| Multiple Linear Regression - Estimated Regression Equation |
| Monthly_births[t] = + 9394.56324695302 -401.305821796236Dummy[t] + 92.0419582635944M1[t] -657.549905336646M2[t] -316.284626079755M3[t] -6.62558530689533M4[t] -901.574591764287M5[t] + 47.4764017783186M6[t] -344.305938012408M7[t] -182.421611136468M8[t] -244.537284260528M9[t] + 380.064679581452M10[t] + 240.949006457393M11[t] + 17.4490064573931t + 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) | 9394.56324695302 | 126.030594 | 74.5419 | 0 | 0 |
| Dummy | -401.305821796236 | 110.821847 | -3.6212 | 0.000598 | 0.000299 |
| M1 | 92.0419582635944 | 149.134046 | 0.6172 | 0.539416 | 0.269708 |
| M2 | -657.549905336646 | 149.133792 | -4.4091 | 4.3e-05 | 2.1e-05 |
| M3 | -316.284626079755 | 149.168548 | -2.1203 | 0.038054 | 0.019027 |
| M4 | -6.62558530689533 | 155.004069 | -0.0427 | 0.966045 | 0.483022 |
| M5 | -901.574591764287 | 154.963297 | -5.818 | 0 | 0 |
| M6 | 47.4764017783186 | 154.956216 | 0.3064 | 0.760354 | 0.380177 |
| M7 | -344.305938012408 | 154.98283 | -2.2216 | 0.030033 | 0.015016 |
| M8 | -182.421611136468 | 155.043122 | -1.1766 | 0.243932 | 0.121966 |
| M9 | -244.537284260528 | 155.137054 | -1.5763 | 0.120137 | 0.060068 |
| M10 | 380.064679581452 | 154.587541 | 2.4586 | 0.016803 | 0.008401 |
| M11 | 240.949006457393 | 154.536865 | 1.5592 | 0.12413 | 0.062065 |
| t | 17.4490064573931 | 2.285108 | 7.636 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.87560757853449 |
| R-squared | 0.766688631587034 |
| Adjusted R-squared | 0.716966536679353 |
| F-TEST (value) | 15.4194756478089 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 61 |
| p-value | 1.13242748511766e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 267.636437453185 |
| Sum Squared Residuals | 4369385.02181058 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9504.05421167407 | 195.945788325931 |
| 2 | 9081 | 8771.91135453116 | 309.08864546884 |
| 3 | 9084 | 9130.62564024545 | -46.6256402454448 |
| 4 | 9743 | 9457.7336874757 | 285.266312524301 |
| 5 | 8587 | 8580.2336874757 | 6.76631252430321 |
| 6 | 9731 | 9546.7336874757 | 184.266312524302 |
| 7 | 9563 | 9172.40035414237 | 390.599645857634 |
| 8 | 9998 | 9351.7336874757 | 646.266312524301 |
| 9 | 9437 | 9307.06702080903 | 129.932979190968 |
| 10 | 10038 | 9949.1179911084 | 88.8820088915959 |
| 11 | 9918 | 9827.45132444174 | 90.5486755582625 |
| 12 | 9252 | 9603.95132444174 | -351.951324441737 |
| 13 | 9737 | 9713.44228916273 | 23.5577108372739 |
| 14 | 9035 | 8981.29943201988 | 53.7005679801232 |
| 15 | 9133 | 9340.01371773416 | -207.013717734163 |
| 16 | 9487 | 9667.12176496441 | -180.121764964415 |
| 17 | 8700 | 8789.62176496441 | -89.6217649644153 |
| 18 | 9627 | 9756.12176496441 | -129.121764964415 |
| 19 | 8947 | 9381.78843163108 | -434.788431631081 |
| 20 | 9283 | 9561.12176496441 | -278.121764964415 |
