| Multiple Linear Regression - Estimated Regression Equation |
| X_1[t] = -0.293680794030562 + 0.978370136065127X_2[t] -1.1065710161433X_3[t] -0.93424923909017X_4[t] + 3.97683039702274Y_1[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) | -0.293680794030562 | 0.579935 | -0.5064 | 0.614002 | 0.307001 |
| X_2 | 0.978370136065127 | 0.018676 | 52.3878 | 0 | 0 |
| X_3 | -1.1065710161433 | 0.11765 | -9.4056 | 0 | 0 |
| X_4 | -0.93424923909017 | 0.044671 | -20.9138 | 0 | 0 |
| Y_1 | 3.97683039702274 | 0.07186 | 55.341 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.993907933164318 |
| R-squared | 0.987852979606966 |
| Adjusted R-squared | 0.987230055484246 |
| F-TEST (value) | 1585.83195541369 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 78 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.33580309255728 |
| Sum Squared Residuals | 139.180852362675 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 0 | -0.487620656901071 | 0.487620656901071 |
| 2 | -2 | -2.8757451025338 | 0.875745102533799 |
| 3 | -4 | -2.93909495529603 | -1.06090504470397 |
| 4 | -6 | -6.61274205889447 | 0.612742058894466 |
| 5 | -2 | -1.85741588034041 | -0.142584119659593 |
| 6 | 1 | 0.186065011186049 | 0.813934988813951 |
| 7 | 7 | 7.11723477219144 | -0.117234772191438 |
| 8 | 2 | 3.15963333095597 | -1.15963333095597 |
| 9 | 2 | 1.52830765714471 | 0.471692342855292 |
| 10 | 13 | 12.3891845690904 | 0.610815430909555 |
| 11 | 7 | 8.32561355267151 | -1.32561355267151 |
| 12 | -1 | -2.87840573882677 | 1.87840573882677 |
| 13 | 1 | 1.98555065120375 | -0.98555065120375 |
| 14 | 0 | 2.33019420531001 | -2.33019420531001 |
| 15 | 0 | -1.75144630515693 | 1.75144630515693 |
| 16 | 5 | 4.91499807399871 | 0.0850019260012877 |
| 17 | 3 | 5.30792433592663 | -2.30792433592663 |
| 18 | 6 | 7.17642281410697 | -1.17642281410697 |
| 19 | 7 | 8.23887293327531 | -1.23887293327531 |
| 20 | -6 | -3.45594662797754 | -2.54405337202246 |
| 21 | -8 | -7.6960012322963 | -0.303998767703699 |
| 22 | -5 | -5.45830897163646 | 0.45830897163646 |
| 23 | -14 | -15.4139903965264 | 1.41399039652642 |
| 24 | -13 | -12.5245020598597 | -0.47549794014029 |
| 25 | -15 | -14.3941599997793 | -0.605840000220685 |
| 26 | -14 | -13.7619345923742 | -0.238065407625838 |
| 27 | -10 | -10.5070725712602 | 0.507072571260207 |
| 28 | -14 | -15.6123635765065 | 1.6123635765065 |
| 29 | -18 | -16.5865719017249 | -1.41342809827507 |
| 30 | -22 | -19.3961420661351 | -2.60385793386488 |
| 31 | -24 | -23.4762814020483 | -0.523718597951658 |
| 32 | -17 | -15.8657629875554 | -1.13423701244459 |
| 33 | -16 | -13.8181202851823 | -2.18187971481773 |
| 34 | -17 | -17.7339197529213 | 0.73391975292131 |
| 35 | -22 | -22.9798181468934 | 0.979818146893363 |
| 36 | -25 | -25.154160554791 | 0.154160554790966 |
| 37 | -18 | -20.2113665303507 | 2.2113665303507 |
| 38 | -23 | -22.4905190516925 | -0.509480948307489 |
| 39 | -20 | -20.1257853726938 | 0.12578537269377 |
| 40 | -9 | -8.56066786607281 | -0.439332133927195 |
| 41 | -4 | -6.82187144252436 | 2.82187144252436 |
| 42 | 0 | 1.3523938363959 | -1.3523938363959 |
| 43 | 3 | 3.60399378025705 | -0.603993780257049 |
| 44 | 14 | 15.6238862270144 | -1.62388622701444 |
| 45 | 13 | 12.5813050690819 | 0.418694930918129 |
| 46 | 12 | 13.3432325311189 | -1.34323253111891 |
