| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = + 20.9273860060955 + 0.486433189652739X_1t[t] -0.385377789795854X_2t[t] -0.864929940639701X_4t[t] -0.503718759631577M1[t] -0.507766600114035M2[t] + 0.447784853848473M3[t] + 3.16643897790194M4[t] + 0.255771035076966M5[t] + 0.325357546496257M6[t] -0.775616655495947M7[t] -0.221084905953848M8[t] -1.06540418890865M9[t] + 0.628688971148661M10[t] + 0.991759519914183M11[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) | 20.9273860060955 | 2.61614 | 7.9993 | 0 | 0 |
| X_1t | 0.486433189652739 | 0.045041 | 10.7998 | 0 | 0 |
| X_2t | -0.385377789795854 | 0.029986 | -12.8519 | 0 | 0 |
| X_4t | -0.864929940639701 | 0.215395 | -4.0155 | 0.000152 | 7.6e-05 |
| M1 | -0.503718759631577 | 2.353852 | -0.214 | 0.831199 | 0.415599 |
| M2 | -0.507766600114035 | 2.361114 | -0.2151 | 0.830379 | 0.415189 |
| M3 | 0.447784853848473 | 2.353495 | 0.1903 | 0.849678 | 0.424839 |
| M4 | 3.16643897790194 | 2.357483 | 1.3431 | 0.183758 | 0.091879 |
| M5 | 0.255771035076966 | 2.366274 | 0.1081 | 0.914247 | 0.457124 |
| M6 | 0.325357546496257 | 2.354624 | 0.1382 | 0.890514 | 0.445257 |
| M7 | -0.775616655495947 | 2.3689 | -0.3274 | 0.744374 | 0.372187 |
| M8 | -0.221084905953848 | 2.367022 | -0.0934 | 0.925863 | 0.462931 |
| M9 | -1.06540418890865 | 2.356379 | -0.4521 | 0.652631 | 0.326316 |
| M10 | 0.628688971148661 | 2.352049 | 0.2673 | 0.790064 | 0.395032 |
| M11 | 0.991759519914183 | 2.441082 | 0.4063 | 0.685833 | 0.342916 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.918349480127501 |
| R-squared | 0.843365767650451 |
| Adjusted R-squared | 0.810636226562486 |
| F-TEST (value) | 25.7677235798627 |
| F-TEST (DF numerator) | 14 |
| F-TEST (DF denominator) | 67 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.22277306424807 |
| Sum Squared Residuals | 1194.73142759331 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | -3 | -7.51372633483899 | 4.51372633483899 |
| 2 | -4 | -5.11821411430721 | 1.11821411430721 |
| 3 | -7 | -3.78416590935774 | -3.21583409064226 |
| 4 | -7 | -3.07281301771376 | -3.92718698228624 |
| 5 | -7 | -4.05151027954556 | -2.94848972045444 |
| 6 | -3 | -1.95397941929012 | -1.04602058070988 |
| 7 | 0 | -1.19831349170545 | 1.19831349170545 |
| 8 | -5 | -2.98865436818795 | -2.01134563181205 |
| 9 | -3 | -3.02961218430157 | 0.029612184301569 |
| 10 | 3 | 1.27303287529263 | 1.72696712470737 |
| 11 | 2 | -1.14883442675193 | 3.14883442675193 |
| 12 | -7 | -5.83503039618816 | -1.16496960381184 |
| 13 | -1 | -1.19697590816227 | 0.196975908162268 |
| 14 | 0 | -2.53862480131938 | 2.53862480131938 |
| 15 | -3 | 0.720513045814369 | -3.72051304581437 |
| 16 | 4 | 6.08032495665419 | -2.08032495665419 |
| 17 | 2 | 1.02181345550449 | 0.978186544495507 |
| 18 | 3 | 1.47677775671964 | 1.52322224328036 |
| 19 | 0 | -3.01726600201894 | 3.01726600201894 |
| 20 | -10 | -3.72680406053019 | -6.27319593946981 |
| 21 | -10 | -7.87510027119728 | -2.12489972880272 |
| 22 | -9 | -4.72858858099064 | -4.27141141900936 |
| 23 | -22 | -12.9278849918645 | -9.07211500813547 |
| 24 | -16 | -15.2847697196889 | -0.715230280311065 |
| 25 | -18 | -18.234416505202 | 0.234416505201991 |
