| Multiple Linear Regression - Estimated Regression Equation |
| Birth[t] = + 9433.57874165147 + 302.401411657555x[t] + 98.9596904183565M1[t] -638.140798927342M2[t] -284.384145415907M3[t] + 10.727959565733M4[t] -922.129907913377M5[t] + 39.4124598837721M6[t] -339.878505652412M7[t] -165.50280452193M8[t] -215.127103391447M9[t] + 355.081931072368M10[t] + 228.457632202851M11[t] + 4.95763220285092t + 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) | 9433.57874165147 | 139.583711 | 67.5837 | 0 | 0 |
| x | 302.401411657555 | 132.823529 | 2.2767 | 0.026324 | 0.013162 |
| M1 | 98.9596904183565 | 157.795511 | 0.6271 | 0.532909 | 0.266454 |
| M2 | -638.140798927342 | 157.688002 | -4.0469 | 0.000149 | 7.4e-05 |
| M3 | -284.384145415907 | 157.639891 | -1.804 | 0.076167 | 0.038084 |
| M4 | 10.727959565733 | 163.967849 | 0.0654 | 0.948048 | 0.474024 |
| M5 | -922.129907913377 | 164.913195 | -5.5916 | 1e-06 | 0 |
| M6 | 39.4124598837721 | 164.543343 | 0.2395 | 0.811501 | 0.40575 |
| M7 | -339.878505652412 | 164.229741 | -2.0695 | 0.042739 | 0.02137 |
| M8 | -165.50280452193 | 163.972711 | -1.0093 | 0.316803 | 0.158401 |
| M9 | -215.127103391447 | 163.77252 | -1.3136 | 0.193909 | 0.096955 |
| M10 | 355.081931072368 | 163.629376 | 2.17 | 0.033908 | 0.016954 |
| M11 | 228.457632202851 | 163.54343 | 1.3969 | 0.167498 | 0.083749 |
| t | 4.95763220285092 | 3.06155 | 1.6193 | 0.110537 | 0.055269 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.85949714743181 |
| R-squared | 0.73873534644342 |
| Adjusted R-squared | 0.683055994046116 |
| F-TEST (value) | 13.2676713114786 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 61 |
| p-value | 2.94209101525666e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 283.215891843633 |
| Sum Squared Residuals | 4892885.72495986 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9537.49606427275 | 162.503935727248 |
| 2 | 9081 | 8805.35320712984 | 275.646792870157 |
| 3 | 9084 | 9164.06749284413 | -80.0674928441278 |
| 4 | 9743 | 9464.13723002862 | 278.862769971378 |
| 5 | 8587 | 8536.23699475236 | 50.7630052476382 |
| 6 | 9731 | 9502.73699475236 | 228.263005247639 |
| 7 | 9563 | 9128.40366141903 | 434.596338580973 |
| 8 | 9998 | 9307.73699475236 | 690.263005247639 |
| 9 | 9437 | 9263.0703280857 | 173.929671914305 |
| 10 | 10038 | 9838.23699475236 | 199.763005247639 |
| 11 | 9918 | 9716.5703280857 | 201.429671914305 |
| 12 | 9252 | 9493.0703280857 | -241.070328085695 |
| 13 | 9737 | 9596.9876507069 | 140.012349293097 |
| 14 | 9035 | 8864.84479356405 | 170.155206435946 |
| 15 | 9133 | 9223.55907927834 | -90.55907927834 |
| 16 | 9487 | 9523.62881646283 | -36.6288164628315 |
| 17 | 8700 | 8595.72858118657 | 104.271418813428 |
| 18 | 9627 | 9562.22858118657 | 64.7714188134276 |
| 19 | 8947 | 9187.89524785324 | -240.895247853239 |
| 20 | 9283 | 9367.22858118657 | -84.2285811865722 |
| 21 | 8829 | 9322.5619145199 | -493.561914519906 |
