| Multiple Linear Regression - Estimated Regression Equation |
| births[t] = + 9490.9744697614 + 0.0169475520578264marriages[t] + 112.608867133597M1[t] -617.071094776177M2[t] + 299.958719086564M3[t] -56.3202608524251M4[t] + 112.035020095399M5[t] + 54.79846687321M6[t] + 596.171664979584M7[t] + 341.269535167487M8[t] + 157.120642050651M9[t] + 205.505306775077M10[t] -497.358074526631M11[t] + 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) | 9490.9744697614 | 164.836973 | 57.5779 | 0 | 0 |
| marriages | 0.0169475520578264 | 0.059211 | 0.2862 | 0.775205 | 0.387602 |
| M1 | 112.608867133597 | 135.132206 | 0.8333 | 0.406332 | 0.203166 |
| M2 | -617.071094776177 | 126.504551 | -4.8779 | 3e-06 | 2e-06 |
| M3 | 299.958719086564 | 126.809947 | 2.3654 | 0.019626 | 0.009813 |
| M4 | -56.3202608524251 | 142.274214 | -0.3959 | 0.692919 | 0.34646 |
| M5 | 112.035020095399 | 200.305955 | 0.5593 | 0.576995 | 0.288497 |
| M6 | 54.79846687321 | 222.076279 | 0.2468 | 0.805523 | 0.402761 |
| M7 | 596.171664979584 | 231.812537 | 2.5718 | 0.011348 | 0.005674 |
| M8 | 341.269535167487 | 257.068363 | 1.3275 | 0.18687 | 0.093435 |
| M9 | 157.120642050651 | 226.395705 | 0.694 | 0.489029 | 0.244515 |
| M10 | 205.505306775077 | 137.242705 | 1.4974 | 0.136941 | 0.06847 |
| M11 | -497.358074526631 | 128.196817 | -3.8796 | 0.000172 | 8.6e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.769552131893597 |
| R-squared | 0.59221048370198 |
| Adjusted R-squared | 0.551088851806381 |
| F-TEST (value) | 14.4014343887302 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 119 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 296.084211333431 |
| Sum Squared Residuals | 10432237.3639118 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9506 | 9633.66524179767 | -127.665241797667 |
| 2 | 8704 | 8911.13714685626 | -207.137146856263 |
| 3 | 10079 | 9840.42004085681 | 238.579959143186 |
| 4 | 8993 | 9506.51182963416 | -513.511829634157 |
| 5 | 9957 | 9694.78048424993 | 262.219515750072 |
| 6 | 10240 | 9649.76311606143 | 590.23688393857 |
| 7 | 10098 | 10201.0167370175 | -103.016737017518 |
| 8 | 10090 | 9937.89504445737 | 152.104955542625 |
| 9 | 9867 | 9769.30400412962 | 97.6959958703767 |
| 10 | 9736 | 9758.2705513393 | -22.2705513393106 |
| 11 | 9040 | 9030.30784543996 | 9.69215456003966 |
| 12 | 9232 | 9538.47845817948 | -306.478458179485 |
| 13 | 9520 | 9630.95363346839 | -110.953633468384 |
| 14 | 9217 | 8913.73012232111 | 303.269877678888 |
| 15 | 9868 | 9847.70748824168 | 20.2925117583198 |
| 16 | 9455 | 9494.58075298545 | -39.5807529854470 |
| 17 | 9984 | 9701.88150856216 | 282.118491437843 |
| 18 | 9556 | 9660.45702140992 | -104.457021409920 |
| 19 | 10190 | 10188.7128142235 | 1.28718577646445 |
| 20 | 9906 | 9955.55439370163 | -49.5543937016304 |
| 21 | 9824 | 9743.69625297025 | 80.3037470297523 |
| 22 | 9972 | 9755.40641504154 | 216.593584958462 |
| 23 | 9185 | 9031.6975447087 | 153.302455291298 |
| 24 | 9765 | 9532.767133136 | 232.232866864002 |
| 25 | 9838 | 9630.14015096961 | 207.859849030391 |
| 26 | 9084 | 8911.81504893858 | 172.184951061422 |
| 27 | 9643 | 9834.9629290942 | -191.962929094195 |
