| Multiple Linear Regression - Estimated Regression Equation |
| Births[t] = + 5632.42646760897 + 233.327295316956x[t] + 0.184925679115300`y-1`[t] + 0.141855719535449`y-2`[t] + 485.518122007314M1[t] + 884.077057591996M2[t] -117.371735721934M3[t] + 921.654299160091M4[t] + 567.78584832305M5[t] + 616.785989141178M6[t] + 611.199861323609M7[t] + 1154.83556367848M8[t] + 916.246498776956M9[t] + 598.938676886247M10[t] + 725.272206498409M11[t] + 4.70384799637204t + 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) | 5632.42646760897 | 1521.695785 | 3.7014 | 0.000485 | 0.000242 |
| x | 233.327295316956 | 122.061409 | 1.9116 | 0.060965 | 0.030483 |
| `y-1` | 0.184925679115300 | 0.130178 | 1.4206 | 0.160892 | 0.080446 |
| `y-2` | 0.141855719535449 | 0.129205 | 1.0979 | 0.276861 | 0.13843 |
| M1 | 485.518122007314 | 176.827297 | 2.7457 | 0.008064 | 0.004032 |
| M2 | 884.077057591996 | 177.463322 | 4.9817 | 6e-06 | 3e-06 |
| M3 | -117.371735721934 | 157.726562 | -0.7441 | 0.459844 | 0.229922 |
| M4 | 921.654299160091 | 196.252407 | 4.6963 | 1.7e-05 | 9e-06 |
| M5 | 567.78584832305 | 191.711759 | 2.9617 | 0.004455 | 0.002228 |
| M6 | 616.785989141178 | 162.79502 | 3.7887 | 0.000367 | 0.000184 |
| M7 | 611.199861323609 | 159.618277 | 3.8291 | 0.000322 | 0.000161 |
| M8 | 1154.83556367848 | 157.843079 | 7.3164 | 0 | 0 |
| M9 | 916.246498776956 | 162.994281 | 5.6213 | 1e-06 | 0 |
| M10 | 598.938676886247 | 161.398589 | 3.7109 | 0.000471 | 0.000235 |
| M11 | 725.272206498409 | 158.07279 | 4.5882 | 2.5e-05 | 1.3e-05 |
| t | 4.70384799637204 | 2.45333 | 1.9173 | 0.060212 | 0.030106 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.882356647284765 |
| R-squared | 0.77855325300761 |
| Adjusted R-squared | 0.720277793272771 |
| F-TEST (value) | 13.3598817847191 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 57 |
| p-value | 1.54876111935209e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 267.664628275107 |
| Sum Squared Residuals | 4083728.13409011 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9084 | 9204.61931413246 | -120.619314132463 |
| 2 | 9743 | 9493.83866949976 | 249.161330500238 |
| 3 | 8587 | 8591.13142039341 | -4.13142039341149 |
| 4 | 9731 | 9592.74211402581 | 138.257885974188 |
| 5 | 9563 | 9192.08636927641 | 370.91363072359 |
| 6 | 9998 | 9433.51357411686 | 564.486425883143 |
| 7 | 9437 | 9463.2710182022 | -26.2710182022101 |
| 8 | 10038 | 10012.4721803092 | 25.5278196907818 |
| 9 | 9918 | 9760.0989448612 | 157.901055138809 |
| 10 | 9252 | 9541.6126177709 | -289.612617770896 |
| 11 | 9737 | 9555.98300467498 | 181.016995325014 |
| 12 | 9035 | 8781.05416785685 | 253.945832143149 |
| 13 | 9133 | 9261.38237711757 | -128.382377117572 |
| 14 | 9487 | 9548.72919447416 | -61.7291944741601 |
| 15 | 8700 | 8620.32389042545 | 79.6761095745493 |
| 16 | 9627 | 9617.87701243627 | 9.12298756373444 |
| 17 | 8947 | 9254.67615214122 | -307.676152141217 |
| 18 | 9283 | 9383.3443562115 | -100.344356211494 |
| 19 | 8829 | 9304.3761363558 | -475.376136355804 |
| 20 | 9947 | 9850.4482182207 | 96.5517817793093 |
| 21 | 9628 | 9691.20143743783 | -63.2014374378281 |
| 22 | 9318 | 9540.09239826259 | -222.092398262588 |
| 23 | 9605 | 9568.16321117735 | 36.8367888226475 |
| 24 | 8640 | 8830.98048365625 | -190.980483656246 |
| 25 | 9214 | 9237.38535421432 | -23.385354214315 |
| 26 | 9567 | 9543.62004046245 | 23.3799595375478 |
| 27 | 8547 | 8703.09750395309 | -156.09750395309 |
| 28 | 9185 | 9667.41331763303 | -482.413317633031 |
| 29 | 9470 | 9220.12847115837 | 249.871528841628 |
| 30 | 9123 | 9432.24392331603 | -309.243923316035 |
| 31 | 9278 | 9434.8415273639 | -156.841527363899 |
| 32 | 10170 | 9940.99950359012 | 229.000496409876 |
| 33 | 9434 | 9862.31306877347 | -428.313068773467 |
| 34 | 9655 | 9610.25699107189 | 44.7430089281129 |
| 35 | 9429 | 9636.5391828689 | -207.539182868895 |
| 36 | 8739 | 8924.78000683633 | -185.780006836327 |
| 37 | 9552 | 9275.3283268805 | 276.671673119504 |
| 38 | 9687 | 9666.32109185431 | 20.6789081456868 |
| 39 | 9019 | 8839.07124579478 | 179.92875420522 |
| 40 | 9672 | 9813.00647470406 | -141.006474704063 |
| 41 | 9206 | 9432.94330307102 | -226.943303071022 |
