| Multiple Linear Regression - Estimated Regression Equation |
| O[t] = + 20.8400279089439 + 0.347329743559927PS[t] + 0.0089567410966607CMD[t] -0.22783385858432PEC[t] -0.0737135911517484happiness[t] -0.0560868512284809depression[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) | 20.8400279089439 | 4.323281 | 4.8204 | 4e-06 | 2e-06 |
| PS | 0.347329743559927 | 0.078795 | 4.408 | 2.3e-05 | 1.1e-05 |
| CMD | 0.0089567410966607 | 0.048935 | 0.183 | 0.85508 | 0.42754 |
| PEC | -0.22783385858432 | 0.061304 | -3.7164 | 0.000308 | 0.000154 |
| happiness | -0.0737135911517484 | 0.251993 | -0.2925 | 0.770392 | 0.385196 |
| depression | -0.0560868512284809 | 0.246594 | -0.2274 | 0.820464 | 0.410232 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.443449335678153 |
| R-squared | 0.196647313313395 |
| Adjusted R-squared | 0.163174284701453 |
| F-TEST (value) | 5.87479894912285 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 120 |
| p-value | 6.83532930995101e-05 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3.62619197983225 |
| Sum Squared Residuals | 1577.91219295197 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 26 | 22.9220278935852 | 3.07797210641484 |
| 2 | 23 | 25.0741150236263 | -2.0741150236263 |
| 3 | 25 | 24.4159875213261 | 0.584012478673851 |
| 4 | 23 | 22.2528945399338 | 0.747105460066184 |
| 5 | 19 | 22.575555230474 | -3.575555230474 |
| 6 | 29 | 23.0312229476426 | 5.96877705235736 |
| 7 | 25 | 24.7431469523626 | 0.25685304763739 |
| 8 | 21 | 22.7040078565463 | -1.70400785654626 |
| 9 | 22 | 21.3662281586163 | 0.633771841383713 |
| 10 | 25 | 22.3650057566934 | 2.63499424330657 |
| 11 | 24 | 20.4839641178392 | 3.51603588216078 |
| 12 | 18 | 20.5377045644192 | -2.53770456441919 |
| 13 | 22 | 20.1890307310378 | 1.81096926896219 |
| 14 | 22 | 23.3785526912026 | -1.37855269120256 |
| 15 | 28 | 24.4010766297919 | 3.59892337020807 |
| 16 | 12 | 20.2257147758732 | -8.22571477587324 |
| 17 | 20 | 21.4982260447802 | -1.49822604478024 |
| 18 | 21 | 20.2023898126749 | 0.79761018732506 |
| 19 | 23 | 22.0399159128238 | 0.9600840871762 |
| 20 | 28 | 22.3723904249094 | 5.62760957509057 |
| 21 | 24 | 22.2214699160876 | 1.77853008391236 |
| 22 | 24 | 23.36718705976 | 0.632812940239969 |
| 23 | 24 | 21.2325920345983 | 2.76740796540175 |
| 24 | 23 | 22.4036629887399 | 0.596337011260127 |
| 25 | 29 | 25.056201541433 | 3.94379845856702 |
| 26 | 24 | 21.1373851595675 | 2.86261484043254 |
| 27 | 18 | 24.6497198702881 | -6.64971987028811 |
| 28 | 25 | 26.5672175709185 | -1.56721757091853 |
| 29 | 26 | 26.5709148910259 | -0.570914891025935 |
| 30 | 22 | 26.1877581830794 | -4.18775818307937 |
| 31 | 22 | 21.7771121703016 | 0.222887829698377 |
| 32 | 22 | 22.6612832333163 | -0.661283233316288 |
| 33 | 30 | 22.5223017932667 | 7.4776982067333 |
| 34 | 23 | 23.2066604494684 | -0.20666044946844 |
| 35 | 17 | 19.3591630470193 | -2.35916304701926 |
| 36 | 23 | 23.6175444611538 | -0.617544461153775 |
| 37 | 23 | 24.6842027448533 | -1.6842027448533 |
| 38 | 25 | 21.9769522458607 | 3.0230477541393 |