| 26 | -14 | -17.359772327427 | 3.35977232742697 |
| 27 | -12 | -17.9526130714568 | 5.95261307145676 |
| 28 | -17 | -19.889299005408 | 2.88929900540802 |
| 29 | -23 | -21.3801543053331 | -1.61984569466685 |
| 30 | -28 | -23.4515303134297 | -4.54846968657031 |
| 31 | -31 | -28.5587875101185 | -2.44121248988152 |
| 32 | -21 | -26.5449561916182 | 5.54495619161816 |
| 33 | -19 | -25.1316961707875 | 6.13169617078747 |
| 34 | -22 | -24.4568373549029 | 2.4568373549029 |
| 35 | -22 | -21.5725082288396 | -0.427491771160411 |
| 36 | -25 | -23.7530070053908 | -1.24699299460919 |
| 37 | -16 | -19.4351632197723 | 3.43516321977227 |
| 38 | -22 | -19.8365516208734 | -2.16344837912662 |
| 39 | -21 | -14.2445039185378 | -6.75549608146217 |
| 40 | -10 | -11.4179133558186 | 1.41791335581859 |
| 41 | -7 | -10.3686662688142 | 3.36866626881424 |
| 42 | -5 | -10.4667853630643 | 5.46678536306426 |
| 43 | -4 | -5.20140343540402 | 1.20140343540402 |
| 44 | 7 | -2.18209985034876 | 9.18209985034876 |
| 45 | 6 | 0.65097281338179 | 5.34902718661821 |
| 46 | 3 | 5.04779223402398 | -2.04779223402398 |
| 47 | 10 | 6.12513162059659 | 3.87486837940341 |
| 48 | 0 | 6.65603945023413 | -6.65603945023413 |
| 49 | -2 | 1.42165008118152 | -3.42165008118152 |
| 50 | -1 | 2.67987274195742 | -3.67987274195742 |
| 51 | 2 | -0.211472663229716 | 2.21147266322972 |
| 52 | 8 | 7.01186041599587 | 0.988139584004133 |
| 53 | -6 | -1.85082328013664 | -4.14917671986336 |
| 54 | -4 | -0.524047999472908 | -3.47595200052709 |
| 55 | 4 | 1.3193017848919 | 2.6806982151081 |
| 56 | 7 | 6.06158421241768 | 0.938415787582318 |
| 57 | 3 | 0.878853148646593 | 2.12114685135341 |
| 58 | 3 | -2.15084326190824 | 5.15084326190824 |
| 59 | 8 | 0.940678395882746 | 7.05932160411725 |
| 60 | 3 | -1.32711370290757 | 4.32711370290757 |
| 61 | -3 | -2.33790876861857 | -0.662091231381435 |
| 62 | 4 | 0.122815226412145 | 3.87718477358785 |
| 63 | -5 | -6.10003126172285 | 1.10003126172285 |
| 64 | -1 | 0.686474330825723 | -1.68647433082572 |
| 65 | 5 | -0.170524414722514 | 5.17052441472251 |
| 66 | 0 | -1.29475889195416 | 1.29475889195416 |
| 67 | -6 | -4.30885996530785 | -1.69114003469215 |
| 68 | -13 | -11.1518814604137 | -1.84811853958628 |
| 69 | -15 | -7.00693259244911 | -7.99306740755089 |
| 70 | -8 | -9.75918765187386 | 1.75918765187386 |
| 71 | -20 | -15.4165823690233 | -4.58341763097671 |
| 72 | -10 | -15.4561186260587 | 5.45611862605867 |
| 73 | -22 | -17.7034593445874 | -4.29654065541256 |
| 74 | -25 | -19.9495251044426 | -5.05047489555738 |
| 75 | -10 | -14.4277262215095 | 4.42772622150947 |
| 76 | -8 | -10.3986343245354 | 2.39863432453541 |
| 77 | -9 | -8.20013490695238 | -0.799865093047616 |
| 78 | -5 | -5.7856757695085 | 0.785675769508497 |
| 79 | -7 | -3.03467138033715 | -3.96532861966285 |
| 80 | -11 | -5.46718828131891 | -5.53281171868109 |
| 81 | -11 | -7.48648474329295 | -3.51351525670705 |
| 82 | -16 | -11.225368259641 | -4.77463174035903 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 18 | 0.151981399042744 | 0.303962798085488 | 0.848018600957256 |
| 19 | 0.0623213913634468 | 0.124642782726894 | 0.937678608636553 |
