| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 12.0629978135911 + 4.10249057534315D[t] + 1.26715012400874Y1[t] -0.0818377397940402Y2[t] -0.306104094987486Y3[t] + 8.12828354888152M1[t] + 1.82765873193793M2[t] + 8.39071715010505M3[t] + 3.13299489510839M4[t] + 6.63553113116698M5[t] + 8.96123770976727M6[t] -0.419420596737340M7[t] -5.56120073377028M8[t] -10.1703238068274M9[t] -3.70759284651021M10[t] + 1.00728573412857M11[t] + 0.248197689412285t + 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) | 12.0629978135911 | 9.998003 | 1.2065 | 0.23205 | 0.116025 |
| D | 4.10249057534315 | 7.905934 | 0.5189 | 0.605611 | 0.302806 |
| Y1 | 1.26715012400874 | 0.120146 | 10.5468 | 0 | 0 |
| Y2 | -0.0818377397940402 | 0.201534 | -0.4061 | 0.686043 | 0.343021 |
| Y3 | -0.306104094987486 | 0.124114 | -2.4663 | 0.01634 | 0.00817 |
| M1 | 8.12828354888152 | 10.637038 | 0.7641 | 0.447587 | 0.223793 |
| M2 | 1.82765873193793 | 10.719273 | 0.1705 | 0.865153 | 0.432577 |
| M3 | 8.39071715010505 | 10.823729 | 0.7752 | 0.441068 | 0.220534 |
| M4 | 3.13299489510839 | 10.86559 | 0.2883 | 0.774018 | 0.387009 |
| M5 | 6.63553113116698 | 10.972058 | 0.6048 | 0.547473 | 0.273736 |
| M6 | 8.96123770976727 | 10.933532 | 0.8196 | 0.41548 | 0.20774 |
| M7 | -0.419420596737340 | 11.029918 | -0.038 | 0.969786 | 0.484893 |
| M8 | -5.56120073377028 | 11.000799 | -0.5055 | 0.614925 | 0.307463 |
| M9 | -10.1703238068274 | 10.810949 | -0.9407 | 0.350374 | 0.175187 |
| M10 | -3.70759284651021 | 11.080287 | -0.3346 | 0.739012 | 0.369506 |
| M11 | 1.00728573412857 | 11.027544 | 0.0913 | 0.927506 | 0.463753 |
| t | 0.248197689412285 | 0.182391 | 1.3608 | 0.178351 | 0.089175 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.980859105002279 |
| R-squared | 0.962084583865872 |
| Adjusted R-squared | 0.95260572983234 |
| F-TEST (value) | 101.497984931769 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 64 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 19.0574718264531 |
| Sum Squared Residuals | 23243.9828746274 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 107.1 | 105.715276237056 | 1.38472376294368 |
| 2 | 115.2 | 115.586799599612 | -0.38679959961207 |
| 3 | 106.1 | 128.931356038502 | -22.8313560385025 |
| 4 | 89.5 | 108.421955426242 | -18.9219554262423 |
| 5 | 91.3 | 89.4032775558953 | 1.89672244410471 |
| 6 | 97.6 | 98.4021057920908 | -0.802105792090774 |
| 7 | 100.7 | 102.186711001416 | -1.48671100141647 |
| 8 | 104.6 | 100.154728806543 | 4.44527119345701 |
| 9 | 94.7 | 98.5535361147495 | -3.85353611474951 |
| 10 | 101.8 | 91.4515886571345 | 10.3484113428655 |
| 11 | 102.5 | 105.027818461157 | -2.52781846115744 |
| 12 | 105.3 | 107.605118091086 | -2.30511809108570 |
| 13 | 110.3 | 117.298994184337 | -6.99899418433698 |
| 14 | 109.8 | 117.138899138935 | -7.3388991389348 |
| 15 | 117.3 | 122.050300019575 | -4.75030001957469 |
| 16 | 118.8 | 125.054799779015 | -6.25479977901542 |
| 17 | 131.3 | 130.245527889538 | 1.05447211046218 |
| 18 | 125.9 | 146.240271385562 | -20.3402713855624 |
| 19 | 133.1 | 128.783072208916 | 4.31692779108381 |
| 20 | 147 | 129.628593261703 | 17.3714067382973 |
| 21 | 145.8 | 143.944784988195 | 1.85521501180541 |