| 28 | 10051 | 9497.8516305326 | 553.148369467393 |
| 29 | 9987 | 9699.86474986727 | 287.135250132725 |
| 30 | 9827 | 9643.66199732061 | 183.338002679387 |
| 31 | 10491 | 10186.3232093834 | 304.676790616618 |
| 32 | 9722 | 9948.80926798261 | -226.809267982615 |
| 33 | 9472 | 9741.1032775054 | -269.103277505400 |
| 34 | 9728 | 9757.20285555967 | -29.2028555596671 |
| 35 | 8510 | 9028.42666716154 | -518.426667161541 |
| 36 | 9511 | 9529.64878355736 | -18.6487835573578 |
| 37 | 9492 | 9629.88593768874 | -137.885937688742 |
| 38 | 8638 | 8912.22179018796 | -274.221790187966 |
| 39 | 9792 | 9832.3869011814 | -40.386901181405 |
| 40 | 9605 | 9494.29264460046 | 110.707355399536 |
| 41 | 9237 | 9690.47580602724 | -453.475806027239 |
| 42 | 9533 | 9631.95123884865 | -98.9512388486553 |
| 43 | 10293 | 10183.9336045432 | 109.066395456772 |
| 44 | 9938 | 9934.89532774314 | 3.10467225686013 |
| 45 | 9984 | 9736.62912376213 | 247.370876237866 |
| 46 | 9563 | 9753.47439410694 | -190.474394106945 |
| 47 | 8871 | 9025.79979659258 | -154.799796592579 |
| 48 | 9301 | 9526.8185423637 | -225.818542363701 |
| 49 | 9215 | 9628.85213701321 | -413.852137013215 |
| 50 | 8834 | 8908.8322797764 | -74.8322797764004 |
| 51 | 9998 | 9831.92931727584 | 166.070682724156 |
| 52 | 9604 | 9492.78431246732 | 111.215687532683 |
| 53 | 9507 | 9683.9848935891 | -176.984893589092 |
| 54 | 9718 | 9628.17193473976 | 89.82806526024 |
| 55 | 10095 | 10191.8142162501 | -96.8142162501177 |
| 56 | 9583 | 9928.23493978441 | -345.234939784414 |
| 57 | 9883 | 9741.79812713977 | 141.201872860229 |
| 58 | 9365 | 9754.40650947013 | -389.406509470126 |
| 59 | 8919 | 9026.511593779 | -107.511593779007 |
| 60 | 9449 | 9531.6824898043 | -82.682489804297 |
| 61 | 9769 | 9630.3435215943 | 138.656478405697 |
| 62 | 9321 | 8910.27282170132 | 410.727178298684 |
| 63 | 9939 | 9832.65806201433 | 106.341937985670 |
| 64 | 9336 | 9497.27541376264 | -161.275413762642 |
| 65 | 10195 | 9684.88311384816 | 510.116886151843 |
| 66 | 9464 | 9632.78166889949 | -168.781668899489 |
| 67 | 10010 | 10193.0683351024 | -183.068335102397 |
| 68 | 10213 | 9929.86190478196 | 283.138095218035 |
| 69 | 9563 | 9754.0003646214 | -191.000364621406 |
| 70 | 9890 | 9745.91578588915 | 144.084214110845 |
| 71 | 9305 | 9023.12208336744 | 281.877916632558 |
| 72 | 9391 | 9530.9537450658 | -139.953745065811 |
| 73 | 9743 | 9629.19108805437 | 113.808911945629 |
| 74 | 8587 | 8908.79838467229 | -321.798384672285 |
| 75 | 9731 | 9835.58998852033 | -104.589988520334 |
| 76 | 9563 | 9483.24284065876 | 79.757159341239 |
| 77 | 9998 | 9677.6295615674 | 320.370438432593 |
| 78 | 9437 | 9642.71293440538 | -205.712934405375 |
| 79 | 10038 | 10163.4440141053 | -125.444014105316 |
| 80 | 9918 | 9929.67548170933 | -11.6754817093293 |
| 81 | 9252 | 9743.45898724144 | -491.458987241438 |
| 82 | 9737 | 9744.71250969305 | -7.71250969304891 |
| 83 | 9035 | 9023.47798196066 | 11.5220180393436 |
| 84 | 9133 | 9532.14007370986 | -399.140073709858 |
| 85 | 9487 | 9623.3950252506 | -136.395025250594 |
| 86 | 8700 | 8910.40840211778 | -210.408402117778 |
| 87 | 9627 | 9829.04823342601 | -202.048233426013 |
| 88 | 8947 | 9480.19228128835 | -533.192281288352 |
