| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 3.30821434872672 -0.272802800787046X[t] + 0.0702404974155654Y1[t] -0.00157170726815757Y2[t] + 0.00350368217653026M1[t] + 0.00247072088343351M2[t] -0.205170993272856M3[t] -0.266929670970975M4[t] + 0.327279121223635M5[t] + 0.349232147671393M6[t] + 0.495317702851394M7[t] + 0.328181865572133M8[t] + 0.252601193983415M9[t] + 0.183724384734404M10[t] -0.0281642113791766M11[t] + 0.0185621130818993t + 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) | 3.30821434872672 | 2.519453 | 1.3131 | 0.195403 | 0.097701 |
| X | -0.272802800787046 | 0.340819 | -0.8004 | 0.427404 | 0.213702 |
| Y1 | 0.0702404974155654 | 0.232244 | 0.3024 | 0.763622 | 0.381811 |
| Y2 | -0.00157170726815757 | 0.21132 | -0.0074 | 0.994097 | 0.497048 |
| M1 | 0.00350368217653026 | 0.758324 | 0.0046 | 0.996333 | 0.498166 |
| M2 | 0.00247072088343351 | 0.761527 | 0.0032 | 0.997425 | 0.498712 |
| M3 | -0.205170993272856 | 0.747499 | -0.2745 | 0.784896 | 0.392448 |
| M4 | -0.266929670970975 | 0.762942 | -0.3499 | 0.727968 | 0.363984 |
| M5 | 0.327279121223635 | 0.777999 | 0.4207 | 0.675875 | 0.337938 |
| M6 | 0.349232147671393 | 0.785483 | 0.4446 | 0.658601 | 0.329301 |
| M7 | 0.495317702851394 | 0.76622 | 0.6464 | 0.521072 | 0.260536 |
| M8 | 0.328181865572133 | 0.774618 | 0.4237 | 0.673699 | 0.33685 |
| M9 | 0.252601193983415 | 0.766335 | 0.3296 | 0.743119 | 0.37156 |
| M10 | 0.183724384734404 | 0.768576 | 0.239 | 0.812088 | 0.406044 |
| M11 | -0.0281642113791766 | 0.770074 | -0.0366 | 0.970977 | 0.485488 |
| t | 0.0185621130818993 | 0.010941 | 1.6965 | 0.096268 | 0.048134 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.454844093786271 |
| R-squared | 0.206883149652254 |
| Adjusted R-squared | -0.0409658660814167 |
| F-TEST (value) | 0.834714429023849 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 48 |
| p-value | 0.635944893191229 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.20872056478554 |
| Sum Squared Residuals | 70.1282593793028 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.17538538425463 | 0.224614615745371 |
| 2 | 1.2 | 1.23374133817136 | -0.0337413381713568 |
| 3 | 1 | 1.23054582713502 | -0.230545827135018 |
| 4 | 1.7 | 1.7846059129923 | -0.0846059129923012 |
| 5 | 2.4 | 2.42093340815871 | -0.0209334081587133 |
| 6 | 2 | 2.41419631347271 | -0.414196313472706 |
| 7 | 2.1 | 2.31353674286956 | -0.213536742869565 |
| 8 | 2 | 2.12592522504613 | -0.125925225046134 |
| 9 | 1.8 | 2.06815087815868 | -0.268150878158679 |
| 10 | 2.7 | 2.13335266914068 | 0.566647330859321 |
| 11 | 2.3 | 1.96633337657337 | 0.333666623426635 |
| 12 | 1.9 | 1.97236000437989 | -0.0723600043798864 |
| 13 | 2 | 1.94720363067609 | 0.0527963693239052 |
| 14 | 2.3 | 1.97862371122119 | 0.321376288778806 |
| 15 | 2.8 | 1.78922976869317 | 1.01077023130683 |
| 16 | 2.4 | 1.82787404431307 | 0.572125955686933 |
| 17 | 2.3 | 2.41957280036491 | -0.119572800364906 |
| 18 | 2.7 | 2.56968057238983 | 0.130319427610171 |
| 19 | 2.7 | 2.59711092137069 | 0.102889078629315 |
| 20 | 2.9 | 2.47726207904681 | 0.422737920953188 |
| 21 | 3 | 2.39233455755403 | 0.607665442445973 |
| 22 | 2.2 | 2.32176363104977 | -0.121763631049766 |
| 23 | 2.3 | 2.13530402703283 | 0.164695972967174 |
| 24 | 2.8 | 2.12731262060968 | 0.672687379390324 |
| 25 | 2.8 | 2.10886595519381 | 0.69113404480619 |
| 26 | 2.8 | 2.11284858493339 | 0.68715141506661 |
| 27 | 2.2 | 1.93047869214692 | 0.269521307853076 |
| 28 | 2.6 | 1.88712495680389 | 0.712875043196111 |
| 29 | 2.8 | 2.58173670231651 | 0.218263297683488 |
| 30 | 2.5 | 2.76486137309373 | -0.264861373093727 |
| 31 | 2.4 | 2.99695737540155 | -0.596957375401555 |
| 32 | 2.3 | 2.90307131683497 | -0.603071316834975 |
| 33 | 1.9 | 2.79832901193205 | -0.898329011932045 |
