 34 | 16.8 | 17.0246570594209 | -0.224657059420876 |
| 35 | 18.9 | 18.9484980497248 | -0.0484980497247513 |
| 36 | 19 | 18.6925896730361 | 0.307410326963870 |
| 37 | 18.1 | 17.7873564293182 | 0.312643570681843 |
| 38 | 17.8 | 17.5739090233424 | 0.22609097665759 |
| 39 | 21.5 | 20.9549091943035 | 0.545090805696458 |
| 40 | 17.1 | 16.7378617660134 | 0.362138233986633 |
| 41 | 18.7 | 18.8767741563951 | -0.176774156395147 |
| 42 | 19 | 19.3587850007467 | -0.358785000746719 |
| 43 | 16.4 | 16.8176393852423 | -0.417639385242326 |
| 44 | 16.9 | 17.0283574567016 | -0.128357456701596 |
| 45 | 18.6 | 18.8651541008194 | -0.265154100819445 |
| 46 | 19.3 | 19.5371999124751 | -0.237199912475135 |
| 47 | 19.4 | 20.1228978746750 | -0.722897874675023 |
| 48 | 17.6 | 18.2200442326277 | -0.620044232627649 |
| 49 | 18.6 | 19.4764266496930 | -0.876426649693039 |
| 50 | 18.1 | 18.6453747692078 | -0.545374769207761 |
| 51 | 20.4 | 21.5117045447443 | -1.11170454474428 |
| 52 | 18.1 | 18.4269319863883 | -0.326931986388252 |
| 53 | 19.6 | 19.5365035859208 | 0.0634964140791905 |
| 54 | 19.9 | 20.6361189047819 | -0.736118904781916 |
| 55 | 19.2 | 19.1243140801267 | 0.07568591987326 |
| 56 | 17.8 | 18.8203617561614 | -1.0203617561614 |
| 57 | 19.2 | 19.4219494512602 | -0.221949451260188 |
| 58 | 22 | 22.1526768446143 | -0.152676844614318 |
| 59 | 21.1 | 21.0914295414555 | 0.0085704585445521 |
| 60 | 19.5 | 19.0856418203232 | 0.414358179676845 |
| 61 | 22.2 | 21.7831013445775 | 0.416898655422544 |
| 62 | 20.9 | 21.5696539386017 | -0.669653938601709 |
| 63 | 22.2 | 21.7596976579303 | 0.440302342069745 |
| 64 | 23.5 | 23.2040245793108 | 0.295975420689204 |
| 65 | 21.5 | 21.3285078853806 | 0.171492114619383 |
| 66 | 24.3 | 24.0750684696005 | 0.224931530399530 |
| 67 | 22.8 | 22.2544614076905 | 0.545538592309473 |
| 68 | 20.3 | 19.6859593438569 | 0.614040656143092 |
| 69 | 23.7 | 22.7579649369938 | 0.942035063006176 |
| 70 | 23.3 | 22.5036040368852 | 0.796395963114784 |
| 71 | 19.6 | 18.3543343611787 | 1.24566563882132 |
| 72 | 18 | 17.7896237472353 | 0.210376252764702 |
| 73 | 17.3 | 16.9873245826023 | 0.31267541739775 |
| 74 | 16.8 | 16.8768112557114 | -0.0768112557114228 |
| 75 | 18.2 | 18.1991298449741 | 0.000870155025885298 |
| 76 | 16.5 | 16.8642366310618 | -0.364236631061762 |
| 77 | 16 | 16.3268629652356 | -0.326862965235565 |
| 78 | 18.4 | 18.5587531540308 | -0.158753154030814 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0313688529875117 | 0.0627377059750234 | 0.968631147012488 |
| 18 | 0.0833286195208506 | 0.166657239041701 | 0.91667138047915 |
| 19 | 0.035871276501243 | 0.071742553002486 | 0.964128723498757 |
| 20 | 0.0156812911347599 | 0.0313625822695197 | 0.98431870886524 |
| 21 | 0.00771997830931302 | 0.0154399566186260 | 0.992280021690687 |
| 22 | 0.00419693075659303 | 0.00839386151318606 | 0.995803069243407 |
| 23 | 0.00272594133801842 | 0.00545188267603684 | 0.997274058661982 |
