| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2.80871688717935 + 0.00219088351317846X[t] + 0.68729913105026Y1[t] -0.239085441528047Y2[t] -0.0409734428967782Y3[t] + 0.21095965078892Y4[t] + 0.141196595109811M1[t] -0.242648801192167M2[t] + 0.681888267994503M3[t] + 0.334352165097872M4[t] + 0.298794143047685M5[t] + 0.308872252168863M6[t] + 0.129614560491464M7[t] + 0.324046218241749M8[t] + 0.42947025602853M9[t] + 0.248535643118973M10[t] + 0.138288439029698M11[t] -0.00505416953979656t + 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) | 2.80871688717935 | 1.173255 | 2.394 | 0.019168 | 0.009584 |
| X | 0.00219088351317846 | 0.010836 | 0.2022 | 0.840319 | 0.42016 |
| Y1 | 0.68729913105026 | 0.104841 | 6.5557 | 0 | 0 |
| Y2 | -0.239085441528047 | 0.131833 | -1.8135 | 0.073748 | 0.036874 |
| Y3 | -0.0409734428967782 | 0.131618 | -0.3113 | 0.756432 | 0.378216 |
| Y4 | 0.21095965078892 | 0.085342 | 2.4719 | 0.015706 | 0.007853 |
| M1 | 0.141196595109811 | 0.215567 | 0.655 | 0.514472 | 0.257236 |
| M2 | -0.242648801192167 | 0.22589 | -1.0742 | 0.286182 | 0.143091 |
| M3 | 0.681888267994503 | 0.288252 | 2.3656 | 0.020587 | 0.010293 |
| M4 | 0.334352165097872 | 0.243105 | 1.3753 | 0.17312 | 0.08656 |
| M5 | 0.298794143047685 | 0.229515 | 1.3018 | 0.196953 | 0.098476 |
| M6 | 0.308872252168863 | 0.228625 | 1.351 | 0.180758 | 0.090379 |
| M7 | 0.129614560491464 | 0.208424 | 0.6219 | 0.535906 | 0.267953 |
| M8 | 0.324046218241749 | 0.225254 | 1.4386 | 0.154428 | 0.077214 |
| M9 | 0.42947025602853 | 0.222787 | 1.9277 | 0.057677 | 0.028839 |
| M10 | 0.248535643118973 | 0.222361 | 1.1177 | 0.267258 | 0.133629 |
| M11 | 0.138288439029698 | 0.22411 | 0.6171 | 0.539066 | 0.269533 |
| t | -0.00505416953979656 | 0.002206 | -2.2915 | 0.024744 | 0.012372 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.871851262816224 |
| R-squared | 0.760124624474244 |
| Adjusted R-squared | 0.705752872688407 |
| F-TEST (value) | 13.9801385739466 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 75 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.402113921449158 |
| Sum Squared Residuals | 12.1271704367415 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 6.3 | 4.34360880362798 | 1.95639119637202 |
| 2 | 6 | 6.92434898907602 | -0.924348989076022 |
| 3 | 6.2 | 6.41176551366118 | -0.21176551366118 |
| 4 | 6.4 | 6.25756972225082 | 0.142430277749177 |
| 5 | 6.8 | 7.30310926119637 | -0.503109261196373 |
| 6 | 7.5 | 7.48215660258692 | 0.0178433974130835 |
| 7 | 7.5 | 7.70176192512855 | -0.201761925128545 |
| 8 | 7.6 | 7.7241679085156 | -0.124167908515603 |
| 9 | 7.6 | 7.96101999947792 | -0.361019999477918 |
| 10 | 7.4 | 7.89857534007669 | -0.498575340076686 |
| 11 | 7.3 | 7.66340654272835 | -0.363406542728353 |
| 12 | 7.1 | 7.51389351225011 | -0.413893512250115 |
| 13 | 6.9 | 7.54226937247774 | -0.642269372477741 |
| 14 | 6.8 | 7.031547868349 | -0.231547868349001 |
| 15 | 7.5 | 7.87624714500048 | -0.376247145000484 |
| 16 | 7.6 | 8.008041956304 | -0.408041956304002 |
| 17 | 7.8 | 7.86313035887635 | -0.0631303588763472 |
| 18 | 8 | 7.94441624143346 | 0.0555837585665431 |
| 19 | 8.1 | 7.96944089908962 | 0.130559100910375 |
| 20 | 8.2 | 8.17138091852124 | 0.0286190814787650 |
| 21 | 8.3 | 8.36240016827003 | -0.0624001682700315 |
| 22 | 8.2 | 8.25845098723574 | -0.0584509872357365 |
| 23 | 8 | 8.08591319864875 | -0.0859131986487455 |
| 24 | 7.9 | 7.84010254332564 | 0.0598974566743637 |
| 25 | 7.6 | 7.97044738930418 | -0.370447389304184 |
| 26 | 7.6 | 7.40038700628494 | 0.199612993715058 |
| 27 | 8.3 | 8.31603684444677 | -0.0160368444467706 |
| 28 | 8.4 | 8.44122924031861 | -0.041229240318613 |