| 39 | 24 | 20.5743886092546 | 3.42561139074538 |
| 40 | 24 | 27.6039473806091 | -3.60394738060905 |
| 41 | 21 | 22.5309920078664 | -1.53099200786643 |
| 42 | 24 | 22.465016086595 | 1.53498391340495 |
| 43 | 28 | 22.1445565663251 | 5.8554434336749 |
| 44 | 20 | 20.2035818424807 | -0.203581842480664 |
| 45 | 29 | 23.6144862104348 | 5.38551378956524 |
| 46 | 27 | 24.246448509878 | 2.75355149012201 |
| 47 | 22 | 23.4890918350815 | -1.48909183508151 |
| 48 | 28 | 24.7911966286406 | 3.20880337135943 |
| 49 | 16 | 19.8237875052846 | -3.82378750528456 |
| 50 | 25 | 23.1612476465956 | 1.83875235340443 |
| 51 | 24 | 23.4934385155621 | 0.506561484437935 |
| 52 | 28 | 23.3149984230772 | 4.68500157692285 |
| 53 | 24 | 24.2263338574144 | -0.226333857414431 |
| 54 | 24 | 23.1476605818992 | 0.852339418100776 |
| 55 | 21 | 24.3301174304669 | -3.33011743046695 |
| 56 | 25 | 22.6369083283292 | 2.36309167167083 |
| 57 | 25 | 24.1179958838057 | 0.882004116194282 |
| 58 | 22 | 22.4261308714894 | -0.426130871489389 |
| 59 | 23 | 23.385308262029 | -0.385308262028988 |
| 60 | 26 | 23.7451400067773 | 2.25485999322274 |
| 61 | 25 | 23.6981551310237 | 1.30184486897628 |
| 62 | 21 | 22.1714267896151 | -1.17142678961509 |
| 63 | 25 | 22.6928499451794 | 2.30715005482063 |
| 64 | 24 | 22.182584700982 | 1.81741529901802 |
| 65 | 29 | 23.6511702552702 | 5.34882974472981 |
| 66 | 22 | 24.189649812579 | -2.189649812579 |
| 67 | 27 | 23.2604008960484 | 3.7395991039516 |
| 68 | 26 | 21.2766607476497 | 4.72333925235032 |
| 69 | 24 | 22.2190610257418 | 1.78093897425823 |
| 70 | 27 | 23.1775333958483 | 3.82246660415169 |
| 71 | 24 | 21.4789684727655 | 2.52103152723453 |
| 72 | 24 | 24.8715995784349 | -0.871599578434878 |
| 73 | 29 | 23.5838630069775 | 5.41613699302254 |
| 74 | 22 | 22.387093596368 | -0.387093596368001 |
| 75 | 24 | 20.7364670294433 | 3.26353297055671 |
| 76 | 24 | 23.0298788578212 | 0.970121142178815 |
| 77 | 23 | 22.333733192863 | 0.666266807137023 |
| 78 | 20 | 22.5203286060557 | -2.52032860605568 |
| 79 | 27 | 22.2461389691074 | 4.75386103089261 |
| 80 | 26 | 23.4491974795113 | 2.55080252048866 |
| 81 | 25 | 21.9606493327753 | 3.0393506672247 |
| 82 | 21 | 20.3210286172018 | 0.678971382798237 |
| 83 | 19 | 20.8297420042916 | -1.82974200429162 |
| 84 | 21 | 22.0742467273733 | -1.07424672737327 |
| 85 | 16 | 20.0850950979696 | -4.08509509796957 |
| 86 | 29 | 21.9794198954174 | 7.02058010458259 |
| 87 | 15 | 22.0945134398526 | -7.09451343985255 |
| 88 | 17 | 22.1244419138616 | -5.12444191386155 |
| 89 | 15 | 21.1405954703022 | -6.1405954703022 |
| 90 | 21 | 20.7635652357925 | 0.236434764207512 |
| 91 | 19 | 20.2078012936799 | -1.20780129367992 |
| 92 | 24 | 19.6809666571107 | 4.31903334288934 |
| 93 | 17 | 25.3219114746584 | -8.32191147465845 |
| 94 | 23 | 25.3640070004989 | -2.36400700049885 |
| 95 | 14 | 22.5882852147216 | -8.58828521472155 |
| 96 | 19 | 23.2658123770534 | -4.26581237705338 |
| 97 | 24 | 22.0084912889776 | 1.99150871102237 |
| 98 | 13 | 21.4359089001786 | -8.43590890017855 |
