| Multiple Linear Regression - Estimated Regression Equation |
| Yt[t] = + 12.2406247261314 + 0.232373289440401Yt_1[t] + 0.334514566579160Yt_2[t] + 0.0190532461610643Yt_3[t] -0.0846729256870996Yt_4[t] -3.48048732019389M1[t] -0.467043484880352M2[t] -4.48331016033904M3[t] -5.27300518640634M4[t] -1.33980579687569M5[t] + 1.53664584963875M6[t] -4.77797385546277M7[t] -10.3001636157727M8[t] + 9.78306552323733M9[t] + 5.88075610040622M10[t] + 4.15159268968920M11[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) | 12.2406247261314 | 4.418009 | 2.7706 | 0.007315 | 0.003658 |
| Yt_1 | 0.232373289440401 | 0.125063 | 1.858 | 0.067763 | 0.033881 |
| Yt_2 | 0.334514566579160 | 0.127477 | 2.6241 | 0.01085 | 0.005425 |
| Yt_3 | 0.0190532461610643 | 0.128115 | 0.1487 | 0.882242 | 0.441121 |
| Yt_4 | -0.0846729256870996 | 0.122991 | -0.6884 | 0.493658 | 0.246829 |
| M1 | -3.48048732019389 | 2.455267 | -1.4176 | 0.16117 | 0.080585 |
| M2 | -0.467043484880352 | 2.331374 | -0.2003 | 0.841858 | 0.420929 |
| M3 | -4.48331016033904 | 2.821579 | -1.5889 | 0.117003 | 0.058502 |
| M4 | -5.27300518640634 | 2.787288 | -1.8918 | 0.063043 | 0.031522 |
| M5 | -1.33980579687569 | 2.629014 | -0.5096 | 0.612069 | 0.306034 |
| M6 | 1.53664584963875 | 2.885375 | 0.5326 | 0.59618 | 0.29809 |
| M7 | -4.77797385546277 | 2.31827 | -2.061 | 0.04337 | 0.021685 |
| M8 | -10.3001636157727 | 2.210753 | -4.6591 | 1.7e-05 | 8e-06 |
| M9 | 9.78306552323733 | 2.840305 | 3.4444 | 0.001015 | 0.000507 |
| M10 | 5.88075610040622 | 3.148711 | 1.8677 | 0.066388 | 0.033194 |
| M11 | 4.15159268968920 | 2.677194 | 1.5507 | 0.125899 | 0.062949 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.95387231448526 |
| R-squared | 0.909872392341468 |
| Adjusted R-squared | 0.8887487342965 |
| F-TEST (value) | 43.0736187077311 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 64 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.89712768075047 |
| Sum Squared Residuals | 230.341979972458 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 22.397 | 22.5291181340573 | -0.132118134057304 |
| 2 | 23.843 | 23.9797145325185 | -0.136714532518468 |
| 3 | 21.705 | 18.7926649080345 | 2.91233509196549 |
| 4 | 18.089 | 18.2034614271835 | -0.114461427183472 |
| 5 | 20.764 | 20.9227250611481 | -0.158725061148055 |
| 6 | 25.316 | 23.0479976933294 | 2.26800230667058 |
| 7 | 17.704 | 18.7981018443605 | -1.09410184436047 |
| 8 | 15.548 | 13.3869416446639 | 2.16105835533607 |
| 9 | 28.029 | 30.2830793911521 | -2.25407939115208 |
| 10 | 29.383 | 28.0293431207762 | 1.35365687922375 |
| 11 | 36.438 | 31.393340961043 | 5.04465903895703 |
| 12 | 32.034 | 29.7544329446216 | 2.27956705537838 |
| 13 | 22.679 | 26.5795692347496 | -3.90056923474957 |
| 14 | 24.319 | 25.9657323064195 | -1.64673230641951 |
| 15 | 18.004 | 18.5198960684792 | -0.515896068479212 |
| 16 | 17.537 | 17.0060240556748 | 0.530975944325163 |
| 17 | 20.366 | 19.5416081745964 | 0.824391825403613 |
| 18 | 22.782 | 22.6600407067113 | 0.121959293288710 |
| 19 | 19.169 | 18.3789882375070 | 0.790011762492963 |
| 20 | 13.807 | 12.9188648649897 | 0.888135135010294 |
| 21 | 29.743 | 30.3540002329261 | -0.611000232926145 |