| 47 | 16 | 17.4950453414878 | -1.49504534148775 |
| 48 | 7 | 7.39193408073237 | -0.391934080732367 |
| 49 | 2 | 2.50158457496044 | -0.501584574960441 |
| 50 | 1 | -0.324553908944037 | 1.32455390894404 |
| 51 | 7 | 4.65253621622408 | 2.34746378377592 |
| 52 | 10 | 9.72877346943599 | 0.271226530564007 |
| 53 | 3 | 3.8174341051777 | -0.817434105177705 |
| 54 | 2 | 3.68773205054582 | -1.68773205054582 |
| 55 | 12 | 10.6132388261508 | 1.38676117384921 |
| 56 | 14 | 13.6792107507173 | 0.320789249282671 |
| 57 | 11 | 11.8906304447935 | -0.890630444793508 |
| 58 | 13 | 11.8725609507455 | 1.12743904925449 |
| 59 | 17 | 15.2141635912557 | 1.78583640874434 |
| 60 | 14 | 12.4954958570884 | 1.50450414291163 |
| 61 | 7 | 5.62501531255222 | 1.37498468744778 |
| 62 | 16 | 13.4282439216248 | 2.57175607837518 |
| 63 | 5 | 4.48939054437454 | 0.510609455625463 |
| 64 | 5 | 5.64424426833949 | -0.644244268339493 |
| 65 | 15 | 13.228369567091 | 1.77163043290898 |
| 66 | 9 | 8.38364213284777 | 0.616357867152227 |
| 67 | 4 | 5.27204813675257 | -1.27204813675257 |
| 68 | -9 | -10.3224579440373 | 1.32245794403735 |
| 69 | -14 | -14.8006522320941 | 0.800652232094088 |
| 70 | -4 | -3.10317203454825 | -0.896827965451745 |
| 71 | -19 | -20.7285599158467 | 1.72855991584667 |
| 72 | -10 | -9.76253117764228 | -0.237468822357722 |
| 73 | -22 | -21.3624790801759 | -0.637520919824097 |
| 74 | -25 | -25.0274608492665 | 0.0274608492665128 |
| 75 | -8 | -8.14627264877158 | 0.146272648771585 |
| 76 | -8 | -7.21202340968141 | -0.787976590318586 |
| 77 | -8 | -9.97215140453068 | 1.97215140453068 |
| 78 | -2 | -0.293260157323618 | -1.70673984267638 |
| 79 | -6 | -6.81662909383089 | 0.81662909383089 |
| 80 | -10 | -11.6379657614402 | 1.63796576144017 |
| 81 | -11 | -11.6394669359939 | 0.639466935993882 |
| 82 | -14 | -13.1384299188803 | -0.861570081119718 |
| 83 | -25 | -22.5403029340679 | -2.45969706593212 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.362993638824343 | 0.725987277648685 | 0.637006361175657 |
| 9 | 0.20975963010137 | 0.41951926020274 | 0.79024036989863 |
| 10 | 0.12086934636322 | 0.24173869272644 | 0.87913065363678 |
| 11 | 0.10796046449908 | 0.21592092899816 | 0.89203953550092 |
| 12 | 0.228812054955138 | 0.457624109910275 | 0.771187945044862 |
| 13 | 0.150773487190375 | 0.301546974380749 | 0.849226512809625 |
| 14 | 0.306461081385959 | 0.612922162771918 | 0.693538918614041 |
| 15 | 0.428369778509219 | 0.856739557018437 | 0.571630221490781 |
| 16 | 0.368680694450497 | 0.737361388900994 | 0.631319305549503 |
| 17 | 0.468014235174539 | 0.936028470349078 | 0.531985764825461 |
| 18 | 0.394875299635567 | 0.789750599271133 | 0.605124700364433 |
| 19 | 0.327372725246898 | 0.654745450493797 | 0.672627274753102 |
| 20 | 0.37892249332907 | 0.75784498665814 | 0.62107750667093 |
| 21 | 0.384306012052298 | 0.768612024104597 | 0.615693987947701 |
| 22 | 0.33660295566678 | 0.67320591133356 | 0.66339704433322 |
| 23 | 0.343584754441949 | 0.687169508883899 | 0.656415245558051 |
| 24 | 0.295251635568464 | 0.590503271136928 | 0.704748364431536 |
| 25 | 0.237387297201781 | 0.474774594403562 | 0.762612702798219 |
| 26 | 0.187797442839138 | 0.375594885678277 | 0.812202557160862 |
| 27 | 0.173468015099754 | 0.346936030199508 | 0.826531984900246 |
