| Multiple Linear Regression - Estimated Regression Equation |
| Births[t] = + 3513.15322119259 + 1.81853714940414e-07`Y-1`[t] + 0.375914107327586`Y-2`[t] + 0.238512132682298`Y-3`[t] + 0.0192032651388202`Y-4`[t] -455.243573208415M1[t] -340.490770887514M2[t] -1.15456343944968M3[t] -131.707497084488M4[t] -175.963277570170M5[t] + 308.85928331459M6[t] + 125.997921695407M7[t] -124.082645567172M8[t] -162.455132647671M9[t] -554.306360664536M10[t] -649.343791013937M11[t] + 5.95960793016406t + 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) | 3513.15322119259 | 1973.915859 | 1.7798 | 0.080738 | 0.040369 |
| `Y-1` | 1.81853714940414e-07 | 0 | 0.4529 | 0.652454 | 0.326227 |
| `Y-2` | 0.375914107327586 | 0.13056 | 2.8792 | 0.005703 | 0.002851 |
| `Y-3` | 0.238512132682298 | 0.130548 | 1.827 | 0.073228 | 0.036614 |
| `Y-4` | 0.0192032651388202 | 0.113252 | 0.1696 | 0.865988 | 0.432994 |
| M1 | -455.243573208415 | 238.441023 | -1.9093 | 0.061549 | 0.030775 |
| M2 | -340.490770887514 | 234.199356 | -1.4539 | 0.151775 | 0.075888 |
| M3 | -1.15456343944968 | 221.399277 | -0.0052 | 0.995858 | 0.497929 |
| M4 | -131.707497084488 | 239.726328 | -0.5494 | 0.584991 | 0.292495 |
| M5 | -175.963277570170 | 227.913236 | -0.7721 | 0.443443 | 0.221722 |
| M6 | 308.85928331459 | 230.077465 | 1.3424 | 0.185078 | 0.092539 |
| M7 | 125.997921695407 | 227.773926 | 0.5532 | 0.582429 | 0.291215 |
| M8 | -124.082645567172 | 255.842326 | -0.485 | 0.629641 | 0.31482 |
| M9 | -162.455132647671 | 238.882886 | -0.6801 | 0.499371 | 0.249685 |
| M10 | -554.306360664536 | 241.348727 | -2.2967 | 0.025541 | 0.01277 |
| M11 | -649.343791013937 | 233.390116 | -2.7822 | 0.007422 | 0.003711 |
| t | 5.95960793016406 | 3.114315 | 1.9136 | 0.060976 | 0.030488 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.783419237471422 |
| R-squared | 0.613745701640305 |
| Adjusted R-squared | 0.499299983607802 |
| F-TEST (value) | 5.36276683996165 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 54 |
| p-value | 1.45945058027674e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 360.796934403332 |
| Sum Squared Residuals | 7029419.10524147 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8587 | 8830.87512741333 | -243.875127413334 |
| 2 | 9731 | 9188.14343944753 | 542.856560552469 |
| 3 | 9563 | 9256.11986002877 | 306.88013997123 |
| 4 | 9998 | 9298.50716889098 | 699.492831109024 |
| 5 | 9437 | 9447.71641069886 | -10.7164106988626 |
| 6 | 10038 | 10083.9196112095 | -45.9196112095373 |
| 7 | 9918 | 9796.6567817773 | 121.343218222697 |
| 8 | 9252 | 9653.00829302694 | -401.008293026938 |
| 9 | 9737 | 9708.0583598819 | 28.9416401180976 |
| 10 | 9035 | 9054.72773894064 | -19.7277389406363 |
| 11 | 9133 | 8986.8146587309 | 146.185341269097 |
| 12 | 9487 | 9481.11538192116 | 5.88461807883782 |
| 13 | 8700 | 8910.54912998658 | -210.549129986584 |
| 14 | 9627 | 9174.22848798815 | 452.771512011846 |
| 15 | 8947 | 9309.9952844311 | -362.995284431105 |
| 16 | 9283 | 9352.96311998655 | -69.9631199865498 |
| 17 | 8829 | 9265.03319288336 | -436.03319288336 |
| 18 | 9947 | 9737.7355957585 | 209.264404241509 |
| 19 | 9628 | 9457.25089694206 | 170.749103057944 |
| 20 | 9318 | 9531.56964043943 | -213.569640439427 |
| 21 | 9605 | 9637.17838664272 | -32.1783866427248 |
| 22 | 8640 | 9080.13732557604 | -440.137325576037 |
| 23 | 9214 | 9018.88207376019 | 195.117926239815 |
| 24 | 9567 | 9373.92843340398 | 193.071566596016 |
| 25 | 8547 | 8915.76635898255 | -368.766358982553 |
| 26 | 9185 | 9287.55107693014 | -102.551076930144 |
| 27 | 9470 | 9344.63207588344 | 125.367924116561 |
| 28 | 9123 | 9223.36837972993 | -100.368379729933 |
| 29 | 9278 | 9424.79107486925 | -146.791074869247 |
| 30 | 10170 | 9865.35871760185 | 304.641282398153 |
| 31 | 9434 | 9669.43303328592 | -235.433033285924 |
| 32 | 9655 | 9790.93317140797 | -135.933171407967 |
| 33 | 9429 | 9697.57687790333 | -268.576877903327 |
| 34 | 8739 | 9236.34661728674 | -497.346617286739 |
| 35 | 9552 | 9100.88965931302 | 451.110340686979 |
| 36 | 9687 | 9447.15265165764 | 239.847348342362 |