| 89 | 9283 | 9676.88386927686 | -393.883869276862 |
| 90 | 8829 | 9636.98466180983 | -807.98466180983 |
| 91 | 9947 | 10162.7152693668 | -215.715269366830 |
| 92 | 9628 | 9940.67444299486 | -312.674442994859 |
| 93 | 9318 | 9725.98606106982 | -407.986061069819 |
| 94 | 9605 | 9747.72917395934 | -142.729173959342 |
| 95 | 8640 | 9025.59642596789 | -385.596425967885 |
| 96 | 9214 | 9526.0559025211 | -312.055902521099 |
| 97 | 9676 | 9626.47947972512 | 49.5205202748811 |
| 98 | 8642 | 8911.49304544948 | -269.493045449479 |
| 99 | 9402 | 9832.64111446227 | -430.641114462272 |
| 100 | 9610 | 9485.97139654007 | 124.028603459929 |
| 101 | 9294 | 9684.08657890144 | -390.086578901439 |
| 102 | 9448 | 9630.0870081223 | -182.087008122294 |
| 103 | 10319 | 10165.2235070714 | 153.776492928612 |
| 104 | 9548 | 9938.14925773824 | -390.149257738243 |
| 105 | 9801 | 9729.59588965814 | 71.4041103418639 |
| 106 | 9596 | 9749.98319838303 | -153.983198383033 |
| 107 | 8923 | 9025.98621966521 | -102.986219665215 |
| 108 | 9746 | 9528.73361574624 | 217.266384253765 |
| 109 | 9829 | 9630.59773487517 | 198.402265124829 |
| 110 | 9125 | 8915.71298591188 | 209.287014088122 |
| 111 | 9782 | 9828.59064952045 | -46.5906495204520 |
| 112 | 9441 | 9495.78402918155 | -54.7840291815526 |
| 113 | 9162 | 9682.40877124771 | -520.408771247714 |
| 114 | 9915 | 9629.86668994554 | 285.133310054457 |
| 115 | 10444 | 10184.9335101146 | 259.06648988536 |
| 116 | 10209 | 9925.11659020577 | 283.883409794226 |
| 117 | 9985 | 9732.83287210118 | 252.167127898819 |
| 118 | 9842 | 9751.18647457914 | 90.8135254208613 |
| 119 | 9429 | 9027.39286648601 | 401.607133513986 |
| 120 | 10132 | 9529.7504688697 | 602.249531130295 |
| 121 | 9849 | 9630.49604956282 | 218.503950437176 |
| 122 | 9172 | 8909.57797206695 | 262.422027933055 |
| 123 | 10313 | 9828.06527540666 | 484.934724593341 |
| 124 | 9819 | 9495.51286834863 | 323.487131651373 |
| 125 | 9955 | 9682.12066286273 | 272.879337137269 |
| 126 | 10048 | 9628.5617284371 | 419.43827156291 |
| 127 | 10082 | 10185.8147828216 | -103.814782821647 |
| 128 | 10541 | 9927.13334890066 | 613.866651099344 |
| 129 | 10208 | 9738.59503980084 | 469.404960199158 |
| 130 | 10233 | 9748.7121319787 | 484.287868021304 |
| 131 | 9439 | 9027.680974871 | 411.319025129003 |
| 132 | 9963 | 9529.97078704646 | 433.029212953544 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.428469295891054 | 0.856938591782108 | 0.571530704108946 |
| 17 | 0.308047364164632 | 0.616094728329265 | 0.691952635835368 |
| 18 | 0.301746860802684 | 0.603493721605368 | 0.698253139197316 |
| 19 | 0.245131066918463 | 0.490262133836925 | 0.754868933081537 |
| 20 | 0.183815924959726 | 0.367631849919452 | 0.816184075040274 |
| 21 | 0.203624955362842 | 0.407249910725683 | 0.796375044637158 |
| 22 | 0.153090018936832 | 0.306180037873663 | 0.846909981063168 |
| 23 | 0.107458438249777 | 0.214916876499555 | 0.892541561750223 |
| 24 | 0.133776066622502 | 0.267552133245003 | 0.866223933377498 |
| 25 | 0.123489814132159 | 0.246979628264319 | 0.87651018586784 |
| 26 | 0.0872687370332102 | 0.174537474066420 | 0.91273126296679 |
