| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 302.521504071985 -1.72123794877019X[t] + 0.866754928207082`Y(t-1)`[t] + 0.134467604277825`Y(t-2)`[t] -0.125706630975887`Y(t-3)`[t] -0.380598880377657`Y(t-4)`[t] + 0.226892520847359`Y(t-5) `[t] + 0.764686012256499t + 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) | 302.521504071985 | 46.185592 | 6.5501 | 0 | 0 |
| X | -1.72123794877019 | 0.223008 | -7.7183 | 0 | 0 |
| `Y(t-1)` | 0.866754928207082 | 0.094569 | 9.1653 | 0 | 0 |
| `Y(t-2)` | 0.134467604277825 | 0.14831 | 0.9067 | 0.368272 | 0.184136 |
| `Y(t-3)` | -0.125706630975887 | 0.137991 | -0.911 | 0.366013 | 0.183006 |
| `Y(t-4)` | -0.380598880377657 | 0.141786 | -2.6843 | 0.009419 | 0.004709 |
| `Y(t-5) ` | 0.226892520847359 | 0.094162 | 2.4096 | 0.019108 | 0.009554 |
| t | 0.764686012256499 | 0.226221 | 3.3803 | 0.001289 | 0.000645 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.975983400744419 |
| R-squared | 0.95254359852864 |
| Adjusted R-squared | 0.94691317801509 |
| F-TEST (value) | 169.178056281247 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 11.6937803278994 |
| Sum Squared Residuals | 8067.9254030729 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 431 | 432.531768903009 | -1.53176890300867 |
| 2 | 484 | 475.004075426774 | 8.99592457322623 |
| 3 | 510 | 497.513705283016 | 12.4862947169842 |
| 4 | 513 | 519.255266091415 | -6.2552660914153 |
| 5 | 503 | 505.310271144082 | -2.31027114408167 |
| 6 | 471 | 485.457024453743 | -14.4570244537435 |
| 7 | 471 | 478.859849748493 | -7.85984974849263 |
| 8 | 476 | 471.86923891628 | 4.13076108372011 |
| 9 | 475 | 485.649101921996 | -10.6491019219959 |
| 10 | 470 | 479.089354298221 | -9.08935429822093 |
| 11 | 461 | 472.488294294603 | -11.4882942946028 |
| 12 | 455 | 464.895921904341 | -9.89592190434128 |
| 13 | 456 | 456.746122086669 | -0.746122086669211 |
| 14 | 517 | 492.565368603292 | 24.4346313967077 |
| 15 | 525 | 538.882188457978 | -13.8821884579780 |
| 16 | 523 | 529.424970078703 | -6.42497007870345 |
| 17 | 519 | 510.310772265787 | 8.68922773421258 |
| 18 | 509 | 502.105704768258 | 6.89429523174182 |
| 19 | 512 | 521.408045175023 | -9.40804517502284 |
| 20 | 519 | 517.212799457201 | 1.78720054279898 |
| 21 | 517 | 527.462344748823 | -10.4623447488234 |
| 22 | 510 | 515.4976941924 | -5.4976941924004 |
| 23 | 509 | 510.282834693893 | -1.28283469389343 |
| 24 | 501 | 515.425085774191 | -14.4250857741912 |
| 25 | 507 | 501.334733707902 | 5.66526629209798 |
| 26 | 569 | 537.993491131073 | 31.0065088689265 |
| 27 | 580 | 588.798697728164 | -8.79869772816376 |
| 28 | 578 | 575.245702971715 | 2.75429702828488 |
| 29 | 565 | 560.5931261024 | 4.40687389759962 |
| 30 | 547 | 548.750731569233 | -1.75073156923332 |
| 31 | 555 | 545.224016401394 | 9.77598359860627 |
| 32 | 562 | 558.491754962855 | 3.50824503714482 |
| 33 | 561 | 569.885833964901 | -8.88583396490128 |
| 34 | 555 | 546.597126511179 | 8.40287348882148 |
| 35 | 544 | 550.886144412758 | -6.88614441275765 |
| 36 | 537 | 550.053183942416 | -13.0531839424165 |
| 37 | 543 | 521.897196839549 | 21.1028031604509 |
| 38 | 594 | 571.670323663741 | 22.3296763362587 |
| 39 | 611 | 604.971858897687 | 6.02814110231254 |
| 40 | 613 | 596.965944641376 | 16.0340553586235 |
| 41 | 611 | 598.007914880129 | 12.9920851198708 |
| 42 | 594 | 588.13774861589 | 5.86225138411006 |
| 43 | 595 | 582.707437257085 | 12.2925627429148 |
| 44 | 591 | 597.448982921819 | -6.4489829218187 |
| 45 | 589 | 595.995503021163 | -6.99550302116352 |
| 46 | 584 | 585.232604104466 | -1.23260410446644 |
| 47 | 573 | 580.929987158916 | -7.92998715891604 |
| 48 | 567 | 581.578550603035 | -14.5785506030352 |
| 49 | 569 | 548.950164640669 | 20.0498353593306 |
| 50 | 621 | 610.274389494018 | 10.7256105059823 |
| 51 | 629 | 634.711310205572 | -5.71131020557207 |
| 52 | 628 | 618.817049253447 | 9.18295074655298 |
| 53 | 612 | 623.696460501156 | -11.6964605011559 |
| 54 | 595 | 585.124000220637 | 9.8759997793629 |