| 34 | 1.7 | 2.70094931752953 | -1.00094931752953 |
| 35 | 2 | 2.49423348317544 | -0.494233483175439 |
| 36 | 2.1 | 2.52038923584574 | -0.420389235845735 |
| 37 | 1.7 | 2.5220416300402 | -0.822041630040201 |
| 38 | 1.8 | 2.57371794092245 | -0.773717940922449 |
| 39 | 1.8 | 2.43201767953710 | -0.632017679537096 |
| 40 | 1.8 | 2.34764990608587 | -0.547649906085874 |
| 41 | 1.3 | 3.02231976271498 | -1.72231976271498 |
| 42 | 1.3 | 3.15775075234953 | -1.85775075234953 |
| 43 | 1.3 | 3.21277572286272 | -1.91277572286272 |
| 44 | 1.2 | 3.11318311087600 | -1.91318311087600 |
| 45 | 1.4 | 3.10322955060458 | -1.70322955060458 |
| 46 | 2.2 | 3.06630420575988 | -0.866304205759877 |
| 47 | 2.9 | 2.89354829451898 | 0.00645170548102447 |
| 48 | 3.1 | 2.85156689972920 | 0.248433100270803 |
| 49 | 3.5 | 2.813021174703 | 0.686978825297002 |
| 50 | 3.6 | 2.85115096353602 | 0.748849036463978 |
| 51 | 4.4 | 2.77072097059600 | 1.62927902940400 |
| 52 | 4.1 | 2.78126904724967 | 1.31873095275033 |
| 53 | 5.1 | 3.45543732644489 | 1.64456267355511 |
| 54 | 5.8 | 3.39351098869421 | 2.40648901130579 |
| 55 | 5.9 | 3.27961923749548 | 2.62038076250452 |
| 56 | 5.4 | 3.18055826819608 | 2.21944173180392 |
| 57 | 5.5 | 3.23795600175067 | 2.26204399824933 |
| 58 | 4.8 | 3.37763017652015 | 1.42236982347985 |
| 59 | 3.2 | 3.21058081869939 | -0.0105808186993931 |
| 60 | 2.7 | 3.12837123943551 | -0.428371239435507 |
| 61 | 2.1 | 2.93348222513227 | -0.833482225132268 |
| 62 | 1.9 | 2.84991746121559 | -0.949917461215588 |
| 63 | 0.6 | 2.64700706189179 | -2.04700706189179 |
| 64 | 0.7 | 2.67147613255520 | -1.97147613255520 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.0266577072731589 | 0.0533154145463178 | 0.97334229272684 |
| 20 | 0.00746071889374525 | 0.0149214377874905 | 0.992539281106255 |
| 21 | 0.00229984861666121 | 0.00459969723332242 | 0.997700151383339 |
| 22 | 0.00208734051999588 | 0.00417468103999177 | 0.997912659480004 |
| 23 | 0.000553162622799151 | 0.00110632524559830 | 0.9994468373772 |
| 24 | 0.000224377589932822 | 0.000448755179865644 | 0.999775622410067 |
| 25 | 5.8722781171827e-05 | 0.000117445562343654 | 0.999941277218828 |
| 26 | 1.58471115452228e-05 | 3.16942230904455e-05 | 0.999984152888455 |
| 27 | 8.42400272603909e-06 | 1.68480054520782e-05 | 0.999991575997274 |
| 28 | 3.23245383325265e-06 | 6.4649076665053e-06 | 0.999996767546167 |
| 29 | 1.51974072916483e-06 | 3.03948145832966e-06 | 0.999998480259271 |
| 30 | 7.67921468425358e-07 | 1.53584293685072e-06 | 0.999999232078532 |
| 31 | 6.8165858847117e-07 | 1.36331717694234e-06 | 0.999999318341412 |
| 32 | 5.42688907420529e-07 | 1.08537781484106e-06 | 0.999999457311093 |
| 33 | 2.41476903059539e-07 | 4.82953806119078e-07 | 0.999999758523097 |
| 34 | 1.11068516516172e-07 | 2.22137033032345e-07 | 0.999999888931484 |
| 35 | 2.68833244954545e-08 | 5.37666489909089e-08 | 0.999999973116676 |
| 36 | 8.20177681400673e-09 | 1.64035536280135e-08 | 0.999999991798223 |
| 37 | 7.44822461663e-09 | 1.489644923326e-08 | 0.999999992551775 |
| 38 | 6.5938855544015e-09 | 1.3187771108803e-08 | 0.999999993406114 |
| 39 | 4.89932015414293e-09 | 9.79864030828586e-09 | 0.99999999510068 |
| 40 | 7.04951851799092e-08 | 1.40990370359818e-07 | 0.999999929504815 |
| 41 | 1.82837706763651e-07 | 3.65675413527302e-07 | 0.999999817162293 |
| 42 | 2.23198220597419e-06 | 4.46396441194839e-06 | 0.999997768017794 |
| 43 | 2.38140371191107e-05 | 4.76280742382214e-05 | 0.99997618596288 |
| 44 | 3.03107815266728e-05 | 6.06215630533456e-05 | 0.999969689218473 |
| 45 | 0.233879724802656 | 0.467759449605312 | 0.766120275197344 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 24 | 0.888888888888889 | NOK |
| 5% type I error level | 25 | 0.925925925925926 | NOK |
| 10% type I error level | 26 | 0.962962962962963 | NOK |