| 27 | 0.114314707942611 | 0.228629415885223 | 0.885685292057389 |
| 28 | 0.365677033996537 | 0.731354067993075 | 0.634322966003463 |
| 29 | 0.312569778040793 | 0.625139556081585 | 0.687430221959207 |
| 30 | 0.272619669158251 | 0.545239338316503 | 0.727380330841749 |
| 31 | 0.250964463680516 | 0.501928927361032 | 0.749035536319484 |
| 32 | 0.219742208235716 | 0.439484416471431 | 0.780257791764284 |
| 33 | 0.274134923306819 | 0.548269846613637 | 0.725865076693181 |
| 34 | 0.222793911161626 | 0.445587822323252 | 0.777206088838374 |
| 35 | 0.341267579925405 | 0.68253515985081 | 0.658732420074595 |
| 36 | 0.280428437107616 | 0.560856874215232 | 0.719571562892384 |
| 37 | 0.235263559966969 | 0.470527119933938 | 0.764736440033031 |
| 38 | 0.239406208590949 | 0.478812417181897 | 0.760593791409051 |
| 39 | 0.195429884414929 | 0.390859768829859 | 0.80457011558507 |
| 40 | 0.156663615801206 | 0.313327231602412 | 0.843336384198794 |
| 41 | 0.313803821281608 | 0.627607642563217 | 0.686196178718391 |
| 42 | 0.297615340742852 | 0.595230681485705 | 0.702384659257148 |
| 43 | 0.250169801289801 | 0.500339602579602 | 0.749830198710199 |
| 44 | 0.203991535986623 | 0.407983071973246 | 0.796008464013377 |
| 45 | 0.188053034814978 | 0.376106069629956 | 0.811946965185022 |
| 46 | 0.166561592849768 | 0.333123185699535 | 0.833438407150232 |
| 47 | 0.135810625827595 | 0.27162125165519 | 0.864189374172405 |
| 48 | 0.118777396071408 | 0.237554792142815 | 0.881222603928592 |
| 49 | 0.137353313431134 | 0.274706626862268 | 0.862646686568866 |
| 50 | 0.108998546568528 | 0.217997093137055 | 0.891001453431472 |
| 51 | 0.0903563850370043 | 0.180712770074009 | 0.909643614962996 |
| 52 | 0.0710130560869455 | 0.142026112173891 | 0.928986943913054 |
| 53 | 0.0621764385295033 | 0.124352877059007 | 0.937823561470497 |
| 54 | 0.0475010256182521 | 0.0950020512365042 | 0.952498974381748 |
| 55 | 0.0372131289050968 | 0.0744262578101937 | 0.962786871094903 |
| 56 | 0.0386259612374103 | 0.0772519224748207 | 0.96137403876259 |
| 57 | 0.0302151806681549 | 0.0604303613363099 | 0.969784819331845 |
| 58 | 0.0352613316598047 | 0.0705226633196094 | 0.964738668340195 |
| 59 | 0.0266903118967951 | 0.0533806237935903 | 0.973309688103205 |
| 60 | 0.0194434129353150 | 0.0388868258706299 | 0.980556587064685 |
| 61 | 0.0160944645104593 | 0.0321889290209185 | 0.98390553548954 |
| 62 | 0.0221373225142798 | 0.0442746450285596 | 0.97786267748572 |
| 63 | 0.0164811631104850 | 0.0329623262209700 | 0.983518836889515 |
| 64 | 0.0128974879587655 | 0.0257949759175310 | 0.987102512041234 |
| 65 | 0.0257555274101711 | 0.0515110548203423 | 0.97424447258983 |
| 66 | 0.0221335163456032 | 0.0442670326912065 | 0.977866483654397 |
| 67 | 0.0176764521377542 | 0.0353529042755084 | 0.982323547862246 |
| 68 | 0.0181581904483262 | 0.0363163808966524 | 0.981841809551674 |
| 69 | 0.0146571963414812 | 0.0293143926829625 | 0.985342803658519 |
| 70 | 0.0114207434442114 | 0.0228414868884228 | 0.988579256555789 |
| 71 | 0.0116196206899549 | 0.0232392413799099 | 0.988380379310045 |
| 72 | 0.00874935460273151 | 0.0174987092054630 | 0.991250645397268 |
| 73 | 0.00644199379781378 | 0.0128839875956276 | 0.993558006202186 |
