| Multiple Linear Regression - Estimated Regression Equation |
| births[t] = + 9.10405454545455 + 0.276662121212123M1[t] -0.550166666666666M2[t] + 0.348186363636364M3[t] + 0.0224484848484851M4[t] + 0.200074242424243M5[t] + 0.116881818181818M6[t] + 0.712507575757576M7[t] + 0.523860606060606M8[t] + 0.317940909090909M9[t] + 0.348748484848485M10[t] -0.389534848484848M11[t] + 0.0085560606060606t + 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) | 9.10405454545455 | 0.105876 | 85.9878 | 0 | 0 |
| M1 | 0.276662121212123 | 0.131553 | 2.1031 | 0.037568 | 0.018784 |
| M2 | -0.550166666666666 | 0.131513 | -4.1834 | 5.5e-05 | 2.8e-05 |
| M3 | 0.348186363636364 | 0.131477 | 2.6483 | 0.009188 | 0.004594 |
| M4 | 0.0224484848484851 | 0.131445 | 0.1708 | 0.864685 | 0.432342 |
| M5 | 0.200074242424243 | 0.131416 | 1.5224 | 0.13055 | 0.065275 |
| M6 | 0.116881818181818 | 0.131391 | 0.8896 | 0.375492 | 0.187746 |
| M7 | 0.712507575757576 | 0.131371 | 5.4236 | 0 | 0 |
| M8 | 0.523860606060606 | 0.131353 | 3.9882 | 0.000115 | 5.8e-05 |
| M9 | 0.317940909090909 | 0.13134 | 2.4207 | 0.017 | 0.0085 |
| M10 | 0.348748484848485 | 0.131331 | 2.6555 | 0.009004 | 0.004502 |
| M11 | -0.389534848484848 | 0.131325 | -2.9662 | 0.003645 | 0.001822 |
| t | 0.0085560606060606 | 0.000706 | 12.1121 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.850782901773075 |
| R-squared | 0.723831545949414 |
| Adjusted R-squared | 0.69598262621322 |
| F-TEST (value) | 25.9913688863376 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 119 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.307979959265853 |
| Sum Squared Residuals | 11.2873469818182 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9.492 | 9.38927272727271 | 0.102727272727289 |
| 2 | 8.641 | 8.571 | 0.07 |
| 3 | 9.793 | 9.4779090909091 | 0.315090909090909 |
| 4 | 9.603 | 9.16072727272727 | 0.442272727272727 |
| 5 | 9.238 | 9.3469090909091 | -0.108909090909092 |
| 6 | 9.535 | 9.27227272727273 | 0.262727272727272 |
| 7 | 10.295 | 9.87645454545455 | 0.418545454545454 |
| 8 | 9.941 | 9.69636363636364 | 0.244636363636364 |
| 9 | 9.984 | 9.499 | 0.485 |
| 10 | 9.563 | 9.53836363636364 | 0.0246363636363633 |
| 11 | 8.872 | 8.80863636363636 | 0.0633636363636357 |
| 12 | 9.302 | 9.20672727272727 | 0.095272727272727 |
| 13 | 9.215 | 9.49194545454546 | -0.276945454545456 |
| 14 | 8.834 | 8.67367272727273 | 0.160327272727272 |
| 15 | 9.998 | 9.58058181818182 | 0.417418181818181 |
| 16 | 9.604 | 9.2634 | 0.340599999999999 |
| 17 | 9.507 | 9.44958181818182 | 0.0574181818181812 |
| 18 | 9.718 | 9.37494545454545 | 0.343054545454545 |
| 19 | 10.095 | 9.97912727272727 | 0.115872727272727 |
| 20 | 9.583 | 9.79903636363636 | -0.216036363636364 |
| 21 | 9.883 | 9.60167272727273 | 0.281327272727272 |
| 22 | 9.365 | 9.64103636363636 | -0.276036363636364 |
| 23 | 8.919 | 8.9113090909091 | 0.00769090909090921 |
| 24 | 9.449 | 9.3094 | 0.1396 |
| 25 | 9.769 | 9.59461818181818 | 0.174381818181816 |
| 26 | 9.321 | 8.77634545454545 | 0.544654545454545 |
| 27 | 9.939 | 9.68325454545455 | 0.255745454545455 |
| 28 | 9.336 | 9.36607272727273 | -0.0300727272727273 |