| 42 | 9069 | 9541.2989950443 | -472.298995044292 |
| 43 | 9788 | 9434.80711517901 | 353.192884820990 |
| 44 | 10312 | 10059.8061098374 | 252.193890162559 |
| 45 | 10105 | 10033.2148532528 | 71.7851467472319 |
| 46 | 9863 | 9788.14780127101 | 74.8521987289898 |
| 47 | 9656 | 9846.5764791751 | -190.576479175099 |
| 48 | 9295 | 9051.89197238332 | 243.108027616679 |
| 49 | 9946 | 9452.62441205784 | 493.375587942157 |
| 50 | 9701 | 9881.47709889585 | -180.477098895851 |
| 51 | 9049 | 8970.36411939617 | 78.6358806038313 |
| 52 | 10190 | 9876.2972817542 | 313.702718245795 |
| 53 | 9706 | 9568.4185121203 | 137.581487879692 |
| 54 | 9765 | 9764.4645325502 | 0.535467449793721 |
| 55 | 9893 | 9682.4477114898 | 210.552288510204 |
| 56 | 9994 | 10259.8554090094 | -265.855409009376 |
| 57 | 10433 | 10297.2954020210 | 135.704597978978 |
| 58 | 10073 | 10065.6435825934 | 7.35641740660755 |
| 59 | 10112 | 10226.7952743008 | -114.795274300782 |
| 60 | 9266 | 9445.18604437912 | -179.186044379119 |
| 61 | 9820 | 9822.61017714131 | -2.61017714131218 |
| 62 | 10097 | 10148.0139048135 | -51.0139048134611 |
| 63 | 9115 | 9293.0118200371 | -178.011820037099 |
| 64 | 10411 | 10248.6637994466 | 162.336200553376 |
| 65 | 9678 | 9901.74719223267 | -223.747192232672 |
| 66 | 10408 | 10091.1346187611 | 316.865381238885 |
| 67 | 10153 | 10058.2564914093 | 94.7435085907183 |
| 68 | 10368 | 10705.4185790332 | -337.418579033151 |
| 69 | 10581 | 10454.8762936537 | 126.123706346277 |
| 70 | 10597 | 10212.2466090302 | 384.753390969774 |
| 71 | 10680 | 10384.9428478029 | 295.057152197114 |
| 72 | 9738 | 9679.10732488813 | 58.8926751118645 |
| 73 | 9556 | 10051.050038456 | -495.050038455999 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.722416958132689 | 0.555166083734622 | 0.277583041867311 |
| 20 | 0.694757275701564 | 0.610485448596872 | 0.305242724298436 |
| 21 | 0.597392911243731 | 0.805214177512537 | 0.402607088756269 |
| 22 | 0.583922238097266 | 0.832155523805467 | 0.416077761902734 |
| 23 | 0.476526460963469 | 0.953052921926939 | 0.523473539036531 |
| 24 | 0.383682946082648 | 0.767365892165295 | 0.616317053917352 |
| 25 | 0.509918947750997 | 0.980162104498006 | 0.490081052249003 |
| 26 | 0.431390823401617 | 0.862781646803233 | 0.568609176598383 |
| 27 | 0.336067772354845 | 0.672135544709689 | 0.663932227645155 |
| 28 | 0.344518556101432 | 0.689037112202865 | 0.655481443898568 |
| 29 | 0.497821783578187 | 0.995643567156373 | 0.502178216421813 |
| 30 | 0.462961157724357 | 0.925922315448714 | 0.537038842275643 |
| 31 | 0.407167522464835 | 0.81433504492967 | 0.592832477535165 |
| 32 | 0.532559660479788 | 0.934880679040424 | 0.467440339520212 |
| 33 | 0.53161246076555 | 0.9367750784689 | 0.46838753923445 |
| 34 | 0.564035048406048 | 0.871929903187904 | 0.435964951593952 |
| 35 | 0.532193176938636 | 0.935613646122728 | 0.467806823061364 |
| 36 | 0.465282394551828 | 0.930564789103656 | 0.534717605448172 |
| 37 | 0.574605858158626 | 0.850788283682748 | 0.425394141841374 |
| 38 | 0.513267448129986 | 0.973465103740027 | 0.486732551870014 |
| 39 | 0.552088545837763 | 0.895822908324474 | 0.447911454162237 |
| 40 | 0.468435732481262 | 0.936871464962524 | 0.531564267518738 |
| 41 | 0.406984218252647 | 0.813968436505293 | 0.593015781747353 |
| 42 | 0.69446502839964 | 0.611069943200721 | 0.305534971600361 |
| 43 | 0.744496965357579 | 0.511006069284842 | 0.255503034642421 |
| 44 | 0.728528443001407 | 0.542943113997186 | 0.271471556998593 |
| 45 | 0.66122487451998 | 0.677550250960039 | 0.338775125480020 |
| 46 | 0.591943590782632 | 0.816112818434737 | 0.408056409217368 |
| 47 | 0.634965879046198 | 0.730068241907604 | 0.365034120953802 |
| 48 | 0.550837340144558 | 0.898325319710884 | 0.449162659855442 |
| 49 | 0.78590511568797 | 0.428189768624061 | 0.214094884312031 |
| 50 | 0.695163037145905 | 0.60967392570819 | 0.304836962854095 |
| 51 | 0.60515170020158 | 0.78969659959684 | 0.39484829979842 |
| 52 | 0.515026900603477 | 0.969946198793046 | 0.484973099396523 |
| 53 | 0.582099673288738 | 0.835800653422524 | 0.417900326711262 |
| 54 | 0.408364486409824 | 0.816728972819649 | 0.591635513590176 |
| 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 |