| 74 | 0.00697000337189522 | 0.0139400067437904 | 0.993029996628105 |
| 75 | 0.00495665028201107 | 0.00991330056402213 | 0.995043349717989 |
| 76 | 0.00334110647014846 | 0.00668221294029692 | 0.996658893529851 |
| 77 | 0.00382618181573984 | 0.00765236363147967 | 0.99617381818426 |
| 78 | 0.00307039926227455 | 0.00614079852454909 | 0.996929600737726 |
| 79 | 0.00225870507544064 | 0.00451741015088129 | 0.99774129492456 |
| 80 | 0.00145500201276848 | 0.00291000402553697 | 0.998544997987232 |
| 81 | 0.00295224765668204 | 0.00590449531336407 | 0.997047752343318 |
| 82 | 0.0019227109485727 | 0.0038454218971454 | 0.998077289051427 |
| 83 | 0.00123608075032111 | 0.00247216150064221 | 0.998763919249679 |
| 84 | 0.00203840871753650 | 0.00407681743507299 | 0.997961591282464 |
| 85 | 0.00151423321432551 | 0.00302846642865102 | 0.998485766785674 |
| 86 | 0.00120425725500039 | 0.00240851451000079 | 0.998795742745 |
| 87 | 0.0009113250341575 | 0.001822650068315 | 0.999088674965843 |
| 88 | 0.00269173800945986 | 0.00538347601891972 | 0.99730826199054 |
| 89 | 0.00313225132685393 | 0.00626450265370786 | 0.996867748673146 |
| 90 | 0.0291055808192445 | 0.058211161638489 | 0.970894419180756 |
| 91 | 0.0264317895046172 | 0.0528635790092344 | 0.973568210495383 |
| 92 | 0.0284729896982986 | 0.0569459793965972 | 0.971527010301701 |
| 93 | 0.0515794963929869 | 0.103158992785974 | 0.948420503607013 |
| 94 | 0.043911862838016 | 0.087823725676032 | 0.956088137161984 |
| 95 | 0.0720655619353627 | 0.144131123870725 | 0.927934438064637 |
| 96 | 0.151315151181419 | 0.302630302362838 | 0.848684848818581 |
| 97 | 0.126476171243944 | 0.252952342487888 | 0.873523828756056 |
| 98 | 0.154567625692103 | 0.309135251384205 | 0.845432374307897 |
| 99 | 0.225127137976169 | 0.450254275952338 | 0.774872862023831 |
| 100 | 0.187309458325151 | 0.374618916650302 | 0.812690541674849 |
| 101 | 0.178468491495112 | 0.356936982990223 | 0.821531508504888 |
| 102 | 0.214204192126755 | 0.428408384253509 | 0.785795807873245 |
| 103 | 0.207173218821966 | 0.414346437643931 | 0.792826781178034 |
| 104 | 0.397451886220607 | 0.794903772441215 | 0.602548113779393 |
| 105 | 0.346074333513492 | 0.692148667026984 | 0.653925666486508 |
| 106 | 0.382403948699787 | 0.764807897399574 | 0.617596051300213 |
| 107 | 0.465927178441299 | 0.931854356882598 | 0.534072821558701 |
| 108 | 0.461631939397953 | 0.923263878795907 | 0.538368060602047 |
| 109 | 0.376687879763607 | 0.753375759527213 | 0.623312120236393 |
| 110 | 0.294639972700540 | 0.589279945401079 | 0.70536002729946 |
| 111 | 0.350864484310401 | 0.701728968620802 | 0.649135515689599 |
| 112 | 0.335852380127941 | 0.671704760255882 | 0.66414761987206 |
| 113 | 0.75293024591123 | 0.494139508177542 | 0.247069754088771 |
| 114 | 0.66467933628295 | 0.6706413274341 | 0.33532066371705 |
| 115 | 0.692305482607014 | 0.615389034785972 | 0.307694517392986 |
| 116 | 0.664748671972499 | 0.670502656055002 | 0.335251328027501 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 15 | 0.148514851485149 | NOK |
| 5% type I error level | 29 | 0.287128712871287 | NOK |
| 10% type I error level | 40 | 0.396039603960396 | NOK |