| 29 | 8.4 | 8.2822978394396 | 0.117702160560403 |
| 30 | 8.4 | 8.23889450351547 | 0.161105496484531 |
| 31 | 8.4 | 8.1694564795382 | 0.230543520461798 |
| 32 | 8.6 | 8.37620543085518 | 0.223794569144820 |
| 33 | 8.9 | 8.61009153498849 | 0.289908465011507 |
| 34 | 8.8 | 8.58663808222365 | 0.213361917776352 |
| 35 | 8.3 | 8.35708334560868 | -0.0570833456086827 |
| 36 | 7.5 | 7.90242895452646 | -0.402428954526465 |
| 37 | 7.2 | 7.66361017622417 | -0.463610176224167 |
| 38 | 7.4 | 7.28985234984375 | 0.110147650156252 |
| 39 | 8.8 | 8.29323843276577 | 0.506761567234233 |
| 40 | 9.3 | 8.71916847275587 | 0.580831527244132 |
| 41 | 9.3 | 8.6539059295137 | 0.646094070486296 |
| 42 | 8.7 | 8.51589090108328 | 0.184109098916720 |
| 43 | 8.2 | 8.18003469640768 | 0.0199653035923150 |
| 44 | 8.3 | 8.26965467732402 | 0.03034532267598 |
| 45 | 8.5 | 8.56754506058587 | -0.067545060585873 |
| 46 | 8.6 | 8.39186663973594 | 0.208133360264065 |
| 47 | 8.5 | 8.20718069613811 | 0.292819303861888 |
| 48 | 8.2 | 7.97993822813528 | 0.220061771864714 |
| 49 | 8.1 | 7.9615968918992 | 0.138403108100807 |
| 50 | 7.9 | 7.6355023142876 | 0.264497685712404 |
| 51 | 8.6 | 8.36033084373248 | 0.239669156267524 |
| 52 | 8.7 | 8.50990157638488 | 0.190098423615119 |
| 53 | 8.7 | 8.39609867381138 | 0.303901326188622 |
| 54 | 8.5 | 8.29034727940822 | 0.209652720591777 |
| 55 | 8.4 | 8.11850356543176 | 0.281496434568241 |
| 56 | 8.5 | 8.29382345108606 | 0.206176548913937 |
| 57 | 8.7 | 8.48779654957674 | 0.212203450423255 |
| 58 | 8.7 | 8.38098896528894 | 0.319011034711064 |
| 59 | 8.6 | 8.22510226998073 | 0.374897730019273 |
| 60 | 8.5 | 7.9935059488107 | 0.506494051189299 |
| 61 | 8.3 | 8.14717506390752 | 0.152824936092481 |
| 62 | 8 | 7.65911871281012 | 0.340881287189885 |
| 63 | 8.2 | 8.3392565420735 | -0.139256542073495 |
| 64 | 8.1 | 8.21603279285499 | -0.116032792854991 |
| 65 | 8.1 | 8.06030333680407 | 0.039696663195926 |
| 66 | 8 | 8.02147773869463 | -0.0214777386946323 |
| 67 | 7.9 | 7.80683805817243 | 0.0931619418275705 |
| 68 | 7.9 | 7.90641758205816 | -0.00641758205815926 |
| 69 | 8 | 8.04355687280034 | -0.0435568728003401 |
| 70 | 8 | 7.90776576420757 | 0.0922342357924267 |
| 71 | 7.9 | 7.77703680877471 | 0.122963191225286 |
| 72 | 8 | 7.53304272219315 | 0.46695727780685 |
| 73 | 7.7 | 7.78993039734206 | -0.0899303973420581 |
| 74 | 7.2 | 7.19233787207619 | 0.00766212792381141 |
| 75 | 7.5 | 7.76058870651227 | -0.260588706512269 |
| 76 | 7.3 | 7.79275222920706 | -0.492752229207055 |
| 77 | 7 | 7.5183377383197 | -0.518337738319700 |
| 78 | 7 | 7.26890691540859 | -0.268906915408587 |
| 79 | 7 | 7.20786623049591 | -0.207866230495913 |
| 80 | 7.2 | 7.33820507069238 | -0.138205070692377 |
| 81 | 7.3 | 7.53618932350375 | -0.236189323503747 |
| 82 | 7.1 | 7.37571422123149 | -0.275714221231485 |
| 83 | 6.8 | 7.08427713812067 | -0.284277138120665 |
| 84 | 6.4 | 6.83708809075865 | -0.437088090758647 |
| 85 | 6.1 | 6.78136190521716 | -0.681361905217156 |
| 86 | 6.5 | 6.26690488727238 | 0.233095112727615 |
| 87 | 7.7 | 7.44253597180756 | 0.257464028192440 |
| 88 | 7.9 | 7.75530400992377 | 0.144695990076231 |
| 89 | 7.5 | 7.52281686203883 | -0.0228168620388276 |
| 90 | 6.9 | 7.23790981786943 | -0.337909817869434 |
| 91 | 6.6 | 6.94609814573584 | -0.346098145735842 |
| 92 | 6.9 | 7.12014496094736 | -0.220144960947364 |
| 93 | 7.7 | 7.43140049079685 | 0.268599509203149 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.183778709681325 | 0.367557419362651 | 0.816221290318675 |
| 22 | 0.276495184312843 | 0.552990368625687 | 0.723504815687157 |
| 23 | 0.231282555413019 | 0.462565110826038 | 0.768717444586981 |