| 21 | 8829 | 9516.45509829775 | -687.455098297748 |
| 22 | 9947 | 9757.20024680088 | 189.799753199114 |
| 23 | 9628 | 9635.53358013422 | -7.5335801342187 |
| 24 | 9318 | 9412.03358013422 | -94.0335801342194 |
| 25 | 9605 | 9521.52454485521 | 83.4754551447925 |
| 26 | 8640 | 8789.38168771236 | -149.381687712359 |
| 27 | 9214 | 9148.09597342665 | 65.9040265733554 |
| 28 | 9567 | 9475.2040206569 | 91.7959793431038 |
| 29 | 8547 | 8597.7040206569 | -50.7040206568965 |
| 30 | 9185 | 9564.2040206569 | -379.204020656896 |
| 31 | 9470 | 9189.87068732356 | 280.129312676437 |
| 32 | 9123 | 9369.2040206569 | -246.204020656896 |
| 33 | 9278 | 9324.53735399023 | -46.5373539902296 |
| 34 | 10170 | 9966.5883242896 | 203.411675710398 |
| 35 | 9434 | 9844.92165762294 | -410.921657622936 |
| 36 | 9655 | 9621.42165762294 | 33.5783423770639 |
| 37 | 9429 | 9730.91262234392 | -301.912622343924 |
| 38 | 8739 | 8998.76976520108 | -259.769765201076 |
| 39 | 9552 | 9357.48405091536 | 194.515949084639 |
| 40 | 9687 | 9684.59209814561 | 2.4079018543869 |
| 41 | 9019 | 8807.09209814561 | 211.907901854387 |
| 42 | 9672 | 9773.59209814561 | -101.592098145613 |
| 43 | 9206 | 9399.25876481228 | -193.258764812280 |
| 44 | 9069 | 9578.59209814561 | -509.592098145613 |
| 45 | 9788 | 9533.92543147895 | 254.074568521054 |
| 46 | 10312 | 10175.9764017783 | 136.023598221681 |
| 47 | 10105 | 10054.3097351117 | 50.6902648883475 |
| 48 | 9863 | 9830.80973511165 | 32.1902648883470 |
| 49 | 9656 | 9940.30069983264 | -284.300699832641 |
| 50 | 9295 | 9208.15784268979 | 86.8421573102074 |
| 51 | 9946 | 9566.87212840408 | 379.127871595922 |
| 52 | 9701 | 9893.98017563433 | -192.98017563433 |
| 53 | 9049 | 9016.48017563433 | 32.5198243656698 |
| 54 | 10190 | 9982.98017563433 | 207.01982436567 |
| 55 | 9706 | 9608.646842301 | 97.3531576990037 |
| 56 | 9765 | 9787.98017563433 | -22.9801756343301 |
| 57 | 9893 | 9743.31350896766 | 149.686491032337 |
| 58 | 9994 | 10385.3644792670 | -391.364479267036 |
| 59 | 10433 | 10263.6978126004 | 169.302187399631 |
| 60 | 10073 | 10040.1978126004 | 32.8021873996302 |
| 61 | 10112 | 10149.6887773214 | -37.688777321358 |
| 62 | 9266 | 9417.54592017851 | -151.545920178510 |
| 63 | 9820 | 9776.2602058928 | 43.7397941072049 |
| 64 | 10097 | 10103.3682531230 | -6.3682531230469 |
| 65 | 9115 | 9225.86825312305 | -110.868253123047 |
| 66 | 10411 | 10192.3682531230 | 218.631746876953 |
| 67 | 9678 | 9818.03491978971 | -140.034919789713 |
| 68 | 10408 | 9997.36825312305 | 410.631746876953 |
| 69 | 10153 | 9952.70158645638 | 200.29841354362 |
| 70 | 10368 | 10594.7525567558 | -226.752556755753 |
| 71 | 10581 | 10473.0858900891 | 107.914109910914 |
| 72 | 10597 | 10249.5858900891 | 347.414109910913 |
| 73 | 10680 | 10359.0768548101 | 320.923145189925 |
| 74 | 9738 | 9626.93399766723 | 111.066002332773 |