| 24 | 0.000982804527422403 | 0.00196560905484481 | 0.999017195472578 |
| 25 | 0.000334437900153502 | 0.000668875800307004 | 0.999665562099846 |
| 26 | 0.000183174418648542 | 0.000366348837297083 | 0.999816825581351 |
| 27 | 0.000110041170330803 | 0.000220082340661606 | 0.99988995882967 |
| 28 | 3.80091115760199e-05 | 7.60182231520398e-05 | 0.999961990888424 |
| 29 | 2.58571994736884e-05 | 5.17143989473768e-05 | 0.999974142800526 |
| 30 | 3.20870617793018e-05 | 6.41741235586037e-05 | 0.99996791293822 |
| 31 | 1.65660096607704e-05 | 3.31320193215408e-05 | 0.99998343399034 |
| 32 | 7.00936240805643e-06 | 1.40187248161129e-05 | 0.999992990637592 |
| 33 | 2.26355105250229e-06 | 4.52710210500459e-06 | 0.999997736448948 |
| 34 | 9.5325310797767e-07 | 1.90650621595534e-06 | 0.999999046746892 |
| 35 | 4.47920801806462e-07 | 8.95841603612924e-07 | 0.999999552079198 |
| 36 | 1.71605148427224e-06 | 3.43210296854447e-06 | 0.999998283948516 |
| 37 | 5.00507964693327e-06 | 1.00101592938665e-05 | 0.999994994920353 |
| 38 | 5.27640354207147e-06 | 1.05528070841429e-05 | 0.999994723596458 |
| 39 | 2.54640171539242e-05 | 5.09280343078485e-05 | 0.999974535982846 |
| 40 | 0.000367133360407381 | 0.000734266720814763 | 0.999632866639593 |
| 41 | 0.000404745527262318 | 0.000809491054524636 | 0.999595254472738 |
| 42 | 0.00189189166959515 | 0.0037837833391903 | 0.998108108330405 |
| 43 | 0.00120612250661343 | 0.00241224501322685 | 0.998793877493387 |
| 44 | 0.00210362937491986 | 0.00420725874983973 | 0.99789637062508 |
| 45 | 0.00124371596914679 | 0.00248743193829358 | 0.998756284030853 |
| 46 | 0.00090354682660439 | 0.00180709365320878 | 0.999096453173396 |
| 47 | 0.00157712312041328 | 0.00315424624082655 | 0.998422876879587 |
| 48 | 0.00123404146573052 | 0.00246808293146105 | 0.99876595853427 |
| 49 | 0.00402207970199572 | 0.00804415940399144 | 0.995977920298004 |
| 50 | 0.00679986718759172 | 0.0135997343751834 | 0.993200132812408 |
| 51 | 0.0429174657055721 | 0.0858349314111443 | 0.957082534294428 |
| 52 | 0.04115650184524 | 0.08231300369048 | 0.95884349815476 |
| 53 | 0.0831606342384393 | 0.166321268476879 | 0.91683936576156 |
| 54 | 0.0781761113161992 | 0.156352222632398 | 0.921823888683801 |
| 55 | 0.135759420913910 | 0.271518841827820 | 0.86424057908609 |
| 56 | 0.226672415405476 | 0.453344830810951 | 0.773327584594524 |
| 57 | 0.169972557103781 | 0.339945114207561 | 0.83002744289622 |
| 58 | 0.115125292024987 | 0.230250584049975 | 0.884874707975013 |
| 59 | 0.528135650236572 | 0.943728699526856 | 0.471864349763428 |
| 60 | 0.476243881482889 | 0.952487762965778 | 0.523756118517111 |
| 61 | 0.364077065184578 | 0.728154130369155 | 0.635922934815422 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 28 | 0.622222222222222 | NOK |
| 5% type I error level | 31 | 0.688888888888889 | NOK |
| 10% type I error level | 35 | 0.777777777777778 | NOK |