| 20 | 0.0887697029751645 | 0.177539405950329 | 0.911230297024836 |
| 21 | 0.0421842854404527 | 0.0843685708809055 | 0.957815714559547 |
| 22 | 0.0254084562423048 | 0.0508169124846095 | 0.974591543757695 |
| 23 | 0.0153177988473771 | 0.0306355976947542 | 0.984682201152623 |
| 24 | 0.106673590626257 | 0.213347181252513 | 0.893326409373743 |
| 25 | 0.0849492853071513 | 0.169898570614303 | 0.915050714692849 |
| 26 | 0.0939249265878096 | 0.187849853175619 | 0.90607507341219 |
| 27 | 0.317835270446518 | 0.635670540893037 | 0.682164729553482 |
| 28 | 0.298740785366319 | 0.597481570732638 | 0.701259214633681 |
| 29 | 0.229691730087948 | 0.459383460175896 | 0.770308269912052 |
| 30 | 0.221019272097184 | 0.442038544194368 | 0.778980727902816 |
| 31 | 0.165380835304899 | 0.330761670609797 | 0.834619164695101 |
| 32 | 0.355700755937186 | 0.711401511874373 | 0.644299244062813 |
| 33 | 0.414014252619396 | 0.828028505238793 | 0.585985747380604 |
| 34 | 0.379622139536563 | 0.759244279073127 | 0.620377860463437 |
| 35 | 0.307352202290196 | 0.614704404580391 | 0.692647797709804 |
| 36 | 0.244188350281409 | 0.488376700562818 | 0.755811649718591 |
| 37 | 0.253037311125054 | 0.506074622250109 | 0.746962688874946 |
| 38 | 0.228984737522287 | 0.457969475044574 | 0.771015262477713 |
| 39 | 0.261951207099008 | 0.523902414198015 | 0.738048792900992 |
| 40 | 0.241093288824172 | 0.482186577648343 | 0.758906711175828 |
| 41 | 0.263438560662817 | 0.526877121325634 | 0.736561439337183 |
| 42 | 0.29920000267542 | 0.598400005350841 | 0.70079999732458 |
| 43 | 0.259428668891224 | 0.518857337782448 | 0.740571331108776 |
| 44 | 0.599946214305484 | 0.800107571389032 | 0.400053785694516 |
| 45 | 0.770336465395496 | 0.459327069209008 | 0.229663534604504 |
| 46 | 0.728911875277928 | 0.542176249444144 | 0.271088124722072 |
| 47 | 0.767429762593606 | 0.465140474812788 | 0.232570237406394 |
| 48 | 0.881318400431153 | 0.237363199137694 | 0.118681599568847 |
| 49 | 0.861872599888251 | 0.276254800223497 | 0.138127400111749 |
| 50 | 0.829935567406283 | 0.340128865187434 | 0.170064432593717 |
| 51 | 0.787219137274896 | 0.425561725450207 | 0.212780862725104 |
| 52 | 0.72200854948007 | 0.55598290103986 | 0.27799145051993 |
| 53 | 0.748325123050365 | 0.503349753899269 | 0.251674876949635 |
| 54 | 0.762753917107277 | 0.474492165785447 | 0.237246082892723 |
| 55 | 0.715179344142831 | 0.569641311714338 | 0.284820655857169 |
| 56 | 0.65387115255651 | 0.692257694886981 | 0.34612884744349 |
| 57 | 0.635621693830224 | 0.728756612339553 | 0.364378306169776 |
| 58 | 0.582369319294647 | 0.835261361410705 | 0.417630680705353 |
| 59 | 0.72697497771797 | 0.54605004456406 | 0.27302502228203 |
| 60 | 0.803688936735371 | 0.392622126529258 | 0.196311063264629 |
| 61 | 0.712206969185474 | 0.575586061629052 | 0.287793030814526 |
| 62 | 0.666112432709428 | 0.667775134581144 | 0.333887567290572 |
| 63 | 0.81080216340265 | 0.3783956731947 | 0.18919783659735 |
| 64 | 0.688475870180768 | 0.623048259638464 | 0.311524129819232 |
| 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 | 1 | 0.0212765957446809 | OK |
| 10% type I error level | 3 | 0.0638297872340425 | OK |