| 22 | 25.591 | 28.0877152777798 | -2.49671527777984 |
| 23 | 29.096 | 30.9283218769036 | -1.83232187690364 |
| 24 | 26.482 | 26.9599418446233 | -0.477941844623321 |
| 25 | 22.405 | 22.6160474798818 | -0.211047479881822 |
| 26 | 27.044 | 24.2260279523563 | 2.81797204764371 |
| 27 | 17.97 | 19.5773412886701 | -1.60734128867007 |
| 28 | 18.73 | 18.3745590517287 | 0.355440948271281 |
| 29 | 19.684 | 19.8825764910623 | -0.198576491062257 |
| 30 | 19.785 | 22.6692564683751 | -2.88425646837505 |
| 31 | 18.479 | 17.4800359567907 | 0.998964043209319 |
| 32 | 10.698 | 11.6419780250115 | -0.943978025011526 |
| 33 | 31.956 | 29.4013809816902 | 2.55461901830979 |
| 34 | 29.506 | 27.8025695982499 | 1.70343040175006 |
| 35 | 34.506 | 32.5775318173118 | 1.92846818268816 |
| 36 | 27.165 | 29.8321188283689 | -2.66711882836893 |
| 37 | 26.736 | 24.4716945159379 | 2.26430548406211 |
| 38 | 23.691 | 25.2324936755626 | -1.54149367556259 |
| 39 | 18.157 | 19.8019090761916 | -1.64490907619155 |
| 40 | 17.328 | 17.3210735159934 | 0.00692648400657125 |
| 41 | 18.205 | 19.1887393876882 | -0.983739387688245 |
| 42 | 20.995 | 22.1440582278097 | -1.14905822780968 |
| 43 | 17.382 | 17.2239141048217 | 0.158085895178314 |
| 44 | 9.367 | 11.8823588427973 | -2.51535884279729 |
| 45 | 31.124 | 28.8734153388538 | 2.25058466114619 |
| 46 | 26.551 | 27.0406404821986 | -0.489640482198587 |
| 47 | 30.651 | 31.6800789564600 | -1.02907895645996 |
| 48 | 25.859 | 28.0446766166183 | -2.18567661661829 |
| 49 | 25.1 | 22.8928068775318 | 2.20719312246822 |
| 50 | 25.778 | 24.5922131815402 | 1.18578681845981 |
| 51 | 20.418 | 20.0411368893676 | 0.37686311063242 |
| 52 | 18.688 | 18.6240131540967 | 0.0639868459032659 |
| 53 | 20.424 | 20.4393935275249 | -0.0153935275249063 |
| 54 | 24.776 | 22.9810013612868 | 1.79499863871322 |
| 55 | 19.814 | 18.6792722652355 | 1.13472773476449 |
| 56 | 12.738 | 13.6394142332491 | -0.901414233249097 |
| 57 | 31.566 | 30.3544362251132 | 1.21156377488677 |
| 58 | 30.111 | 27.9971872427104 | 2.11381275728962 |
| 59 | 30.019 | 32.5134872428337 | -2.4944872428337 |
| 60 | 31.934 | 28.8116776570257 | 3.12232234297426 |
| 61 | 25.826 | 24.1234655279839 | 1.70253447201612 |
| 62 | 26.835 | 26.4796149146225 | 0.355385085377546 |
| 63 | 20.205 | 20.6988747911053 | -0.493874791105269 |
| 64 | 17.789 | 18.4275441734839 | -0.638544173483901 |
| 65 | 20.52 | 20.1179050747800 | 0.402094925219965 |
| 66 | 22.518 | 22.6090229778348 | -0.0910229778348198 |
| 67 | 15.572 | 18.1875932409432 | -2.61559324094324 |
| 68 | 11.509 | 11.9763029199313 | -0.467302919931338 |
| 69 | 25.447 | 28.5986878302645 | -3.15168783026453 |
| 70 | 24.09 | 26.274544278285 | -2.18454427828501 |
| 71 | 27.786 | 29.4032391454479 | -1.61723914544789 |
| 72 | 26.195 | 26.2661521087421 | -0.0711521087420993 |
| 73 | 20.516 | 22.4462982298578 | -1.93029822985775 |
| 74 | 22.759 | 23.7932034369805 | -1.03420343698049 |
| 75 | 19.028 | 18.0551769781518 | 0.972823021848202 |
| 76 | 16.971 | 17.1753246218389 | -0.204324621838907 |
| 77 | 20.036 | 19.9060522832001 | 0.129947716799886 |
| 78 | 22.485 | 22.5456225646530 | -0.0606225646529591 |