| 75 | 9556 | 9985.6482833815 | -429.648283381512 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.129209909522889 | 0.258419819045779 | 0.87079009047711 |
| 18 | 0.0583942985274169 | 0.116788597054834 | 0.941605701472583 |
| 19 | 0.332065864761555 | 0.664131729523111 | 0.667934135238444 |
| 20 | 0.576658759657813 | 0.846682480684375 | 0.423341240342187 |
| 21 | 0.585466042836542 | 0.829067914326916 | 0.414533957163458 |
| 22 | 0.495827054900449 | 0.991654109800898 | 0.504172945099551 |
| 23 | 0.403413001326875 | 0.806826002653749 | 0.596586998673125 |
| 24 | 0.339189162554008 | 0.678378325108016 | 0.660810837445992 |
| 25 | 0.269892135266888 | 0.539784270533777 | 0.730107864733112 |
| 26 | 0.223539919608508 | 0.447079839217016 | 0.776460080391492 |
| 27 | 0.227440585234970 | 0.454881170469940 | 0.77255941476503 |
| 28 | 0.180967320316690 | 0.361934640633381 | 0.81903267968331 |
| 29 | 0.126873690985811 | 0.253747381971622 | 0.873126309014189 |
| 30 | 0.159052039345535 | 0.318104078691069 | 0.840947960654465 |
| 31 | 0.22873113355383 | 0.45746226710766 | 0.77126886644617 |
| 32 | 0.238599414276501 | 0.477198828553003 | 0.761400585723499 |
| 33 | 0.232763097370446 | 0.465526194740893 | 0.767236902629554 |
| 34 | 0.322942415992655 | 0.64588483198531 | 0.677057584007345 |
| 35 | 0.327878318261676 | 0.655756636523352 | 0.672121681738324 |
| 36 | 0.420042841961298 | 0.840085683922595 | 0.579957158038702 |
| 37 | 0.364928393115911 | 0.729856786231822 | 0.635071606884089 |
| 38 | 0.313325698883186 | 0.626651397766371 | 0.686674301116814 |
| 39 | 0.441972124585552 | 0.883944249171105 | 0.558027875414448 |
| 40 | 0.394719008492181 | 0.789438016984363 | 0.605280991507819 |
| 41 | 0.472993520307928 | 0.945987040615856 | 0.527006479692072 |
| 42 | 0.439107578786023 | 0.878215157572046 | 0.560892421213977 |
| 43 | 0.364289202644912 | 0.728578405289825 | 0.635710797355088 |
| 44 | 0.580624930878698 | 0.838750138242604 | 0.419375069121302 |
| 45 | 0.645052858207686 | 0.709894283584628 | 0.354947141792314 |
| 46 | 0.717192793982526 | 0.565614412034949 | 0.282807206017474 |
| 47 | 0.6800808106739 | 0.6398383786522 | 0.3199191893261 |
| 48 | 0.638735097269915 | 0.722529805460171 | 0.361264902730085 |
| 49 | 0.681520047837735 | 0.63695990432453 | 0.318479952162265 |
| 50 | 0.615305744602649 | 0.769388510794702 | 0.384694255397351 |
| 51 | 0.860701252467385 | 0.278597495065230 | 0.139298747532615 |
| 52 | 0.798793871375885 | 0.402412257248231 | 0.201206128624115 |
| 53 | 0.744562475998056 | 0.510875048003888 | 0.255437524001944 |
| 54 | 0.672021418829337 | 0.655957162341326 | 0.327978581170663 |
| 55 | 0.658005964511227 | 0.683988070977546 | 0.341994035488773 |
| 56 | 0.627994162987721 | 0.744011674024557 | 0.372005837012279 |
| 57 | 0.490539842942782 | 0.981079685885564 | 0.509460157057218 |
| 58 | 0.353562935020145 | 0.70712587004029 | 0.646437064979855 |
| 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 |