| 99 | 22 | 26.3686071659101 | -4.36860716591015 |
| 100 | 16 | 21.2856174887463 | -5.28561748874634 |
| 101 | 19 | 22.7957764377831 | -3.7957764377831 |
| 102 | 25 | 23.904530247323 | 1.09546975267696 |
| 103 | 25 | 23.0170067855567 | 1.98299321444328 |
| 104 | 23 | 21.3616737580601 | 1.63832624193991 |
| 105 | 24 | 24.1435220172743 | -0.143522017274251 |
| 106 | 26 | 23.7706661402458 | 2.22933385975421 |
| 107 | 26 | 21.6815041809405 | 4.31849581905953 |
| 108 | 25 | 24.4996664139139 | 0.500333586086067 |
| 109 | 21 | 20.7104538866021 | 0.289546113397905 |
| 110 | 26 | 23.9530871959572 | 2.04691280404276 |
| 111 | 23 | 22.4509585018127 | 0.549041498187338 |
| 112 | 13 | 22.0362185927164 | -9.0362185927164 |
| 113 | 24 | 21.7176937162198 | 2.28230628378024 |
| 114 | 14 | 23.2868662313111 | -9.28686623131107 |
| 115 | 10 | 17.0955276326346 | -7.09552763263464 |
| 116 | 24 | 24.3682976251396 | -0.368297625139552 |
| 117 | 22 | 21.1224742680332 | 0.877525731966756 |
| 118 | 24 | 24.8921424338498 | -0.89214243384981 |
| 119 | 20 | 22.938597285957 | -2.93859728595701 |
| 120 | 13 | 18.3986415666582 | -5.39864156665822 |
| 121 | 20 | 21.2332211319878 | -1.23322113198783 |
| 122 | 22 | 24.2016648043947 | -2.20166480439468 |
| 123 | 24 | 22.7479344815808 | 1.25206551841922 |
| 124 | 20 | 20.5809921200653 | -0.580992120065317 |
| 125 | 22 | 21.7448304660067 | 0.255169533993337 |
| 126 | 20 | 17.8373240555238 | 2.16267594447624 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.789487876015771 | 0.421024247968457 | 0.210512123984229 |
| 10 | 0.659993281638657 | 0.680013436722687 | 0.340006718361343 |
| 11 | 0.530216927668033 | 0.939566144663935 | 0.469783072331967 |
| 12 | 0.560396332028488 | 0.879207335943023 | 0.439603667971512 |
| 13 | 0.443824736552885 | 0.887649473105769 | 0.556175263447115 |
| 14 | 0.360537538824683 | 0.721075077649366 | 0.639462461175317 |
| 15 | 0.28510840221015 | 0.5702168044203 | 0.71489159778985 |
| 16 | 0.607951483930378 | 0.784097032139245 | 0.392048516069622 |
| 17 | 0.57678716194685 | 0.8464256761063 | 0.42321283805315 |
| 18 | 0.492209716017797 | 0.984419432035594 | 0.507790283982203 |
| 19 | 0.419928969345172 | 0.839857938690345 | 0.580071030654828 |
| 20 | 0.550970131991321 | 0.898059736017357 | 0.449029868008679 |
| 21 | 0.482801427463313 | 0.965602854926625 | 0.517198572536687 |
| 22 | 0.411486171897891 | 0.822972343795783 | 0.588513828102109 |
| 23 | 0.344810808470437 | 0.689621616940873 | 0.655189191529563 |
| 24 | 0.277800199708289 | 0.555600399416579 | 0.722199800291711 |
| 25 | 0.258183327656064 | 0.516366655312128 | 0.741816672343936 |
| 26 | 0.214540363756841 | 0.429080727513682 | 0.785459636243159 |
| 27 | 0.450387868605568 | 0.900775737211135 | 0.549612131394432 |
| 28 | 0.396341800504182 | 0.792683601008364 | 0.603658199495818 |
| 29 | 0.332836847289079 | 0.665673694578158 | 0.667163152710921 |
| 30 | 0.332966132351049 | 0.665932264702098 | 0.667033867648951 |
| 31 | 0.275150779830368 | 0.550301559660736 | 0.724849220169632 |