| 22 | 164.4 | 145.793639422067 | 18.6063605779335 |
| 23 | 149.8 | 170.169066366107 | -20.3690663661069 |
| 24 | 137.7 | 149.754729464679 | -12.0547294646789 |
| 25 | 151.7 | 138.299989036693 | 13.4000109633073 |
| 26 | 156.8 | 155.447020083609 | 1.35297991639111 |
| 27 | 180 | 171.278873015865 | 8.72112698413508 |
| 28 | 180.4 | 190.964401524509 | -10.5644015245088 |
| 29 | 170.4 | 191.762229051925 | -21.3622290519252 |
| 30 | 191.6 | 174.530281980223 | 17.0697180197768 |
| 31 | 199.5 | 192.957339752061 | 6.54266024793854 |
| 32 | 218.2 | 199.400324150351 | 18.7996758496490 |
| 33 | 217.5 | 211.599181127562 | 5.90081887243807 |
| 34 | 205 | 213.474516605936 | -8.47451660593562 |
| 35 | 194 | 196.931356167467 | -2.93135616746732 |
| 36 | 199.3 | 183.470861372572 | 15.8291386274283 |
| 37 | 219.3 | 203.28975459319 | 16.0102454068102 |
| 38 | 211.1 | 225.513734969787 | -14.4137349697872 |
| 39 | 215.2 | 218.675253561180 | -3.47525356118045 |
| 40 | 240.2 | 213.410032070593 | 26.7899679294067 |
| 41 | 242.2 | 251.014037942024 | -8.81403794202438 |
| 42 | 240.7 | 252.821272173755 | -12.1212721737547 |
| 43 | 255.4 | 233.971808516374 | 21.4281914836260 |
| 44 | 253 | 247.215881311398 | 5.78411868860205 |
| 45 | 218.2 | 239.069936997641 | -20.869936997641 |
| 46 | 203.7 | 197.380721711056 | 6.31927828894391 |
| 47 | 205.6 | 187.552724355783 | 18.0472756442170 |
| 48 | 215.6 | 201.040291279261 | 14.5597087207386 |
| 49 | 188.5 | 226.371291429352 | -37.8712914293525 |
| 50 | 202.9 | 184.579120762768 | 18.3208792372322 |
| 51 | 214 | 208.794100454617 | 5.20589954538335 |
| 52 | 230.3 | 224.966899786656 | 5.33310021334409 |
| 53 | 230 | 244.055882853936 | -14.0558828539356 |
| 54 | 241 | 241.517931471742 | -0.51793147174156 |
| 55 | 259.6 | 245.461667367731 | 14.1383326322694 |
| 56 | 247.8 | 263.328693317434 | -15.5286933174343 |
| 57 | 270.3 | 239.126069465455 | 31.1739305345452 |
| 58 | 289.7 | 269.620025068183 | 20.0799749318167 |
| 59 | 322.7 | 300.93649291949 | 21.7635070805097 |
| 60 | 315 | 333.518364677839 | -18.5183646778394 |
| 61 | 320.2 | 323.498725105305 | -3.29872510530546 |
| 62 | 329.5 | 314.564194084447 | 14.9358059155534 |
| 63 | 360.6 | 335.091391629782 | 25.5086083702181 |
| 64 | 382.2 | 367.13740364685 | 15.0625963531502 |
| 65 | 435.4 | 392.866658459931 | 42.5333415400689 |
| 66 | 464 | 451.565416791546 | 12.4345832084537 |
| 67 | 468.8 | 467.707833512331 | 1.09216648766877 |
| 68 | 403 | 450.271274448509 | -47.2712744485087 |
| 69 | 351.6 | 353.384472637436 | -1.78447263743551 |
| 70 | 252 | 298.879508535624 | -46.8795085356239 |
| 71 | 188 | 201.982541729995 | -13.9825417299951 |
| 72 | 146.5 | 144.010635114563 | 2.48936488543716 |
| 73 | 152.9 | 135.525969414066 | 17.3740305859338 |
| 74 | 148.1 | 160.570231360843 | -12.4702313608426 |
| 75 | 165.1 | 173.478725280479 | -8.37872528047889 |
| 76 | 177 | 188.444507766135 | -11.4445077661345 |
| 77 | 206.1 | 207.352386246751 | -1.25238624675061 |
| 78 | 244.9 | 240.622720405081 | 4.27727959491894 |
| 79 | 228.6 | 274.63156764117 | -46.03156764117 |
| 80 | 253.4 | 237.000504704062 | 16.3994952959376 |
| 81 | 241.1 | 253.522018668963 | -12.4220186689626 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.125549422788242 | 0.251098845576484 | 0.874450577211758 |