| 29 | 10.195 | 9.55225454545455 | 0.642745454545455 |
| 30 | 9.464 | 9.47761818181818 | -0.0136181818181818 |
| 31 | 10.01 | 10.0818 | -0.0718000000000007 |
| 32 | 10.213 | 9.9017090909091 | 0.311290909090908 |
| 33 | 9.563 | 9.70434545454546 | -0.141345454545454 |
| 34 | 9.89 | 9.7437090909091 | 0.146290909090909 |
| 35 | 9.305 | 9.01398181818182 | 0.291018181818181 |
| 36 | 9.391 | 9.41207272727273 | -0.0210727272727273 |
| 37 | 9.928 | 9.69729090909091 | 0.23070909090909 |
| 38 | 8.686 | 8.87901818181818 | -0.193018181818182 |
| 39 | 9.843 | 9.78592727272727 | 0.0570727272727273 |
| 40 | 9.627 | 9.46874545454546 | 0.158254545454546 |
| 41 | 10.074 | 9.65492727272727 | 0.419072727272727 |
| 42 | 9.503 | 9.5802909090909 | -0.0772909090909092 |
| 43 | 10.119 | 10.1844727272727 | -0.065472727272728 |
| 44 | 10 | 10.0043818181818 | -0.00438181818181833 |
| 45 | 9.313 | 9.80701818181818 | -0.494018181818182 |
| 46 | 9.866 | 9.84638181818182 | 0.0196181818181811 |
| 47 | 9.172 | 9.11665454545455 | 0.0553454545454549 |
| 48 | 9.241 | 9.51474545454546 | -0.273745454545455 |
| 49 | 9.659 | 9.79996363636364 | -0.140963636363638 |
| 50 | 8.904 | 8.98169090909091 | -0.0776909090909093 |
| 51 | 9.755 | 9.8886 | -0.133599999999999 |
| 52 | 9.08 | 9.57141818181818 | -0.491418181818182 |
| 53 | 9.435 | 9.7576 | -0.3226 |
| 54 | 8.971 | 9.68296363636364 | -0.711963636363637 |
| 55 | 10.063 | 10.2871454545455 | -0.224145454545454 |
| 56 | 9.793 | 10.1070545454545 | -0.314054545454546 |
| 57 | 9.454 | 9.9096909090909 | -0.455690909090909 |
| 58 | 9.759 | 9.94905454545455 | -0.190054545454545 |
| 59 | 8.82 | 9.21932727272727 | -0.399327272727273 |
| 60 | 9.403 | 9.61741818181818 | -0.214418181818181 |
| 61 | 9.676 | 9.90263636363636 | -0.226636363636365 |
| 62 | 8.642 | 9.08436363636364 | -0.442363636363637 |
| 63 | 9.402 | 9.99127272727273 | -0.589272727272728 |
| 64 | 9.61 | 9.6740909090909 | -0.0640909090909098 |
| 65 | 9.294 | 9.86027272727273 | -0.566272727272727 |
| 66 | 9.448 | 9.78563636363636 | -0.337636363636363 |
| 67 | 10.319 | 10.3898181818182 | -0.0708181818181813 |
| 68 | 9.548 | 10.2097272727273 | -0.661727272727273 |
| 69 | 9.801 | 10.0123636363636 | -0.211363636363636 |
| 70 | 9.596 | 10.0517272727273 | -0.455727272727273 |
| 71 | 8.923 | 9.322 | -0.399 |
| 72 | 9.746 | 9.7200909090909 | 0.0259090909090916 |
| 73 | 9.829 | 10.0053090909091 | -0.176309090909092 |
| 74 | 9.125 | 9.18703636363636 | -0.0620363636363637 |
| 75 | 9.782 | 10.0939454545455 | -0.311945454545454 |
| 76 | 9.441 | 9.77676363636364 | -0.335763636363636 |
| 77 | 9.162 | 9.96294545454545 | -0.800945454545454 |
| 78 | 9.915 | 9.8883090909091 | 0.0266909090909082 |
| 79 | 10.444 | 10.4924909090909 | -0.0484909090909085 |
| 80 | 10.209 | 10.3124 | -0.1034 |
| 81 | 9.985 | 10.1150363636364 | -0.130036363636364 |
| 82 | 9.842 | 10.1544 | -0.3124 |
| 83 | 9.429 | 9.42467272727273 | 0.00432727272727288 |
| 84 | 10.132 | 9.82276363636364 | 0.309236363636364 |
| 85 | 9.849 | 10.1079818181818 | -0.25898181818182 |
| 86 | 9.172 | 9.2897090909091 | -0.11770909090909 |
| 87 | 10.313 | 10.1966181818182 | 0.116381818181819 |