| 37 | 9019 | 9134.5735707148 | -115.573570714807 |
| 38 | 9672 | 9486.69437490174 | 185.305625098264 |
| 39 | 9206 | 9628.69107780558 | -422.691077805584 |
| 40 | 9069 | 9592.83591559376 | -523.835915593758 |
| 41 | 9788 | 9522.28438563844 | 265.715614361565 |
| 42 | 10312 | 9862.959530808 | 449.040469192 |
| 43 | 10105 | 9914.7152318467 | 190.284768153303 |
| 44 | 9863 | 9862.99892077404 | 0.00107922596195564 |
| 45 | 9863 | 10008.3596619558 | -145.359661955810 |
| 46 | 9656 | 9682.1354607746 | -26.1354607745962 |
| 47 | 9295 | 9448.00957531412 | -153.009575314117 |
| 48 | 9946 | 9955.25822341259 | -9.25822341259005 |
| 49 | 9701 | 9342.808297834 | 358.191702165993 |
| 50 | 9049 | 9612.84348717567 | -563.843487175672 |
| 51 | 10190 | 10022.4446187094 | 167.555381290614 |
| 52 | 9706 | 9596.77804794262 | 109.221952057380 |
| 53 | 9765 | 9833.82940310084 | -68.8294031008421 |
| 54 | 9893 | 10423.2417314850 | -530.241731485028 |
| 55 | 9994 | 10146.1658857374 | -152.165885737405 |
| 56 | 10433 | 9964.98309367881 | 468.016906321184 |
| 57 | 10073 | 9984.82120987824 | 88.1787901217598 |
| 58 | 10112 | 9798.68415172883 | 313.315848271169 |
| 59 | 9266 | 9684.30338845494 | -418.303388454939 |
| 60 | 9820 | 10249.5453096046 | -429.545309604625 |
| 61 | 10097 | 9516.42751506872 | 580.572484931285 |
| 62 | 9115 | 9629.53913355676 | -514.539133556763 |
| 63 | 10411 | 10225.1170831417 | 185.882916858284 |
| 64 | 9678 | 9792.54736785616 | -114.547367856164 |
| 65 | 10408 | 10011.3455328093 | 396.654467190746 |
| 66 | 10153 | 10539.7848131371 | -386.784813137097 |
| 67 | 10368 | 10462.7781704106 | -94.7781704106148 |
| 68 | 10581 | 10298.5068806728 | 282.493119327186 |
| 69 | 10597 | 10268.005503738 | 328.994496262004 |
| 70 | 10680 | 10009.9687056932 | 670.03129430684 |
| 71 | 9738 | 9959.10064442684 | -221.100644426835 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.516404362281381 | 0.967191275437238 | 0.483595637718619 |
| 21 | 0.348518062193177 | 0.697036124386355 | 0.651481937806823 |
| 22 | 0.246522463015029 | 0.493044926030057 | 0.753477536984971 |
| 23 | 0.254161905457367 | 0.508323810914735 | 0.745838094542633 |
| 24 | 0.195653038840779 | 0.391306077681559 | 0.80434696115922 |
| 25 | 0.146017441332907 | 0.292034882665814 | 0.853982558667093 |
| 26 | 0.115424067643550 | 0.230848135287099 | 0.88457593235645 |
| 27 | 0.190291640100442 | 0.380583280200884 | 0.809708359899558 |
| 28 | 0.157997288628736 | 0.315994577257473 | 0.842002711371264 |
| 29 | 0.122833455836040 | 0.245666911672079 | 0.87716654416396 |
| 30 | 0.186985931174429 | 0.373971862348859 | 0.81301406882557 |
| 31 | 0.142060002264449 | 0.284120004528899 | 0.85793999773555 |
| 32 | 0.133697084364649 | 0.267394168729298 | 0.866302915635351 |
| 33 | 0.0918751229125984 | 0.183750245825197 | 0.908124877087402 |
| 34 | 0.129175992507754 | 0.258351985015509 | 0.870824007492246 |
| 35 | 0.183561831610821 | 0.367123663221642 | 0.81643816838918 |
| 36 | 0.186801589744421 | 0.373603179488841 | 0.81319841025558 |
| 37 | 0.245531502637144 | 0.491063005274288 | 0.754468497362856 |
| 38 | 0.559818886158455 | 0.880362227683091 | 0.440181113841545 |
| 39 | 0.892938210821239 | 0.214123578357523 | 0.107061789178761 |
| 40 | 0.899311497827786 | 0.201377004344429 | 0.100688502172214 |
| 41 | 0.946330006881184 | 0.107339986237631 | 0.0536699931188156 |
| 42 | 0.941887914443547 | 0.116224171112906 | 0.0581120855564532 |
| 43 | 0.924794791108786 | 0.150410417782427 | 0.0752052088912137 |
| 44 | 0.884339728480172 | 0.231320543039655 | 0.115660271519828 |
| 45 | 0.819437294003603 | 0.361125411992795 | 0.180562705996397 |
| 46 | 0.802816993643211 | 0.394366012713577 | 0.197183006356789 |
| 47 | 0.768804411944524 | 0.462391176110952 | 0.231195588055476 |
| 48 | 0.885573040460596 | 0.228853919078808 | 0.114426959539404 |
| 49 | 0.840817597072849 | 0.318364805854303 | 0.159182402927151 |
| 50 | 0.804528204537375 | 0.390943590925251 | 0.195471795462625 |
| 51 | 0.738377750905351 | 0.523244498189298 | 0.261622249094649 |
| 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 |