| 22 | 9947 | 9897.72858118657 | 49.2714188134276 |
| 23 | 9628 | 9776.0619145199 | -148.061914519906 |
| 24 | 9318 | 9552.5619145199 | -234.561914519906 |
| 25 | 9605 | 9656.47923714111 | -51.4792371411137 |
| 26 | 8640 | 8924.33637999827 | -284.336379998265 |
| 27 | 9214 | 9283.05066571255 | -69.0506657125511 |
| 28 | 9567 | 9583.12040289704 | -16.1204028970426 |
| 29 | 8547 | 8655.22016762078 | -108.220167620784 |
| 30 | 9185 | 9621.72016762078 | -436.720167620783 |
| 31 | 9470 | 9247.38683428745 | 222.613165712550 |
| 32 | 9123 | 9426.72016762078 | -303.720167620783 |
| 33 | 9278 | 9382.05350095412 | -104.053500954117 |
| 34 | 10170 | 9957.22016762078 | 212.779832379217 |
| 35 | 9434 | 9835.55350095412 | -401.553500954117 |
| 36 | 9655 | 9612.05350095412 | 42.946499045883 |
| 37 | 9429 | 9715.97082357532 | -286.970823575325 |
| 38 | 8739 | 8983.82796643248 | -244.827966432476 |
| 39 | 9552 | 9342.54225214676 | 209.457747853238 |
| 40 | 9687 | 9642.61198933125 | 44.3880106687463 |
| 41 | 9019 | 9017.11316571255 | 1.88683428745027 |
| 42 | 9672 | 9983.61316571255 | -311.61316571255 |
| 43 | 9206 | 9609.27983237922 | -403.279832379217 |
| 44 | 9069 | 9788.61316571255 | -719.613165712549 |
| 45 | 9788 | 9743.94649904588 | 44.0535009541169 |
| 46 | 10312 | 10319.1131657125 | -7.11316571254994 |
| 47 | 10105 | 10197.4464990459 | -92.4464990458831 |
| 48 | 9863 | 9973.94649904588 | -110.946499045883 |
| 49 | 9656 | 10077.8638216671 | -421.863821667091 |
| 50 | 9295 | 9345.72096452424 | -50.7209645242425 |
| 51 | 9946 | 9704.43525023853 | 241.564749761472 |
| 52 | 9701 | 10004.5049874230 | -303.50498742302 |
| 53 | 9049 | 9076.60475214676 | -27.6047521467608 |
| 54 | 10190 | 10043.1047521468 | 146.895247853239 |
| 55 | 9706 | 9668.77141881343 | 37.2285811865722 |
| 56 | 9765 | 9848.10475214676 | -83.1047521467606 |
| 57 | 9893 | 9803.4380854801 | 89.5619145199058 |
| 58 | 9994 | 10378.6047521468 | -384.604752146761 |
| 59 | 10433 | 10256.9380854801 | 176.061914519906 |
| 60 | 10073 | 10033.4380854801 | 39.5619145199056 |
| 61 | 10112 | 10137.3554081013 | -25.3554081013022 |
| 62 | 9266 | 9405.21255095845 | -139.212550958454 |
| 63 | 9820 | 9763.92683667274 | 56.0731633272605 |
| 64 | 10097 | 10063.9965738572 | 33.003426142769 |
| 65 | 9115 | 9136.09633858097 | -21.0963385809719 |
| 66 | 10411 | 10102.5963385810 | 308.403661419028 |
| 67 | 9678 | 9728.26300524764 | -50.2630052476388 |
| 68 | 10408 | 9907.59633858097 | 500.403661419028 |
| 69 | 10153 | 9862.9296719143 | 290.070328085695 |
| 70 | 10368 | 10438.0963385810 | -70.0963385809721 |
| 71 | 10581 | 10316.4296719143 | 264.570328085695 |
| 72 | 10597 | 10092.9296719143 | 504.070328085695 |
| 73 | 10680 | 10196.8469945355 | 483.153005464487 |
| 74 | 9738 | 9464.70413739267 | 273.295862607335 |
