| Multiple Linear Regression - Estimated Regression Equation |
| MontlyBirths[t] = + 3873.05299620334 + 0.124837319271829Y1[t] + 0.164886202883664Y2[t] + 0.243791599857208Y3[t] + 0.061698643855855Y4[t] -777.007128192618M1[t] + 184.930867387297M2[t] -260.922022455930M3[t] -1.62807770930776M4[t] -194.014625014349M5[t] + 383.21533040592M6[t] + 170.916446059259M7[t] -137.978095175717M8[t] -156.218164109860M9[t] -891.354225854479M10[t] -335.846833482281M11[t] + 5.57076871659979t + 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) | 3873.05299620334 | 1593.649766 | 2.4303 | 0.018439 | 0.00922 |
| Y1 | 0.124837319271829 | 0.143538 | 0.8697 | 0.388305 | 0.194152 |
| Y2 | 0.164886202883664 | 0.136356 | 1.2092 | 0.231842 | 0.115921 |
| Y3 | 0.243791599857208 | 0.136973 | 1.7798 | 0.080728 | 0.040364 |
| Y4 | 0.061698643855855 | 0.145435 | 0.4242 | 0.673079 | 0.336539 |
| M1 | -777.007128192618 | 209.213307 | -3.7139 | 0.000485 | 0.000242 |
| M2 | 184.930867387297 | 235.63751 | 0.7848 | 0.435994 | 0.217997 |
| M3 | -260.922022455930 | 173.883914 | -1.5006 | 0.139296 | 0.069648 |
| M4 | -1.62807770930776 | 239.647222 | -0.0068 | 0.994605 | 0.497302 |
| M5 | -194.014625014349 | 219.030577 | -0.8858 | 0.37966 | 0.18983 |
| M6 | 383.21533040592 | 190.328241 | 2.0134 | 0.049063 | 0.024532 |
| M7 | 170.916446059259 | 207.856546 | 0.8223 | 0.414533 | 0.207267 |
| M8 | -137.978095175717 | 234.700635 | -0.5879 | 0.559057 | 0.279528 |
| M9 | -156.218164109860 | 214.477531 | -0.7284 | 0.469536 | 0.234768 |
| M10 | -891.354225854479 | 190.692187 | -4.6743 | 2e-05 | 1e-05 |
| M11 | -335.846833482281 | 219.28128 | -1.5316 | 0.131464 | 0.065732 |
| t | 5.57076871659979 | 2.540908 | 2.1924 | 0.032678 | 0.016339 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.88379075383939 |
| R-squared | 0.781086096571998 |
| Adjusted R-squared | 0.716222717778516 |
| F-TEST (value) | 12.0420198747107 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 54 |
| p-value | 1.57818202950466e-12 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 271.206316240123 |
| Sum Squared Residuals | 3971854.76230103 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8587 | 8628.08126909303 | -41.0812690930296 |
| 2 | 9731 | 9522.47801426446 | 208.521985735539 |
| 3 | 9563 | 9195.24509608876 | 367.754903911242 |
| 4 | 9998 | 9386.6032728793 | 611.396727120699 |
| 5 | 9437 | 9433.96480402893 | 3.03519597107351 |
| 6 | 10038 | 10048.0835501038 | -10.0835501037805 |
| 7 | 9918 | 9919.56547730846 | -1.56547730845515 |
| 8 | 9252 | 9590.42965696794 | -338.429656967944 |
| 9 | 9737 | 9586.73817008037 | 150.261829919629 |
| 10 | 9035 | 8815.73065875317 | 219.269341246828 |
| 11 | 9133 | 9199.37378734412 | -66.3737873441204 |
| 12 | 9487 | 9514.42296153005 | -27.4229615300546 |
| 13 | 8700 | 8662.1200001292 | 37.8799998708072 |
| 14 | 9627 | 9570.3306387788 | 56.6693612212096 |
| 15 | 8947 | 9208.35596439503 | -261.355964395031 |
| 16 | 9283 | 9371.15814166392 | -88.1581416639158 |
| 17 | 8829 | 9291.60306474299 | -462.603064742991 |
| 18 | 9947 | 9764.54576505084 | 182.454234949163 |
| 19 | 9628 | 9662.48633598754 | -34.4863359875382 |
| 20 | 9318 | 9413.73159144578 | -95.7315914457795 |
| 21 | 9605 | 9554.31184786388 | 50.6881521361191 |
| 22 | 8640 | 8800.66970604934 | -160.669706049338 |
| 23 | 9214 | 9193.34493092268 | 20.6550690773211 |
| 24 | 9567 | 9498.14557816456 | 68.8544218354422 |
| 25 | 8547 | 8647.87008977114 | -100.870089771143 |
| 26 | 9185 | 9626.64680502546 | -441.646805025463 |
| 27 | 9470 | 9219.30042297578 | 250.699577024220 |
| 28 | 9123 | 9398.05335929802 | -275.053359298016 |
| 29 | 9278 | 9307.51802272002 | -29.5180227200205 |
| 30 | 10170 | 9961.29735968273 | 208.702640317269 |
| 31 | 9434 | 9824.46992263858 | -390.469922638577 |
| 32 | 9655 | 9592.72264466825 | 62.277355331751 |
| 33 | 9429 | 9713.3115435577 | -284.311543557690 |
| 34 | 8739 | 8867.57744003605 | -128.577440036045 |
| 35 | 9552 | 9313.7213106661 | 238.278689333894 |
| 36 | 9687 | 9601.39867216767 | 85.6013278323292 |