| 24 | 0.228276548967333 | 0.456553097934666 | 0.771723451032667 |
| 25 | 0.212186949180747 | 0.424373898361495 | 0.787813050819253 |
| 26 | 0.153244039289497 | 0.306488078578995 | 0.846755960710503 |
| 27 | 0.107175702352426 | 0.214351404704852 | 0.892824297647574 |
| 28 | 0.0814197107573912 | 0.162839421514782 | 0.918580289242609 |
| 29 | 0.0509079167856032 | 0.101815833571206 | 0.949092083214397 |
| 30 | 0.227898635774185 | 0.45579727154837 | 0.772101364225815 |
| 31 | 0.321025832978041 | 0.642051665956082 | 0.678974167021959 |
| 32 | 0.591461579510419 | 0.817076840979162 | 0.408538420489581 |
| 33 | 0.510738831541325 | 0.97852233691735 | 0.489261168458675 |
| 34 | 0.451581218903728 | 0.903162437807456 | 0.548418781096272 |
| 35 | 0.535154965919696 | 0.929690068160607 | 0.464845034080304 |
| 36 | 0.968923481342472 | 0.0621530373150566 | 0.0310765186575283 |
| 37 | 0.99629234185043 | 0.00741531629913951 | 0.00370765814956976 |
| 38 | 0.99881409600829 | 0.00237180798341828 | 0.00118590399170914 |
| 39 | 0.998621889519757 | 0.00275622096048499 | 0.00137811048024250 |
| 40 | 0.998666271482323 | 0.00266745703535437 | 0.00133372851767718 |
| 41 | 0.9990670726631 | 0.00186585467379976 | 0.000932927336899878 |
| 42 | 0.998451123278567 | 0.00309775344286637 | 0.00154887672143319 |
| 43 | 0.999395918413688 | 0.00120816317262407 | 0.000604081586312037 |
| 44 | 0.999900635595037 | 0.000198728809925387 | 9.93644049626935e-05 |
| 45 | 0.999971574436866 | 5.6851126267352e-05 | 2.8425563133676e-05 |
| 46 | 0.999949756926287 | 0.000100486147425625 | 5.02430737128124e-05 |
| 47 | 0.999912375544895 | 0.000175248910209541 | 8.76244551047705e-05 |
| 48 | 0.999885161773606 | 0.000229676452787863 | 0.000114838226393932 |
| 49 | 0.999815717451542 | 0.000368565096916685 | 0.000184282548458343 |
| 50 | 0.999846692378002 | 0.000306615243996369 | 0.000153307621998184 |
| 51 | 0.999688600005488 | 0.000622799989024539 | 0.000311399994512269 |
| 52 | 0.99955515381183 | 0.000889692376338397 | 0.000444846188169198 |
| 53 | 0.999417266435143 | 0.00116546712971336 | 0.000582733564856679 |
| 54 | 0.999389047680862 | 0.00122190463827560 | 0.000610952319137801 |
| 55 | 0.9993633594654 | 0.00127328106920168 | 0.00063664053460084 |
| 56 | 0.999062767443788 | 0.00187446511242428 | 0.000937232556212142 |
| 57 | 0.998336304856334 | 0.00332739028733236 | 0.00166369514366618 |
| 58 | 0.996864391592666 | 0.00627121681466741 | 0.00313560840733371 |
| 59 | 0.995170389772602 | 0.00965922045479562 | 0.00482961022739781 |
| 60 | 0.99133849647975 | 0.0173230070404990 | 0.00866150352024951 |
| 61 | 0.990450423964765 | 0.0190991520704691 | 0.00954957603523454 |
| 62 | 0.985194891643382 | 0.0296102167132352 | 0.0148051083566176 |
| 63 | 0.990136461558484 | 0.0197270768830318 | 0.00986353844151592 |
| 64 | 0.992569174185603 | 0.0148616516287943 | 0.00743082581439714 |
| 65 | 0.989830157771247 | 0.0203396844575067 | 0.0101698422287534 |
| 66 | 0.990789257697462 | 0.0184214846050769 | 0.00921074230253845 |
| 67 | 0.987989018002623 | 0.0240219639947537 | 0.0120109819973769 |
| 68 | 0.975709542234312 | 0.048580915531375 | 0.0242904577656875 |
| 69 | 0.953438030371067 | 0.0931239392578663 | 0.0465619696289332 |
| 70 | 0.905544253699654 | 0.188911492600693 | 0.0944557463003464 |
| 71 | 0.930615160850735 | 0.138769678298530 | 0.0693848391492648 |
| 72 | 0.902736898692558 | 0.194526202614883 | 0.0972631013074415 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 23 | 0.442307692307692 | NOK |
| 5% type I error level | 32 | 0.615384615384615 | NOK |
| 10% type I error level | 34 | 0.653846153846154 | NOK |