| 75 | 9556 | 9823.41842310695 | -267.418423106951 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.128558701500382 | 0.257117403000764 | 0.871441298499618 |
| 18 | 0.0584272284332547 | 0.116854456866509 | 0.941572771566745 |
| 19 | 0.331902517617099 | 0.663805035234199 | 0.6680974823829 |
| 20 | 0.550217150357053 | 0.899565699285895 | 0.449782849642947 |
| 21 | 0.586066000730772 | 0.827867998538456 | 0.413933999269228 |
| 22 | 0.512632885593036 | 0.974734228813928 | 0.487367114406964 |
| 23 | 0.407042968497683 | 0.814085936995367 | 0.592957031502317 |
| 24 | 0.369777912385374 | 0.739555824770749 | 0.630222087614626 |
| 25 | 0.318178362712117 | 0.636356725424234 | 0.681821637287883 |
| 26 | 0.248733708478292 | 0.497467416956583 | 0.751266291521708 |
| 27 | 0.279598148959271 | 0.559196297918542 | 0.720401851040729 |
| 28 | 0.23937542318131 | 0.47875084636262 | 0.76062457681869 |
| 29 | 0.179823048953785 | 0.35964609790757 | 0.820176951046215 |
| 30 | 0.197507730420186 | 0.395015460840371 | 0.802492269579814 |
| 31 | 0.294278771657167 | 0.588557543314335 | 0.705721228342833 |
| 32 | 0.28327434334654 | 0.56654868669308 | 0.71672565665346 |
| 33 | 0.286476358634648 | 0.572952717269295 | 0.713523641365352 |
| 34 | 0.365848282928086 | 0.731696565856171 | 0.634151717071914 |
| 35 | 0.370001253067677 | 0.740002506135353 | 0.629998746932323 |
| 36 | 0.438541623561671 | 0.877083247123343 | 0.561458376438329 |
| 37 | 0.390370261349309 | 0.780740522698618 | 0.609629738650691 |
| 38 | 0.366315396708289 | 0.732630793416579 | 0.633684603291711 |
| 39 | 0.457163000114408 | 0.914326000228816 | 0.542836999885592 |
| 40 | 0.396643297800992 | 0.793286595601984 | 0.603356702199008 |
| 41 | 0.362487553133524 | 0.724975106267049 | 0.637512446866476 |
| 42 | 0.325459407342082 | 0.650918814684165 | 0.674540592657918 |
| 43 | 0.299090327214512 | 0.598180654429025 | 0.700909672785488 |
| 44 | 0.561661054754946 | 0.876677890490108 | 0.438338945245054 |
| 45 | 0.577974413688325 | 0.844051172623349 | 0.422025586311675 |
| 46 | 0.640562753076958 | 0.718874493846085 | 0.359437246923042 |
| 47 | 0.575903352210572 | 0.848193295578857 | 0.424096647789428 |
| 48 | 0.512204152551337 | 0.975591694897325 | 0.487795847448663 |
| 49 | 0.569473229415518 | 0.861053541168965 | 0.430526770584482 |
| 50 | 0.49126777097515 | 0.9825355419503 | 0.50873222902485 |
| 51 | 0.784439926672479 | 0.431120146655042 | 0.215560073327521 |
| 52 | 0.711834598962827 | 0.576330802074346 | 0.288165401037173 |
| 53 | 0.654075034906263 | 0.691849930187475 | 0.345924965093737 |
| 54 | 0.588325914380174 | 0.823348171239652 | 0.411674085619826 |
| 55 | 0.582928354827184 | 0.834143290345632 | 0.417071645172816 |
| 56 | 0.560199089325349 | 0.879601821349301 | 0.439800910674651 |
| 57 | 0.429938510892681 | 0.859877021785362 | 0.570061489107319 |
| 58 | 0.294644039324648 | 0.589288078649297 | 0.705355960675352 |
| 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 |
