| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 579977.785245902 -59810.4631147541X[t] -1321.29754098364M1[t] -5147.96420765032M2[t] -13344.9642076503M3[t] -19440.7975409836M4[t] -29893.4642076503M5[t] -17214.5536885246M6[t] + 33951.2796448087M7[t] + 43299.2796448087M8[t] + 33408.4463114754M9[t] + 12808.4M10[t] -2648.6M11[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) | 579977.785245902 | 9811.90954 | 59.1096 | 0 | 0 |
| X | -59810.4631147541 | 5310.851826 | -11.2619 | 0 | 0 |
| M1 | -1321.29754098364 | 12975.106521 | -0.1018 | 0.919253 | 0.459626 |
| M2 | -5147.96420765032 | 12975.106521 | -0.3968 | 0.693055 | 0.346527 |
| M3 | -13344.9642076503 | 12975.106521 | -1.0285 | 0.308134 | 0.154067 |
| M4 | -19440.7975409836 | 12975.106521 | -1.4983 | 0.139668 | 0.069834 |
| M5 | -29893.4642076503 | 12975.106521 | -2.3039 | 0.024962 | 0.012481 |
| M6 | -17214.5536885246 | 12981.14342 | -1.3261 | 0.190184 | 0.095092 |
| M7 | 33951.2796448087 | 12981.14342 | 2.6154 | 0.011431 | 0.005715 |
| M8 | 43299.2796448087 | 12981.14342 | 3.3356 | 0.001516 | 0.000758 |
| M9 | 33408.4463114754 | 12981.14342 | 2.5736 | 0.012739 | 0.006369 |
| M10 | 12808.4 | 13547.010393 | 0.9455 | 0.348477 | 0.174238 |
| M11 | -2648.6 | 13547.010393 | -0.1955 | 0.8457 | 0.42285 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.87681888043466 |
| R-squared | 0.768811349086691 |
| Adjusted R-squared | 0.719270923890982 |
| F-TEST (value) | 15.5188686017431 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 56 |
| p-value | 1.04360964314765e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21419.7041633918 |
| Sum Squared Residuals | 25693008681.0445 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 562325 | 578656.487704918 | -16331.4877049182 |
| 2 | 560854 | 574829.821038252 | -13975.8210382515 |
| 3 | 555332 | 566632.821038251 | -11300.8210382514 |
| 4 | 543599 | 560536.987704918 | -16937.987704918 |
| 5 | 536662 | 550084.321038251 | -13422.3210382514 |
| 6 | 542722 | 562763.231557377 | -20041.2315573770 |
| 7 | 593530 | 613929.06489071 | -20399.0648907104 |
| 8 | 610763 | 623277.06489071 | -12514.0648907104 |
| 9 | 612613 | 613386.231557377 | -773.231557377052 |
| 10 | 611324 | 592786.185245902 | 18537.8147540984 |
| 11 | 594167 | 577329.185245902 | 16837.8147540984 |
| 12 | 595454 | 579977.785245902 | 15476.2147540984 |
| 13 | 590865 | 578656.487704918 | 12208.512295082 |
| 14 | 589379 | 574829.821038251 | 14549.1789617487 |
| 15 | 584428 | 566632.821038251 | 17795.1789617486 |
| 16 | 573100 | 560536.987704918 | 12563.0122950820 |
| 17 | 567456 | 550084.321038251 | 17371.6789617486 |
| 18 | 569028 | 562763.231557377 | 6264.76844262296 |
| 19 | 620735 | 613929.06489071 | 6805.93510928962 |
| 20 | 628884 | 623277.06489071 | 5606.93510928962 |
| 21 | 628232 | 613386.231557377 | 14845.7684426230 |
| 22 | 612117 | 592786.185245902 | 19330.8147540983 |
| 23 | 595404 | 577329.185245902 | 18074.8147540984 |
| 24 | 597141 | 579977.785245902 | 17163.2147540984 |
| 25 | 593408 | 578656.487704918 | 14751.512295082 |
| 26 | 590072 | 574829.821038251 | 15242.1789617487 |
| 27 | 579799 | 566632.821038251 | 13166.1789617486 |
| 28 | 574205 | 560536.987704918 | 13668.0122950820 |
| 29 | 572775 | 550084.321038251 | 22690.6789617486 |
| 30 | 572942 | 562763.231557377 | 10178.7684426230 |
| 31 | 619567 | 613929.06489071 | 5637.93510928961 |
| 32 | 625809 | 623277.06489071 | 2531.93510928962 |
| 33 | 619916 | 613386.231557377 | 6529.76844262296 |
| 34 | 587625 | 592786.185245902 | -5161.18524590164 |
| 35 | 565742 | 577329.185245902 | -11587.1852459016 |
| 36 | 557274 | 579977.785245902 | -22703.7852459016 |
| 37 | 560576 | 578656.487704918 | -18080.487704918 |
| 38 | 548854 | 574829.821038251 | -25975.8210382513 |
| 39 | 531673 | 566632.821038251 | -34959.8210382514 |
| 40 | 525919 | 560536.987704918 | -34617.987704918 |
| 41 | 511038 | 550084.321038251 | -39046.3210382514 |
| 42 | 498662 | 502952.768442623 | -4290.76844262295 |
| 43 | 555362 | 554118.601775956 | 1243.39822404372 |
| 44 | 564591 | 563466.601775956 | 1124.39822404371 |
| 45 | 541657 | 553575.768442623 | -11918.7684426229 |