| 88 | 9.819 | 9.87943636363636 | -0.0604363636363628 |
| 89 | 9.955 | 10.0656181818182 | -0.110618181818182 |
| 90 | 10.048 | 9.99098181818182 | 0.057018181818182 |
| 91 | 10.082 | 10.5951636363636 | -0.513163636363636 |
| 92 | 10.541 | 10.4150727272727 | 0.125927272727273 |
| 93 | 10.208 | 10.2177090909091 | -0.00970909090909067 |
| 94 | 10.233 | 10.2570727272727 | -0.0240727272727269 |
| 95 | 9.439 | 9.52734545454545 | -0.0883454545454544 |
| 96 | 9.963 | 9.92543636363636 | 0.0375636363636361 |
| 97 | 10.158 | 10.2106545454545 | -0.0526545454545477 |
| 98 | 9.225 | 9.39238181818182 | -0.167381818181818 |
| 99 | 10.474 | 10.2992909090909 | 0.174709090909091 |
| 100 | 9.757 | 9.9821090909091 | -0.225109090909091 |
| 101 | 10.49 | 10.1682909090909 | 0.321709090909091 |
| 102 | 10.281 | 10.0936545454545 | 0.187345454545455 |
| 103 | 10.444 | 10.6978363636364 | -0.253836363636363 |
| 104 | 10.64 | 10.5177454545455 | 0.122254545454546 |
| 105 | 10.695 | 10.3203818181818 | 0.374618181818182 |
| 106 | 10.786 | 10.3597454545455 | 0.426254545454545 |
| 107 | 9.832 | 9.63001818181818 | 0.201981818181819 |
| 108 | 9.747 | 10.0281090909091 | -0.281109090909091 |
| 109 | 10.411 | 10.3133272727273 | 0.0976727272727253 |
| 110 | 9.511 | 9.49505454545455 | 0.0159454545454541 |
| 111 | 10.402 | 10.4019636363636 | 3.63636363631989e-05 |
| 112 | 9.701 | 10.0847818181818 | -0.383781818181818 |
| 113 | 10.54 | 10.2709636363636 | 0.269036363636363 |
| 114 | 10.112 | 10.1963272727273 | -0.0843272727272724 |
| 115 | 10.915 | 10.8005090909091 | 0.114490909090908 |
| 116 | 11.183 | 10.6204181818182 | 0.562581818181818 |
| 117 | 10.384 | 10.4230545454545 | -0.0390545454545449 |
| 118 | 10.834 | 10.4624181818182 | 0.371581818181818 |
| 119 | 9.886 | 9.7326909090909 | 0.15330909090909 |
| 120 | 10.216 | 10.1307818181818 | 0.0852181818181816 |
| 121 | 10.943 | 10.416 | 0.526999999999998 |
| 122 | 9.867 | 9.59772727272727 | 0.269272727272729 |
| 123 | 10.203 | 10.5046363636364 | -0.301636363636364 |
| 124 | 10.837 | 10.1874545454545 | 0.649545454545455 |
| 125 | 10.573 | 10.3736363636364 | 0.199363636363637 |
| 126 | 10.647 | 10.299 | 0.348 |
| 127 | 11.502 | 10.9031818181818 | 0.598818181818182 |
| 128 | 10.656 | 10.7230909090909 | -0.0670909090909082 |
| 129 | 10.866 | 10.5257272727273 | 0.340272727272727 |
| 130 | 10.835 | 10.5650909090909 | 0.269909090909092 |
| 131 | 9.945 | 9.83536363636364 | 0.109636363636364 |
| 132 | 10.331 | 10.2334545454545 | 0.0975454545454547 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.156676645497202 | 0.313353290994404 | 0.843323354502798 |
| 17 | 0.100697552141253 | 0.201395104282505 | 0.899302447858747 |
| 18 | 0.0495253452945626 | 0.0990506905891253 | 0.950474654705437 |
| 19 | 0.0442492829809967 | 0.0884985659619934 | 0.955750717019003 |
| 20 | 0.0622567225310003 | 0.124513445062001 | 0.937743277469 |
| 21 | 0.03594002112934 | 0.07188004225868 | 0.96405997887066 |
| 22 | 0.0225212851030354 | 0.0450425702060708 | 0.977478714896965 |
| 23 | 0.0113296774089064 | 0.0226593548178129 | 0.988670322591094 |
| 24 | 0.00681365027686757 | 0.0136273005537351 | 0.993186349723132 |