| 32 | 0.241541136619828 | 0.483082273239656 | 0.758458863380172 |
| 33 | 0.415948228590627 | 0.831896457181255 | 0.584051771409373 |
| 34 | 0.356623810431562 | 0.713247620863125 | 0.643376189568438 |
| 35 | 0.335391066579616 | 0.670782133159231 | 0.664608933420384 |
| 36 | 0.282619210310497 | 0.565238420620995 | 0.717380789689503 |
| 37 | 0.240211936255059 | 0.480423872510117 | 0.759788063744941 |
| 38 | 0.208405653446288 | 0.416811306892576 | 0.791594346553712 |
| 39 | 0.196302399460353 | 0.392604798920705 | 0.803697600539647 |
| 40 | 0.18373218360077 | 0.367464367201541 | 0.81626781639923 |
| 41 | 0.16270816241737 | 0.32541632483474 | 0.83729183758263 |
| 42 | 0.134239750903095 | 0.268479501806191 | 0.865760249096905 |
| 43 | 0.190031590380504 | 0.380063180761008 | 0.809968409619496 |
| 44 | 0.161119954041182 | 0.322239908082364 | 0.838880045958818 |
| 45 | 0.209043469487937 | 0.418086938975873 | 0.790956530512063 |
| 46 | 0.191828882973318 | 0.383657765946636 | 0.808171117026682 |
| 47 | 0.163250577737481 | 0.326501155474962 | 0.836749422262519 |
| 48 | 0.154431408682642 | 0.308862817365285 | 0.845568591317358 |
| 49 | 0.171382926740734 | 0.342765853481469 | 0.828617073259265 |
| 50 | 0.146108587637366 | 0.292217175274732 | 0.853891412362634 |
| 51 | 0.117989952815611 | 0.235979905631221 | 0.88201004718439 |
| 52 | 0.135342597009094 | 0.270685194018188 | 0.864657402990906 |
| 53 | 0.108031405832875 | 0.21606281166575 | 0.891968594167125 |
| 54 | 0.0855706486889305 | 0.171141297377861 | 0.91442935131107 |
| 55 | 0.0839997662363628 | 0.167999532472726 | 0.916000233763637 |
| 56 | 0.0717065895042771 | 0.143413179008554 | 0.928293410495723 |
| 57 | 0.0557580081324345 | 0.111516016264869 | 0.944241991867566 |
| 58 | 0.0425147181609193 | 0.0850294363218387 | 0.95748528183908 |
| 59 | 0.0319268666323418 | 0.0638537332646836 | 0.968073133367658 |
| 60 | 0.0264397483392631 | 0.0528794966785261 | 0.973560251660737 |
| 61 | 0.0200006548621681 | 0.0400013097243363 | 0.979999345137832 |
| 62 | 0.015114126251213 | 0.030228252502426 | 0.984885873748787 |
| 63 | 0.0122698566936963 | 0.0245397133873926 | 0.987730143306304 |
| 64 | 0.00936940160530582 | 0.0187388032106116 | 0.990630598394694 |
| 65 | 0.0145241293517702 | 0.0290482587035405 | 0.98547587064823 |
| 66 | 0.0117102021192613 | 0.0234204042385226 | 0.988289797880739 |
| 67 | 0.0122055419134885 | 0.0244110838269771 | 0.987794458086511 |
| 68 | 0.0154431101039839 | 0.0308862202079678 | 0.984556889896016 |
| 69 | 0.0123720437735352 | 0.0247440875470703 | 0.987627956226465 |
| 70 | 0.0124914788935698 | 0.0249829577871396 | 0.98750852110643 |
| 71 | 0.0105761059127259 | 0.0211522118254517 | 0.989423894087274 |
| 72 | 0.0077908573885663 | 0.0155817147771326 | 0.992209142611434 |
| 73 | 0.0135340851874653 | 0.0270681703749306 | 0.986465914812535 |
| 74 | 0.00963699965219385 | 0.0192739993043877 | 0.990363000347806 |
| 75 | 0.00876073324956693 | 0.0175214664991339 | 0.991239266750433 |
| 76 | 0.00683564719205188 | 0.0136712943841038 | 0.993164352807948 |