| 21 | 0.04962978960154 | 0.09925957920308 | 0.95037021039846 |
| 22 | 0.0216690565589811 | 0.0433381131179621 | 0.97833094344102 |
| 23 | 0.0205302516342858 | 0.0410605032685715 | 0.979469748365714 |
| 24 | 0.00852163370866007 | 0.0170432674173201 | 0.99147836629134 |
| 25 | 0.00323456605366182 | 0.00646913210732364 | 0.996765433946338 |
| 26 | 0.00183559444985915 | 0.00367118889971831 | 0.99816440555014 |
| 27 | 0.00320158024471357 | 0.00640316048942714 | 0.996798419755286 |
| 28 | 0.00153553220882011 | 0.00307106441764023 | 0.99846446779118 |
| 29 | 0.00154424389719505 | 0.00308848779439009 | 0.998455756102805 |
| 30 | 0.00334858971486137 | 0.00669717942972274 | 0.996651410285139 |
| 31 | 0.00151281855507527 | 0.00302563711015054 | 0.998487181444925 |
| 32 | 0.00101816535138939 | 0.00203633070277879 | 0.99898183464861 |
| 33 | 0.000444231121941818 | 0.000888462243883636 | 0.999555768878058 |
| 34 | 0.00067215266522871 | 0.00134430533045742 | 0.999327847334771 |
| 35 | 0.000334809623714204 | 0.000669619247428408 | 0.999665190376286 |
| 36 | 0.000145017022799282 | 0.000290034045598564 | 0.9998549829772 |
| 37 | 6.73814050148104e-05 | 0.000134762810029621 | 0.999932618594985 |
| 38 | 6.8115814751985e-05 | 0.00013623162950397 | 0.999931884185248 |
| 39 | 3.69029308455588e-05 | 7.38058616911175e-05 | 0.999963097069154 |
| 40 | 6.17858702644598e-05 | 0.000123571740528920 | 0.999938214129735 |
| 41 | 3.79029761361041e-05 | 7.58059522722082e-05 | 0.999962097023864 |
| 42 | 3.50038478885096e-05 | 7.00076957770192e-05 | 0.999964996152112 |
| 43 | 2.19425160535088e-05 | 4.38850321070175e-05 | 0.999978057483947 |
| 44 | 2.46594667591877e-05 | 4.93189335183755e-05 | 0.99997534053324 |
| 45 | 0.000126884000135388 | 0.000253768000270776 | 0.999873115999865 |
| 46 | 0.000175071419906436 | 0.000350142839812871 | 0.999824928580094 |
| 47 | 0.000114131914920165 | 0.00022826382984033 | 0.99988586808508 |
| 48 | 9.97179702781939e-05 | 0.000199435940556388 | 0.999900282029722 |
| 49 | 0.00160317849514561 | 0.00320635699029122 | 0.998396821504854 |
| 50 | 0.00124982545750492 | 0.00249965091500983 | 0.998750174542495 |
| 51 | 0.000835585411376288 | 0.00167117082275258 | 0.999164414588624 |
| 52 | 0.000604563475448113 | 0.00120912695089623 | 0.999395436524552 |
| 53 | 0.000322187722337781 | 0.000644375444675561 | 0.999677812277662 |
| 54 | 0.000139624901501338 | 0.000279249803002675 | 0.999860375098499 |
| 55 | 5.5328327126079e-05 | 0.000110656654252158 | 0.999944671672874 |
| 56 | 0.000259317199087798 | 0.000518634398175596 | 0.999740682800912 |
| 57 | 0.00194326982731245 | 0.00388653965462491 | 0.998056730172687 |
| 58 | 0.00095912637135529 | 0.00191825274271058 | 0.999040873628645 |
| 59 | 0.000973435488021913 | 0.00194687097604383 | 0.999026564511978 |
| 60 | 0.000498352772885365 | 0.00099670554577073 | 0.999501647227115 |
| 61 | 0.0108630437244747 | 0.0217260874489493 | 0.989136956275525 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 36 | 0.857142857142857 | NOK |
| 5% type I error level | 40 | 0.952380952380952 | NOK |
| 10% type I error level | 41 | 0.976190476190476 | NOK |