| 25 | 0.0142752155964171 | 0.0285504311928342 | 0.985724784403583 |
| 26 | 0.0450189985131115 | 0.090037997026223 | 0.954981001486888 |
| 27 | 0.0330817112641076 | 0.0661634225282152 | 0.966918288735892 |
| 28 | 0.0457415369084917 | 0.0914830738169834 | 0.954258463091508 |
| 29 | 0.231794567068901 | 0.463589134137801 | 0.7682054329311 |
| 30 | 0.22974341790273 | 0.459486835805461 | 0.77025658209727 |
| 31 | 0.221770433107823 | 0.443540866215646 | 0.778229566892177 |
| 32 | 0.248877211609892 | 0.497754423219784 | 0.751122788390108 |
| 33 | 0.309090321726492 | 0.618180643452985 | 0.690909678273508 |
| 34 | 0.312500926631107 | 0.625001853262213 | 0.687499073368893 |
| 35 | 0.335837411445403 | 0.671674822890806 | 0.664162588554597 |
| 36 | 0.292651548886418 | 0.585303097772837 | 0.707348451113582 |
| 37 | 0.303141035339055 | 0.60628207067811 | 0.696858964660945 |
| 38 | 0.343472853313923 | 0.686945706627845 | 0.656527146686077 |
| 39 | 0.34537510170185 | 0.6907502034037 | 0.65462489829815 |
| 40 | 0.344248412594851 | 0.688496825189703 | 0.655751587405149 |
| 41 | 0.482659226196651 | 0.965318452393301 | 0.517340773803349 |
| 42 | 0.472725011822998 | 0.945450023645995 | 0.527274988177002 |
| 43 | 0.450715603605454 | 0.901431207210909 | 0.549284396394546 |
| 44 | 0.430164536758305 | 0.86032907351661 | 0.569835463241695 |
| 45 | 0.568116377796404 | 0.863767244407192 | 0.431883622203596 |
| 46 | 0.558014630193247 | 0.883970739613506 | 0.441985369806753 |
| 47 | 0.567644321616599 | 0.864711356766803 | 0.432355678383401 |
| 48 | 0.5407051335766 | 0.9185897328468 | 0.4592948664234 |
| 49 | 0.498090366703193 | 0.996180733406386 | 0.501909633296807 |
| 50 | 0.481827387331946 | 0.963654774663892 | 0.518172612668054 |
| 51 | 0.499223926545227 | 0.998447853090454 | 0.500776073454773 |
| 52 | 0.58382239582702 | 0.83235520834596 | 0.41617760417298 |
| 53 | 0.597009416853396 | 0.805981166293209 | 0.402990583146604 |
| 54 | 0.727632511988237 | 0.544734976023527 | 0.272367488011763 |
| 55 | 0.689659602855703 | 0.620680794288593 | 0.310340397144297 |
| 56 | 0.646633053479356 | 0.706733893041288 | 0.353366946520644 |
| 57 | 0.617262276451206 | 0.765475447097588 | 0.382737723548794 |
| 58 | 0.574042784815571 | 0.851914430368858 | 0.425957215184429 |
| 59 | 0.539225785959103 | 0.921548428081794 | 0.460774214040897 |
| 60 | 0.491384675188915 | 0.98276935037783 | 0.508615324811085 |
| 61 | 0.441300929493542 | 0.882601858987085 | 0.558699070506458 |
| 62 | 0.407416957946416 | 0.814833915892832 | 0.592583042053584 |
| 63 | 0.435149929361336 | 0.870299858722672 | 0.564850070638664 |
| 64 | 0.435580033760543 | 0.871160067521085 | 0.564419966239457 |
| 65 | 0.440497374613695 | 0.88099474922739 | 0.559502625386305 |
| 66 | 0.393403177891744 | 0.786806355783488 | 0.606596822108256 |
| 67 | 0.389980685303625 | 0.77996137060725 | 0.610019314696375 |
| 68 | 0.447645129511962 | 0.895290259023923 | 0.552354870488038 |
| 69 | 0.410188824082478 | 0.820377648164957 | 0.589811175917522 |
| 70 | 0.390454519078599 | 0.780909038157198 | 0.609545480921401 |
| 71 | 0.351381869710418 | 0.702763739420835 | 0.648618130289582 |