| 46 | 527070 | 532975.722131148 | -5905.72213114755 |
| 47 | 509846 | 517518.722131148 | -7672.72213114755 |
| 48 | 514258 | 520167.322131148 | -5909.32213114755 |
| 49 | 516922 | 518846.024590164 | -1924.0245901639 |
| 50 | 507561 | 515019.357923497 | -7458.35792349725 |
| 51 | 492622 | 506822.357923497 | -14200.3579234973 |
| 52 | 490243 | 500726.524590164 | -10483.5245901639 |
| 53 | 469357 | 490273.857923497 | -20916.8579234973 |
| 54 | 477580 | 502952.768442623 | -25372.7684426230 |
| 55 | 528379 | 554118.601775956 | -25739.6017759563 |
| 56 | 533590 | 563466.601775956 | -29876.6017759563 |
| 57 | 517945 | 553575.768442623 | -35630.768442623 |
| 58 | 506174 | 532975.722131148 | -26801.7221311475 |
| 59 | 501866 | 517518.722131148 | -15652.7221311475 |
| 60 | 516141 | 520167.322131148 | -4026.32213114755 |
| 61 | 528222 | 518846.024590164 | 9375.9754098361 |
| 62 | 532638 | 515019.357923497 | 17618.6420765028 |
| 63 | 536322 | 506822.357923497 | 29499.6420765027 |
| 64 | 536535 | 500726.524590164 | 35808.4754098361 |
| 65 | 523597 | 490273.857923497 | 33323.1420765027 |
| 66 | 536214 | 502952.768442623 | 33261.231557377 |
| 67 | 586570 | 554118.601775956 | 32451.3982240437 |
| 68 | 596594 | 563466.601775956 | 33127.3982240437 |
| 69 | 580523 | 553575.768442623 | 26947.2315573770 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.613935162588891 | 0.772129674822218 | 0.386064837411109 |
| 17 | 0.573694560867506 | 0.852610878264989 | 0.426305439132494 |
| 18 | 0.504465221186488 | 0.991069557627024 | 0.495534778813512 |
| 19 | 0.447367628734733 | 0.894735257469465 | 0.552632371265267 |
| 20 | 0.355817947496966 | 0.711635894993932 | 0.644182052503034 |
| 21 | 0.276641275992534 | 0.553282551985068 | 0.723358724007466 |
| 22 | 0.205845408833137 | 0.411690817666275 | 0.794154591166863 |
| 23 | 0.149500688627390 | 0.299001377254779 | 0.85049931137261 |
| 24 | 0.106510998846314 | 0.213021997692627 | 0.893489001153686 |
| 25 | 0.0850573625634396 | 0.170114725126879 | 0.91494263743656 |
| 26 | 0.0666413726513684 | 0.133282745302737 | 0.933358627348632 |
| 27 | 0.0478024953891648 | 0.0956049907783297 | 0.952197504610835 |
| 28 | 0.0376025644499594 | 0.0752051288999189 | 0.96239743555004 |
| 29 | 0.0415001543649843 | 0.0830003087299687 | 0.958499845635016 |
| 30 | 0.0341952294270010 | 0.0683904588540019 | 0.965804770573 |
| 31 | 0.0245122751394213 | 0.0490245502788426 | 0.975487724860579 |
| 32 | 0.0158655466764610 | 0.0317310933529219 | 0.984134453323539 |
| 33 | 0.0125958449358681 | 0.0251916898717362 | 0.987404155064132 |
| 34 | 0.0167071760884845 | 0.0334143521769691 | 0.983292823911516 |
| 35 | 0.0234887796108521 | 0.0469775592217042 | 0.976511220389148 |
| 36 | 0.0378405962587916 | 0.0756811925175833 | 0.962159403741208 |
| 37 | 0.0332138014656297 | 0.0664276029312593 | 0.96678619853437 |
| 38 | 0.0358881319562016 | 0.0717762639124032 | 0.964111868043798 |
| 39 | 0.0491743544721764 | 0.0983487089443528 | 0.950825645527824 |
| 40 | 0.0536812492301169 | 0.107362498460234 | 0.946318750769883 |
| 41 | 0.0716896033993708 | 0.143379206798742 | 0.92831039660063 |
| 42 | 0.0463694011897022 | 0.0927388023794044 | 0.953630598810298 |
| 43 | 0.0283293212039898 | 0.0566586424079796 | 0.97167067879601 |
| 44 | 0.0162909669770051 | 0.0325819339540102 | 0.983709033022995 |
| 45 | 0.0101245441798726 | 0.0202490883597452 | 0.989875455820127 |
| 46 | 0.00622488392530948 | 0.0124497678506190 | 0.99377511607469 |
| 47 | 0.00318928030695518 | 0.00637856061391035 | 0.996810719693045 |
| 48 | 0.00145474713596436 | 0.00290949427192873 | 0.998545252864036 |
| 49 | 0.000655783816870145 | 0.00131156763374029 | 0.99934421618313 |
| 50 | 0.000316384307918566 | 0.000632768615837133 | 0.999683615692081 |
| 51 | 0.000234200191497188 | 0.000468400382994376 | 0.999765799808503 |
| 52 | 0.000188556877370691 | 0.000377113754741382 | 0.99981144312263 |
| 53 | 0.000232556375310099 | 0.000465112750620198 | 0.99976744362469 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 7 | 0.184210526315789 | NOK |
| 5% type I error level | 15 | 0.394736842105263 | NOK |
| 10% type I error level | 25 | 0.657894736842105 | NOK |
