| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.933141956395697 -0.00599446355432254X[t] + 1.55409357038416Y1[t] -0.862743246928274Y2[t] -0.133170668301423Y3[t] + 0.394880751487633Y4[t] -0.107835895318313M1[t] + 0.00865868146602026M2[t] + 0.555132299015706M3[t] -0.358561693549813M4[t] + 0.194164167438996M5[t] + 0.377211037290883M6[t] + 0.0719094385043453M7[t] + 0.228312254709038M8[t] + 0.145801390152894M9[t] -0.0769332094556072M10[t] + 0.0653509691361015M11[t] -0.000644466348359865t + 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) | 0.933141956395697 | 0.500375 | 1.8649 | 0.066109 | 0.033055 |
| X | -0.00599446355432254 | 0.004393 | -1.3645 | 0.176479 | 0.08824 |
| Y1 | 1.55409357038416 | 0.107422 | 14.4672 | 0 | 0 |
| Y2 | -0.862743246928274 | 0.208198 | -4.1439 | 8.9e-05 | 4.4e-05 |
| Y3 | -0.133170668301423 | 0.20837 | -0.6391 | 0.5247 | 0.26235 |
| Y4 | 0.394880751487633 | 0.10641 | 3.7109 | 0.000394 | 0.000197 |
| M1 | -0.107835895318313 | 0.086434 | -1.2476 | 0.216055 | 0.108028 |
| M2 | 0.00865868146602026 | 0.093806 | 0.0923 | 0.926702 | 0.463351 |
| M3 | 0.555132299015706 | 0.117354 | 4.7304 | 1e-05 | 5e-06 |
| M4 | -0.358561693549813 | 0.121642 | -2.9477 | 0.004266 | 0.002133 |
| M5 | 0.194164167438996 | 0.125427 | 1.548 | 0.125826 | 0.062913 |
| M6 | 0.377211037290883 | 0.103936 | 3.6293 | 0.000516 | 0.000258 |
| M7 | 0.0719094385043453 | 0.084564 | 0.8504 | 0.397832 | 0.198916 |
| M8 | 0.228312254709038 | 0.091622 | 2.4919 | 0.014915 | 0.007458 |
| M9 | 0.145801390152894 | 0.094745 | 1.5389 | 0.12804 | 0.06402 |
| M10 | -0.0769332094556072 | 0.093945 | -0.8189 | 0.41543 | 0.207715 |
| M11 | 0.0653509691361015 | 0.092364 | 0.7075 | 0.481426 | 0.240713 |
| t | -0.000644466348359865 | 0.000878 | -0.7343 | 0.465076 | 0.232538 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.980250524311518 |
| R-squared | 0.960891090413006 |
| Adjusted R-squared | 0.952026404239954 |
| F-TEST (value) | 108.395387231424 |
| F-TEST (DF numerator) | 17 |
| F-TEST (DF denominator) | 75 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.162365640018282 |
| Sum Squared Residuals | 1.97719507939096 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 6.3 | 6.4172891034347 | -0.1172891034347 |
| 2 | 6 | 6.2558382209039 | -0.255838220903900 |
| 3 | 6.2 | 6.45986564889862 | -0.259865648898616 |
| 4 | 6.4 | 6.11202087774337 | 0.287979122256635 |
| 5 | 6.8 | 6.80455841717319 | -0.00455841717318884 |
| 6 | 7.5 | 7.24059774648184 | 0.259402253518158 |
| 7 | 7.5 | 7.77232258971748 | -0.27232258971748 |
| 8 | 7.6 | 7.41940432693112 | 0.180595673068879 |
| 9 | 7.6 | 7.52342163630032 | 0.0765783636996842 |
| 10 | 7.4 | 7.4907842180474 | -0.090784218047402 |
| 11 | 7.3 | 7.24894296019598 | 0.0510570398040157 |
| 12 | 7.1 | 7.25695883651506 | -0.156958836515059 |
| 13 | 6.9 | 6.95716212903442 | -0.0571621290344202 |
| 14 | 6.8 | 6.85289803971516 | -0.0528980397151625 |
| 15 | 7.5 | 7.51510901024108 | -0.0151090102410793 |
| 16 | 7.6 | 7.68600213097033 | -0.0860021309703315 |
| 17 | 7.8 | 7.63519546572805 | 0.164804534271954 |
| 18 | 8 | 7.87526627339618 | 0.124733726603819 |
| 19 | 8.1 | 8.03602938490578 | 0.0639706150942221 |
| 20 | 8.2 | 8.24564868038028 | -0.0456486803802792 |
| 21 | 8.3 | 8.25160029526526 | 0.0483997047347368 |
| 22 | 8.2 | 8.1654131305431 | 0.0345868694568924 |
| 23 | 8 | 8.04118667551752 | -0.0411866755175201 |
| 24 | 7.9 | 7.79300291056435 | 0.106997089435653 |
| 25 | 7.6 | 7.7820415155737 | -0.182041515573704 |
| 26 | 7.6 | 7.46671937135111 | 0.133280628648889 |