| 79 | 18.73 | 18.1020943503414 | 0.627905649658635 |
| 80 | 14.538 | 12.7591394693571 | 1.77886053064289 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.226322577501374 | 0.452645155002748 | 0.773677422498626 |
| 20 | 0.129298694921823 | 0.258597389843646 | 0.870701305078177 |
| 21 | 0.0667439956478228 | 0.133487991295646 | 0.933256004352177 |
| 22 | 0.231607612706371 | 0.463215225412743 | 0.768392387293629 |
| 23 | 0.936268425493576 | 0.127463149012848 | 0.0637315745064242 |
| 24 | 0.935894537775867 | 0.128210924448267 | 0.0641054622241335 |
| 25 | 0.900788131901932 | 0.198423736196136 | 0.0992118680980679 |
| 26 | 0.903938348609652 | 0.192123302780697 | 0.0960616513903484 |
| 27 | 0.925876396490294 | 0.148247207019413 | 0.0741236035097064 |
| 28 | 0.891971144562952 | 0.216057710874096 | 0.108028855437048 |
| 29 | 0.84322645553593 | 0.313547088928139 | 0.156773544464069 |
| 30 | 0.90679418920081 | 0.186411621598379 | 0.0932058107991896 |
| 31 | 0.872440447955312 | 0.255119104089376 | 0.127559552044688 |
| 32 | 0.8734749667193 | 0.253050066561399 | 0.126525033280700 |
| 33 | 0.880109598900876 | 0.239780802198248 | 0.119890401099124 |
| 34 | 0.855610948182793 | 0.288778103634415 | 0.144389051817207 |
| 35 | 0.858292855474146 | 0.283414289051707 | 0.141707144525854 |
| 36 | 0.905782705144926 | 0.188434589710148 | 0.094217294855074 |
| 37 | 0.931499473942995 | 0.137001052114010 | 0.0685005260570049 |
| 38 | 0.916189235301504 | 0.167621529396991 | 0.0838107646984957 |
| 39 | 0.906531774746914 | 0.186936450506171 | 0.0934682252530857 |
| 40 | 0.86698331842097 | 0.26603336315806 | 0.13301668157903 |
| 41 | 0.825549553295642 | 0.348900893408716 | 0.174450446704358 |
| 42 | 0.795876249412093 | 0.408247501175815 | 0.204123750587907 |
| 43 | 0.740681186733195 | 0.51863762653361 | 0.259318813266805 |
| 44 | 0.780934235694429 | 0.438131528611142 | 0.219065764305571 |
| 45 | 0.825622646773748 | 0.348754706452504 | 0.174377353226252 |
| 46 | 0.769374448567189 | 0.461251102865623 | 0.230625551432812 |
| 47 | 0.761062216002066 | 0.477875567995868 | 0.238937783997934 |
| 48 | 0.87149518536399 | 0.257009629272020 | 0.128504814636010 |
| 49 | 0.93115822400943 | 0.137683551981141 | 0.0688417759905703 |
| 50 | 0.896021615954446 | 0.207956768091107 | 0.103978384045554 |
| 51 | 0.870180832597439 | 0.259638334805123 | 0.129819167402561 |
| 52 | 0.83475805026639 | 0.330483899467222 | 0.165241949733611 |
| 53 | 0.766706200337978 | 0.466587599324043 | 0.233293799662022 |
| 54 | 0.764987182174378 | 0.470025635651244 | 0.235012817825622 |
| 55 | 0.688956826714916 | 0.622086346570167 | 0.311043173285084 |
| 56 | 0.644080708681889 | 0.711838582636222 | 0.355919291318111 |
| 57 | 0.784814738968301 | 0.430370522063398 | 0.215185261031699 |
| 58 | 0.694528819058535 | 0.610942361882931 | 0.305471180941465 |
| 59 | 0.634137134603605 | 0.73172573079279 | 0.365862865396395 |
| 60 | 0.846879610578524 | 0.306240778842952 | 0.153120389421476 |
| 61 | 0.721648454381738 | 0.556703091236524 | 0.278351545618262 |
| 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 | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