| 72 | 0.388318433116821 | 0.776636866233643 | 0.611681566883179 |
| 73 | 0.355577459655062 | 0.711154919310124 | 0.644422540344938 |
| 74 | 0.34797540352052 | 0.69595080704104 | 0.65202459647948 |
| 75 | 0.298800935155574 | 0.597601870311149 | 0.701199064844426 |
| 76 | 0.253977048602945 | 0.50795409720589 | 0.746022951397055 |
| 77 | 0.465778168549357 | 0.931556337098714 | 0.534221831450643 |
| 78 | 0.493007409616285 | 0.98601481923257 | 0.506992590383715 |
| 79 | 0.479842516408572 | 0.959685032817143 | 0.520157483591428 |
| 80 | 0.46209108719623 | 0.92418217439246 | 0.53790891280377 |
| 81 | 0.433478126072693 | 0.866956252145386 | 0.566521873927307 |
| 82 | 0.441408833959692 | 0.882817667919385 | 0.558591166040308 |
| 83 | 0.431743376041698 | 0.863486752083397 | 0.568256623958302 |
| 84 | 0.626926035924274 | 0.746147928151453 | 0.373073964075726 |
| 85 | 0.603646480737472 | 0.792707038525056 | 0.396353519262528 |
| 86 | 0.556717423243633 | 0.886565153512735 | 0.443282576756367 |
| 87 | 0.601710616152461 | 0.796578767695078 | 0.398289383847539 |
| 88 | 0.564922193072998 | 0.870155613854004 | 0.435077806927002 |
| 89 | 0.534940418865783 | 0.930119162268434 | 0.465059581134217 |
| 90 | 0.517348687568969 | 0.965302624862061 | 0.482651312431031 |
| 91 | 0.577278145725378 | 0.845443708549245 | 0.422721854274622 |
| 92 | 0.571930132914616 | 0.856139734170768 | 0.428069867085384 |
| 93 | 0.533020174364054 | 0.933959651271893 | 0.466979825635946 |
| 94 | 0.516904772037554 | 0.966190455924891 | 0.483095227962446 |
| 95 | 0.462919285787942 | 0.925838571575884 | 0.537080714212058 |
| 96 | 0.439589396746901 | 0.879178793493802 | 0.560410603253099 |
| 97 | 0.412217391900495 | 0.82443478380099 | 0.587782608099505 |
| 98 | 0.365199242120543 | 0.730398484241086 | 0.634800757879457 |
| 99 | 0.420995954918623 | 0.841991909837247 | 0.579004045081377 |
| 100 | 0.376660665571593 | 0.753321331143186 | 0.623339334428407 |
| 101 | 0.394067290830468 | 0.788134581660937 | 0.605932709169532 |
| 102 | 0.373485437370238 | 0.746970874740475 | 0.626514562629762 |
| 103 | 0.413012109894134 | 0.826024219788268 | 0.586987890105866 |
| 104 | 0.358777156241606 | 0.717554312483212 | 0.641222843758394 |
| 105 | 0.401290579839932 | 0.802581159679864 | 0.598709420160068 |
| 106 | 0.42551325381099 | 0.85102650762198 | 0.57448674618901 |
| 107 | 0.410724684434461 | 0.821449368868921 | 0.58927531556554 |
| 108 | 0.336589164918416 | 0.673178329836832 | 0.663410835081584 |
| 109 | 0.2958837322842 | 0.591767464568401 | 0.7041162677158 |
| 110 | 0.227204263675699 | 0.454408527351399 | 0.7727957363243 |
| 111 | 0.219498230066637 | 0.438996460133274 | 0.780501769933363 |
| 112 | 0.562121120561287 | 0.875757758877426 | 0.437878879438713 |
| 113 | 0.470022398376397 | 0.940044796752794 | 0.529977601623603 |
| 114 | 0.447327767079472 | 0.894655534158944 | 0.552672232920528 |
| 115 | 0.530259213732642 | 0.939481572534715 | 0.469740786267358 |
| 116 | 0.844664735896515 | 0.310670528206969 | 0.155335264103485 |
| 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 | 4 | 0.0396039603960396 | OK |
| 10% type I error level | 10 | 0.099009900990099 | OK |