| 27 | 8.3 | 8.30821773994245 | -0.00821773994245075 |
| 28 | 8.4 | 8.46722174675334 | -0.0672217467533438 |
| 29 | 8.4 | 8.3330381754051 | 0.066961824594893 |
| 30 | 8.4 | 8.3245573056516 | 0.0754426943484016 |
| 31 | 8.4 | 8.36023817228953 | 0.0397618277104728 |
| 32 | 8.6 | 8.56567518533697 | 0.0343248146630277 |
| 33 | 8.9 | 8.80412860290708 | 0.095871397092920 |
| 34 | 8.8 | 8.8630394779266 | -0.0630394779266007 |
| 35 | 8.3 | 8.4696996475899 | -0.169699647589903 |
| 36 | 7.5 | 7.81070244424565 | -0.310702444245649 |
| 37 | 7.2 | 7.05506969156099 | 0.144930308439011 |
| 38 | 7.4 | 7.33806109766577 | 0.0619389023342349 |
| 39 | 8.8 | 8.50649522122347 | 0.29350477877653 |
| 40 | 9.3 | 9.26303775335145 | 0.0369622466485494 |
| 41 | 9.3 | 9.13552280888804 | 0.164477191111958 |
| 42 | 8.7 | 8.8018697651094 | -0.101869765109394 |
| 43 | 8.2 | 8.08807984242364 | 0.111920157576364 |
| 44 | 8.3 | 8.19566499716361 | 0.10433500283639 |
| 45 | 8.5 | 8.82115429262278 | -0.321154292622775 |
| 46 | 8.6 | 8.64418369668743 | -0.0441836966874283 |
| 47 | 8.5 | 8.50517539473154 | -0.00517539473154078 |
| 48 | 8.2 | 8.22173969975753 | -0.0217396997575299 |
| 49 | 8.1 | 7.82713865384113 | 0.272861346158865 |
| 50 | 7.9 | 8.00449499913778 | -0.104494999137783 |
| 51 | 8.6 | 8.52406018358941 | 0.0759398164105859 |
| 52 | 8.7 | 8.67627065410998 | 0.0237293458900206 |
| 53 | 8.7 | 8.66208407924993 | 0.0379159207500705 |
| 54 | 8.5 | 8.62977612389866 | -0.129776123898662 |
| 55 | 8.4 | 8.2587268595906 | 0.141273140409403 |
| 56 | 8.5 | 8.51007659004603 | -0.0100765900460287 |
| 57 | 8.7 | 8.71502080426232 | -0.015020804262318 |
| 58 | 8.7 | 8.64033645617973 | 0.0596635438202719 |
| 59 | 8.6 | 8.46790431645454 | 0.132095683545457 |
| 60 | 8.5 | 8.34807152602412 | 0.151928473975882 |
| 61 | 8.3 | 8.19428321760962 | 0.105716782390385 |
| 62 | 8 | 8.07073202678641 | -0.0707320267864107 |
| 63 | 8.2 | 8.47174908372574 | -0.271749083725740 |
| 64 | 8.1 | 8.02368197180843 | 0.0763180281915747 |
| 65 | 8.1 | 8.12305958139089 | -0.0230595813908927 |
| 66 | 8 | 8.23644736243832 | -0.236447362438324 |
| 67 | 7.9 | 7.88896522618824 | 0.0110347738117600 |
| 68 | 7.9 | 8.00144012129234 | -0.101440121292337 |
| 69 | 8 | 7.99389832769351 | 0.00610167230648676 |
| 70 | 8 | 7.90395373494447 | 0.0960462650555279 |
| 71 | 7.9 | 7.83890578936288 | 0.0610942106371242 |
| 72 | 8 | 7.68031361714975 | 0.319686382850246 |
| 73 | 7.7 | 7.83382272898925 | -0.133822728989254 |
| 74 | 7.2 | 7.36313124836815 | -0.163131248368146 |
| 75 | 7.5 | 7.48599469626874 | 0.0140053037312642 |
| 76 | 7.3 | 7.47855998398786 | -0.178559983987857 |
| 77 | 7 | 7.35936675167654 | -0.359366751676536 |
| 78 | 7 | 6.95135296802843 | 0.0486470319715659 |
| 79 | 7 | 7.10387785442293 | -0.103877854422928 |
| 80 | 7.2 | 7.30033761974465 | -0.100337619744651 |
| 81 | 7.3 | 7.34539601743944 | -0.0453960174394394 |
| 82 | 7.1 | 7.09228928567126 | 0.00771071432873867 |
| 83 | 6.8 | 6.82818521614763 | -0.0281852161476333 |
| 84 | 6.4 | 6.48921096574354 | -0.0892109657435433 |
| 85 | 6.1 | 6.13319295995618 | -0.0331929599561825 |
| 86 | 6.5 | 6.04812499607172 | 0.451875003928279 |
| 87 | 7.7 | 7.52850841611049 | 0.171491583889507 |
| 88 | 7.9 | 7.99320488127525 | -0.0932048812752471 |
| 89 | 7.5 | 7.54717472048826 | -0.0471747204882575 |
| 90 | 6.9 | 6.94013245499557 | -0.0401324549955651 |
| 91 | 6.6 | 6.59176007046181 | 0.00823992953818632 |
| 92 | 6.9 | 6.961752479105 | -0.061752479105001 |