| 55 | 597 | 589.069744123952 | 7.93025587604845 |
| 56 | 593 | 599.169121093612 | -6.16912109361154 |
| 57 | 590 | 601.809320380471 | -11.8093203804712 |
| 58 | 580 | 576.550036920107 | 3.44996307989297 |
| 59 | 574 | 589.602548388001 | -15.6025483880012 |
| 60 | 573 | 570.339940115684 | 2.66005988431582 |
| 61 | 573 | 562.832540082349 | 10.1674599176508 |
| 62 | 620 | 617.602457621507 | 2.39754237849277 |
| 63 | 626 | 633.254306937835 | -7.25430693783494 |
| 64 | 620 | 619.945041008271 | 0.0549589917285095 |
| 65 | 588 | 607.254794387329 | -19.2547943873291 |
| 66 | 566 | 567.030586523259 | -1.03058652325947 |
| 67 | 557 | 572.31978940308 | -15.3197894030801 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.0240089362730382 | 0.0480178725460764 | 0.975991063726962 |
| 12 | 0.0129273052309199 | 0.0258546104618398 | 0.98707269476908 |
| 13 | 0.0303471166331473 | 0.0606942332662947 | 0.969652883366853 |
| 14 | 0.188290841918754 | 0.376581683837508 | 0.811709158081246 |
| 15 | 0.443666957688695 | 0.887333915377389 | 0.556333042311305 |
| 16 | 0.41447789204595 | 0.8289557840919 | 0.58552210795405 |
| 17 | 0.416828362236745 | 0.83365672447349 | 0.583171637763255 |
| 18 | 0.470383321904405 | 0.94076664380881 | 0.529616678095595 |
| 19 | 0.403143387443185 | 0.80628677488637 | 0.596856612556815 |
| 20 | 0.344176594911546 | 0.688353189823091 | 0.655823405088454 |
| 21 | 0.298689461675988 | 0.597378923351975 | 0.701310538324012 |
| 22 | 0.244542276084163 | 0.489084552168326 | 0.755457723915837 |
| 23 | 0.1885762780483 | 0.3771525560966 | 0.8114237219517 |
| 24 | 0.270351106103884 | 0.540702212207768 | 0.729648893896116 |
| 25 | 0.269157171605672 | 0.538314343211344 | 0.730842828394328 |
| 26 | 0.52410342315113 | 0.95179315369774 | 0.47589657684887 |
| 27 | 0.529844142575076 | 0.940311714849847 | 0.470155857424924 |
| 28 | 0.565626477235141 | 0.868747045529718 | 0.434373522764859 |
| 29 | 0.488363763878124 | 0.976727527756249 | 0.511636236121876 |
| 30 | 0.466225546073178 | 0.932451092146355 | 0.533774453926823 |
| 31 | 0.447401926000595 | 0.89480385200119 | 0.552598073999405 |
| 32 | 0.378163012475963 | 0.756326024951925 | 0.621836987524037 |
| 33 | 0.410165190000671 | 0.820330380001342 | 0.589834809999329 |
| 34 | 0.377331830714036 | 0.754663661428071 | 0.622668169285964 |
| 35 | 0.456052884859346 | 0.912105769718692 | 0.543947115140654 |
| 36 | 0.819292036150736 | 0.361415927698527 | 0.180707963849264 |
| 37 | 0.849260543282684 | 0.301478913434631 | 0.150739456717316 |
| 38 | 0.829696232642317 | 0.340607534715366 | 0.170303767357683 |
| 39 | 0.787682294873181 | 0.424635410253638 | 0.212317705126819 |
| 40 | 0.781828998071812 | 0.436342003856375 | 0.218171001928188 |
| 41 | 0.749479773457189 | 0.501040453085621 | 0.250520226542811 |
| 42 | 0.696579780793319 | 0.606840438413362 | 0.303420219206681 |
| 43 | 0.67812348640734 | 0.643753027185322 | 0.321876513592661 |
| 44 | 0.626335188077581 | 0.747329623844838 | 0.373664811922419 |
| 45 | 0.602454982586537 | 0.795090034826926 | 0.397545017413463 |
| 46 | 0.52118011566542 | 0.95763976866916 | 0.47881988433458 |
| 47 | 0.596211925297738 | 0.807576149404523 | 0.403788074702262 |
| 48 | 0.907081907163106 | 0.185836185673788 | 0.092918092836894 |
| 49 | 0.86558975515199 | 0.268820489696019 | 0.134410244848010 |
| 50 | 0.804783353409784 | 0.390433293180431 | 0.195216646590216 |
| 51 | 0.784985732929932 | 0.430028534140135 | 0.215014267070068 |
| 52 | 0.687731413220797 | 0.624537173558405 | 0.312268586779202 |
| 53 | 0.629876458636639 | 0.740247082726723 | 0.370123541363361 |
| 54 | 0.498381623410748 | 0.996763246821495 | 0.501618376589252 |
| 55 | 0.616609789631374 | 0.766780420737252 | 0.383390210368626 |
| 56 | 0.558445513790778 | 0.883108972418444 | 0.441554486209222 |
| 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 | 2 | 0.0434782608695652 | OK |
| 10% type I error level | 3 | 0.0652173913043478 | OK |