| 28 | 0.203503159014381 | 0.407006318028761 | 0.796496840985619 |
| 29 | 0.248724513215554 | 0.497449026431108 | 0.751275486784446 |
| 30 | 0.384286110708602 | 0.768572221417203 | 0.615713889291398 |
| 31 | 0.338490400072096 | 0.676980800144191 | 0.661509599927904 |
| 32 | 0.31077222073498 | 0.62154444146996 | 0.68922777926502 |
| 33 | 0.475319279317353 | 0.950638558634706 | 0.524680720682647 |
| 34 | 0.569581092303066 | 0.860837815393867 | 0.430418907696934 |
| 35 | 0.515646315551826 | 0.968707368896349 | 0.484353684448174 |
| 36 | 0.449349226475008 | 0.898698452950016 | 0.550650773524992 |
| 37 | 0.491799367790018 | 0.983598735580037 | 0.508200632209982 |
| 38 | 0.480835674908516 | 0.961671349817032 | 0.519164325091484 |
| 39 | 0.421731524698614 | 0.843463049397228 | 0.578268475301386 |
| 40 | 0.359451882278172 | 0.718903764556344 | 0.640548117721828 |
| 41 | 0.607305892250513 | 0.785388215498974 | 0.392694107749487 |
| 42 | 0.594861422089421 | 0.810277155821157 | 0.405138577910579 |
| 43 | 0.530338996387671 | 0.939322007224658 | 0.469661003612329 |
| 44 | 0.505087562987351 | 0.989824874025299 | 0.494912437012649 |
| 45 | 0.479367632411373 | 0.958735264822745 | 0.520632367588627 |
| 46 | 0.453690431896292 | 0.907380863792583 | 0.546309568103708 |
| 47 | 0.470186426175884 | 0.940372852351769 | 0.529813573824116 |
| 48 | 0.409770014441306 | 0.819540028882612 | 0.590229985558694 |
| 49 | 0.355620024159832 | 0.711240048319664 | 0.644379975840168 |
| 50 | 0.376979420718814 | 0.753958841437628 | 0.623020579281186 |
| 51 | 0.590579953606303 | 0.818840092787394 | 0.409420046393697 |
| 52 | 0.544710981976879 | 0.910578036046243 | 0.455289018023121 |
| 53 | 0.476224133647099 | 0.952448267294197 | 0.523775866352901 |
| 54 | 0.524209529618467 | 0.951580940763067 | 0.475790470381533 |
| 55 | 0.566809012630132 | 0.866381974739736 | 0.433190987369868 |
| 56 | 0.509658061012404 | 0.980683877975192 | 0.490341938987596 |
| 57 | 0.484393904554466 | 0.968787809108933 | 0.515606095445534 |
| 58 | 0.446910124227482 | 0.893820248454964 | 0.553089875772518 |
| 59 | 0.481958016848908 | 0.963916033697815 | 0.518041983151092 |
| 60 | 0.479859321064329 | 0.959718642128658 | 0.520140678935671 |
| 61 | 0.465069961322489 | 0.930139922644978 | 0.534930038677511 |
| 62 | 0.626745553467452 | 0.746508893065096 | 0.373254446532548 |
| 63 | 0.549506735663087 | 0.900986528673826 | 0.450493264336913 |
| 64 | 0.491078081914808 | 0.982156163829615 | 0.508921918085192 |
| 65 | 0.517252052797438 | 0.965495894405124 | 0.482747947202562 |
| 66 | 0.482048136134853 | 0.964096272269706 | 0.517951863865147 |
| 67 | 0.513731568818674 | 0.972536862362653 | 0.486268431181326 |
| 68 | 0.436939283219569 | 0.873878566439138 | 0.563060716780431 |
| 69 | 0.345477064545486 | 0.690954129090972 | 0.654522935454514 |
| 70 | 0.343927949334652 | 0.687855898669305 | 0.656072050665347 |
| 71 | 0.347139805026551 | 0.694279610053103 | 0.652860194973449 |
| 72 | 0.295755829676448 | 0.591511659352896 | 0.704244170323552 |
| 73 | 0.470686760398242 | 0.941373520796484 | 0.529313239601758 |
| 74 | 0.33264361224844 | 0.665287224496879 | 0.66735638775156 |
| 75 | 0.21598145122074 | 0.431962902441481 | 0.78401854877926 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