| 93 | 7.7 | 7.5453800235093 | 0.154619976490705 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 21 | 0.535150433981029 | 0.929699132037942 | 0.464849566018971 |
| 22 | 0.579716029072934 | 0.840567941854132 | 0.420283970927066 |
| 23 | 0.436436994233255 | 0.87287398846651 | 0.563563005766745 |
| 24 | 0.389292707465431 | 0.778585414930862 | 0.610707292534569 |
| 25 | 0.307332857045753 | 0.614665714091506 | 0.692667142954247 |
| 26 | 0.250741525275134 | 0.501483050550267 | 0.749258474724867 |
| 27 | 0.197104030574497 | 0.394208061148993 | 0.802895969425503 |
| 28 | 0.131890434941066 | 0.263780869882132 | 0.868109565058934 |
| 29 | 0.120444856705101 | 0.240889713410202 | 0.8795551432949 |
| 30 | 0.162399237715262 | 0.324798475430524 | 0.837600762284738 |
| 31 | 0.119598551529498 | 0.239197103058996 | 0.880401448470502 |
| 32 | 0.156499820114130 | 0.312999640228261 | 0.84350017988587 |
| 33 | 0.110396179466062 | 0.220792358932123 | 0.889603820533938 |
| 34 | 0.0793787366164238 | 0.158757473232848 | 0.920621263383576 |
| 35 | 0.0956950807791798 | 0.191390161558360 | 0.90430491922082 |
| 36 | 0.224401839915192 | 0.448803679830384 | 0.775598160084808 |
| 37 | 0.189303979551631 | 0.378607959103262 | 0.810696020448369 |
| 38 | 0.141825901226789 | 0.283651802453579 | 0.85817409877321 |
| 39 | 0.217147910597866 | 0.434295821195732 | 0.782852089402134 |
| 40 | 0.215061548465236 | 0.430123096930473 | 0.784938451534763 |
| 41 | 0.211691381494733 | 0.423382762989467 | 0.788308618505267 |
| 42 | 0.169399187228392 | 0.338798374456783 | 0.830600812771608 |
| 43 | 0.125961001336344 | 0.251922002672688 | 0.874038998663656 |
| 44 | 0.118652706438342 | 0.237305412876684 | 0.881347293561658 |
| 45 | 0.513646014321337 | 0.972707971357326 | 0.486353985678663 |
| 46 | 0.451369822435387 | 0.902739644870774 | 0.548630177564613 |
| 47 | 0.4404517061066 | 0.8809034122132 | 0.5595482938934 |
| 48 | 0.441607873462105 | 0.88321574692421 | 0.558392126537895 |
| 49 | 0.513628599154578 | 0.972742801690844 | 0.486371400845422 |
| 50 | 0.562628742552352 | 0.874742514895297 | 0.437371257447648 |
| 51 | 0.49445550910897 | 0.98891101821794 | 0.50554449089103 |
| 52 | 0.432179319951759 | 0.864358639903518 | 0.567820680048241 |
| 53 | 0.413240216259283 | 0.826480432518565 | 0.586759783740717 |
| 54 | 0.464625390879838 | 0.929250781759675 | 0.535374609120162 |
| 55 | 0.425716032443968 | 0.851432064887937 | 0.574283967556032 |
| 56 | 0.362325158686120 | 0.724650317372241 | 0.63767484131388 |
| 57 | 0.296571660651003 | 0.593143321302006 | 0.703428339348997 |
| 58 | 0.238960614491348 | 0.477921228982697 | 0.761039385508652 |
| 59 | 0.214257787498669 | 0.428515574997337 | 0.785742212501331 |
| 60 | 0.196119038759810 | 0.392238077519621 | 0.80388096124019 |
| 61 | 0.20918933221082 | 0.41837866442164 | 0.79081066778918 |
| 62 | 0.185510724182613 | 0.371021448365226 | 0.814489275817387 |
| 63 | 0.312832624155782 | 0.625665248311563 | 0.687167375844218 |
| 64 | 0.322099131430791 | 0.644198262861583 | 0.677900868569209 |
| 65 | 0.282899657438708 | 0.565799314877416 | 0.717100342561292 |
| 66 | 0.372083731192912 | 0.744167462385824 | 0.627916268807088 |
| 67 | 0.362826465534303 | 0.725652931068606 | 0.637173534465697 |
| 68 | 0.270976948578866 | 0.541953897157731 | 0.729023051421134 |
| 69 | 0.195486801289779 | 0.390973602579558 | 0.804513198710221 |
| 70 | 0.127757251831311 | 0.255514503662622 | 0.872242748168689 |
| 71 | 0.300182961202168 | 0.600365922404336 | 0.699817038797832 |
| 72 | 0.385912359492083 | 0.771824718984166 | 0.614087640507917 |
| 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 |