| 77 | 0.0057232851993201 | 0.0114465703986402 | 0.99427671480068 |
| 78 | 0.00525446613172948 | 0.010508932263459 | 0.99474553386827 |
| 79 | 0.00809900590811866 | 0.0161980118162373 | 0.991900994091881 |
| 80 | 0.00738189486329398 | 0.014763789726588 | 0.992618105136706 |
| 81 | 0.00667002205772767 | 0.0133400441154553 | 0.993329977942272 |
| 82 | 0.00478589030837583 | 0.00957178061675167 | 0.995214109691624 |
| 83 | 0.00362540598569518 | 0.00725081197139037 | 0.996374594014305 |
| 84 | 0.00255809594562009 | 0.00511619189124018 | 0.99744190405438 |
| 85 | 0.00285163459967583 | 0.00570326919935166 | 0.997148365400324 |
| 86 | 0.011041208674457 | 0.022082417348914 | 0.988958791325543 |
| 87 | 0.0273746743382822 | 0.0547493486765643 | 0.972625325661718 |
| 88 | 0.0340673329217458 | 0.0681346658434916 | 0.965932667078254 |
| 89 | 0.0529488456232814 | 0.105897691246563 | 0.947051154376719 |
| 90 | 0.0431133535403968 | 0.0862267070807937 | 0.956886646459603 |
| 91 | 0.0321505676346353 | 0.0643011352692706 | 0.967849432365365 |
| 92 | 0.0421282925558704 | 0.0842565851117408 | 0.95787170744413 |
| 93 | 0.106494961086686 | 0.212989922173373 | 0.893505038913314 |
| 94 | 0.0876127250522878 | 0.175225450104576 | 0.912387274947712 |
| 95 | 0.205379393730745 | 0.410758787461489 | 0.794620606269255 |
| 96 | 0.200492124520384 | 0.400984249040767 | 0.799507875479616 |
| 97 | 0.185707296749847 | 0.371414593499695 | 0.814292703250153 |
| 98 | 0.305622432808997 | 0.611244865617995 | 0.694377567191003 |
| 99 | 0.313232980809213 | 0.626465961618425 | 0.686767019190787 |
| 100 | 0.348110122719759 | 0.696220245439518 | 0.651889877280241 |
| 101 | 0.333966180861249 | 0.667932361722497 | 0.666033819138751 |
| 102 | 0.274862936846995 | 0.54972587369399 | 0.725137063153005 |
| 103 | 0.249576148634699 | 0.499152297269397 | 0.750423851365301 |
| 104 | 0.215942228197248 | 0.431884456394496 | 0.784057771802752 |
| 105 | 0.164769739961005 | 0.329539479922011 | 0.835230260038995 |
| 106 | 0.140124129855075 | 0.280248259710151 | 0.859875870144925 |
| 107 | 0.180346350828674 | 0.360692701657347 | 0.819653649171326 |
| 108 | 0.149143823342026 | 0.298287646684052 | 0.850856176657974 |
| 109 | 0.116876352053506 | 0.233752704107012 | 0.883123647946494 |
| 110 | 0.212050978052695 | 0.42410195610539 | 0.787949021947305 |
| 111 | 0.157856590051522 | 0.315713180103045 | 0.842143409948478 |
| 112 | 0.369944926532761 | 0.739889853065521 | 0.630055073467239 |
| 113 | 0.412490928166934 | 0.824981856333868 | 0.587509071833066 |
| 114 | 0.873279409712307 | 0.253441180575386 | 0.126720590287693 |
| 115 | 0.99924937685948 | 0.00150124628104132 | 0.00075062314052066 |
| 116 | 0.998186624687288 | 0.00362675062542415 | 0.00181337531271208 |
| 117 | 0.98888629254427 | 0.02222741491146 | 0.01111370745573 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 6 | 0.055045871559633 | NOK |
| 5% type I error level | 29 | 0.26605504587156 | NOK |
| 10% type I error level | 37 | 0.339449541284404 | NOK |