| 37 | 9019 | 8798.70773632487 | 220.292263675128 |
| 38 | 9672 | 9860.71531516047 | -188.715315160469 |
| 39 | 9206 | 9474.8808434276 | -268.880843427592 |
| 40 | 9069 | 9634.7185848091 | -565.7185848091 |
| 41 | 9788 | 9471.94434354768 | 316.055656452324 |
| 42 | 10312 | 10048.5960193503 | 263.403980649657 |
| 43 | 10105 | 9963.6848216748 | 141.315178325191 |
| 44 | 9863 | 9887.75354046728 | -24.7535404672839 |
| 45 | 9656 | 9982.85028824658 | -326.850288246577 |
| 46 | 9295 | 9169.40643724147 | 125.593562758532 |
| 47 | 9946 | 9579.51769563261 | 366.48230436739 |
| 48 | 9701 | 9877.2845404529 | -176.284540452890 |
| 49 | 9049 | 9081.82356900593 | -32.8235690059256 |
| 50 | 10190 | 10063.9764025058 | 126.023597494212 |
| 51 | 9706 | 9639.06473357331 | 66.9352664266856 |
| 52 | 9765 | 9857.57505114765 | -92.5750511476481 |
| 53 | 9893 | 9836.2584518436 | 56.7415481563922 |
| 54 | 9994 | 10397.1696571260 | -403.169657126049 |
| 55 | 10433 | 10208.6771054769 | 224.322894523107 |
| 56 | 10073 | 10011.6559673793 | 61.3440326206819 |
| 57 | 10112 | 10058.9506532890 | 53.0493467110276 |
| 58 | 9266 | 9388.1510580412 | -122.151058041191 |
| 59 | 9820 | 9789.3681376426 | 30.6318623573906 |
| 60 | 10097 | 10047.7482476848 | 49.2517523151726 |
| 61 | 9115 | 9198.39733567584 | -83.3973356758363 |
| 62 | 10411 | 10171.8528242650 | 239.147175734971 |
| 63 | 9678 | 9833.15293953952 | -155.152939539525 |
| 64 | 10408 | 9997.89159020202 | 410.108409797981 |
| 65 | 10153 | 10036.7113131168 | 116.288686883222 |
| 66 | 10368 | 10609.3076486863 | -241.30764868626 |
| 67 | 10581 | 10520.1163369137 | 60.883663086272 |
| 68 | 10597 | 10261.7065990714 | 335.293400928575 |
| 69 | 10680 | 10322.8374969625 | 357.162503037491 |
| 70 | 9738 | 9671.46469987878 | 66.5353001212155 |
| 71 | 9556 | 10145.6741377919 | -589.674137791875 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.833340761229101 | 0.333318477541798 | 0.166659238770899 |
| 21 | 0.726781058746 | 0.546437882507999 | 0.273218941254000 |
| 22 | 0.627578872527312 | 0.744842254945377 | 0.372421127472688 |
| 23 | 0.654168596707194 | 0.691662806585613 | 0.345831403292806 |
| 24 | 0.622606621870514 | 0.754786756258972 | 0.377393378129486 |
| 25 | 0.545221904467923 | 0.909556191064154 | 0.454778095532077 |
| 26 | 0.502840871755862 | 0.994318256488276 | 0.497159128244138 |
| 27 | 0.729201928198364 | 0.541596143603272 | 0.270798071801636 |
| 28 | 0.690055144068788 | 0.619889711862425 | 0.309944855931212 |
| 29 | 0.632182711768666 | 0.735634576462669 | 0.367817288231334 |
| 30 | 0.800990961641634 | 0.398018076716731 | 0.199009038358366 |
| 31 | 0.784536011742289 | 0.430927976515422 | 0.215463988257711 |
| 32 | 0.773204549526251 | 0.453590900947498 | 0.226795450473749 |
| 33 | 0.70707883591435 | 0.585842328171301 | 0.292921164085650 |
| 34 | 0.703058280876658 | 0.593883438246684 | 0.296941719123342 |
| 35 | 0.701482337227175 | 0.59703532554565 | 0.298517662772825 |
| 36 | 0.684558439295633 | 0.630883121408733 | 0.315441560704367 |
| 37 | 0.678045717784136 | 0.643908564431727 | 0.321954282215864 |
| 38 | 0.59700549907631 | 0.805989001847379 | 0.402994500923690 |
| 39 | 0.518059220163218 | 0.963881559673563 | 0.481940779836782 |
| 40 | 0.7352854894399 | 0.5294290211202 | 0.2647145105601 |
| 41 | 0.818262772849163 | 0.363474454301673 | 0.181737227150837 |
| 42 | 0.807858594729152 | 0.384282810541696 | 0.192141405270848 |
| 43 | 0.794064815488617 | 0.411870369022767 | 0.205935184511383 |
| 44 | 0.751217668895695 | 0.497564662208611 | 0.248782331104305 |
| 45 | 0.690320390660296 | 0.619359218679409 | 0.309679609339704 |
| 46 | 0.606908280419936 | 0.786183439160128 | 0.393091719580064 |
| 47 | 0.839260333677683 | 0.321479332644634 | 0.160739666322317 |
| 48 | 0.74941961119965 | 0.5011607776007 | 0.25058038880035 |
| 49 | 0.924069118314058 | 0.151861763371884 | 0.0759308816859418 |
| 50 | 0.849205886449405 | 0.301588227101189 | 0.150794113550595 |
| 51 | 0.751897709602831 | 0.496204580794338 | 0.248102290397169 |
| 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 |
