| Multiple Linear Regression - Estimated Regression Equation |
| Birth[t] = + 9548.42203608247 + 489.155927835053x[t] + 87.5111377024945M1[t] -644.631719440353M2[t] -285.917433726068M3[t] + 2.19265463917518M4[t] -956.833333333334M5[t] + 9.66666666666654M6[t] -364.666666666667M7[t] -185.333333333334M8[t] -230.000000000000M9[t] + 345.166666666666M10[t] + 223.500000000000M11[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) | 9548.42203608247 | 121.786909 | 78.4027 | 0 | 0 |
| x | 489.155927835053 | 66.745179 | 7.3287 | 0 | 0 |
| M1 | 87.5111377024945 | 159.68598 | 0.548 | 0.585646 | 0.292823 |
| M2 | -644.631719440353 | 159.68598 | -4.0369 | 0.000151 | 7.6e-05 |
| M3 | -285.917433726068 | 159.68598 | -1.7905 | 0.078256 | 0.039128 |
| M4 | 2.19265463917518 | 166.013225 | 0.0132 | 0.989504 | 0.494752 |
| M5 | -956.833333333334 | 165.640101 | -5.7766 | 0 | 0 |
| M6 | 9.66666666666654 | 165.640101 | 0.0584 | 0.95365 | 0.476825 |
| M7 | -364.666666666667 | 165.640101 | -2.2016 | 0.031427 | 0.015713 |
| M8 | -185.333333333334 | 165.640101 | -1.1189 | 0.267503 | 0.133751 |
| M9 | -230.000000000000 | 165.640101 | -1.3886 | 0.169937 | 0.084969 |
| M10 | 345.166666666666 | 165.640101 | 2.0838 | 0.041303 | 0.020652 |
| M11 | 223.500000000000 | 165.640101 | 1.3493 | 0.182144 | 0.091072 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.852938681164412 |
| R-squared | 0.727504393826486 |
| Adjusted R-squared | 0.674763308760644 |
| F-TEST (value) | 13.7938837041042 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 62 |
| p-value | 2.55573340268711e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 286.897071073320 |
| Sum Squared Residuals | 5103215.62220789 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9635.93317378503 | 64.0668262149703 |
| 2 | 9081 | 8903.79031664212 | 177.20968335788 |
| 3 | 9084 | 9262.5046023564 | -178.504602356405 |
| 4 | 9743 | 9550.61469072165 | 192.38530927835 |
| 5 | 8587 | 8591.58870274914 | -4.58870274914076 |
| 6 | 9731 | 9558.08870274914 | 172.91129725086 |
| 7 | 9563 | 9183.7553694158 | 379.244630584194 |
| 8 | 9998 | 9363.08870274914 | 634.91129725086 |
| 9 | 9437 | 9318.42203608247 | 118.577963917526 |
| 10 | 10038 | 9893.58870274914 | 144.411297250860 |
| 11 | 9918 | 9771.92203608247 | 146.077963917526 |
| 12 | 9252 | 9548.42203608247 | -296.422036082474 |
| 13 | 9737 | 9635.93317378497 | 101.066826215031 |
| 14 | 9035 | 8903.79031664212 | 131.209683357880 |
| 15 | 9133 | 9262.5046023564 | -129.504602356406 |
| 16 | 9487 | 9550.61469072165 | -63.614690721649 |
| 17 | 8700 | 8591.58870274914 | 108.411297250860 |
| 18 | 9627 | 9558.08870274914 | 68.9112972508598 |
| 19 | 8947 | 9183.7553694158 | -236.755369415807 |
| 20 | 9283 | 9363.08870274914 | -80.08870274914 |
| 21 | 8829 | 9318.42203608247 | -489.422036082473 |
| 22 | 9947 | 9893.58870274914 | 53.4112972508599 |
| 23 | 9628 | 9771.92203608247 | -143.922036082474 |
| 24 | 9318 | 9548.42203608247 | -230.422036082474 |
| 25 | 9605 | 9635.93317378497 | -30.9331737849686 |
| 26 | 8640 | 8903.79031664212 | -263.79031664212 |
| 27 | 9214 | 9262.5046023564 | -48.5046023564059 |
| 28 | 9567 | 9550.61469072165 | 16.3853092783511 |
| 29 | 8547 | 8591.58870274914 | -44.5887027491402 |
| 30 | 9185 | 9558.08870274914 | -373.08870274914 |
| 31 | 9470 | 9183.7553694158 | 286.244630584193 |
| 32 | 9123 | 9363.08870274914 | -240.08870274914 |
| 33 | 9278 | 9318.42203608247 | -40.4220360824735 |
| 34 | 10170 | 9893.58870274914 | 276.41129725086 |
| 35 | 9434 | 9771.92203608247 | -337.922036082474 |
| 36 | 9655 | 9548.42203608247 | 106.577963917526 |
| 37 | 9429 | 9635.93317378497 | -206.933173784969 |
| 38 | 8739 | 8903.79031664212 | -164.79031664212 |
| 39 | 9552 | 9262.5046023564 | 289.495397643594 |
| 40 | 9687 | 9550.61469072165 | 136.385309278351 |
| 41 | 9019 | 9080.7446305842 | -61.744630584193 |
| 42 | 9672 | 10047.2446305842 | -375.244630584193 |
| 43 | 9206 | 9672.91129725086 | -466.91129725086 |
| 44 | 9069 | 9852.2446305842 | -783.244630584193 |
| 45 | 9788 | 9807.57796391753 | -19.5779639175265 |
| 46 | 10312 | 10382.7446305842 | -70.7446305841933 |
| 47 | 10105 | 10261.0779639175 | -156.077963917526 |
| 48 | 9863 | 10037.5779639175 | -174.577963917527 |
| 49 | 9656 | 10125.0891016200 | -469.089101620022 |
| 50 | 9295 | 9392.94624447717 | -97.946244477173 |
| 51 | 9946 | 9751.66053019146 | 194.339469808541 |
| 52 | 9701 | 10039.7706185567 | -338.770618556702 |
| 53 | 9049 | 9080.7446305842 | -31.744630584193 |
| 54 | 10190 | 10047.2446305842 | 142.755369415807 |
| 55 | 9706 | 9672.91129725086 | 33.08870274914 |
| 56 | 9765 | 9852.2446305842 | -87.2446305841929 |
| 57 | 9893 | 9807.57796391753 | 85.4220360824735 |
| 58 | 9994 | 10382.7446305842 | -388.744630584193 |
| 59 | 10433 | 10261.0779639175 | 171.922036082473 |
| 60 | 10073 | 10037.5779639175 | 35.4220360824733 |
| 61 | 10112 | 10125.0891016200 | -13.0891016200215 |
| 62 | 9266 | 9392.94624447717 | -126.946244477173 |
| 63 | 9820 | 9751.66053019146 | 68.3394698085412 |
| 64 | 10097 | 10039.7706185567 | 57.2293814432981 |
| 65 | 9115 | 9080.7446305842 | 34.255369415807 |
| 66 | 10411 | 10047.2446305842 | 363.755369415807 |
| 67 | 9678 | 9672.91129725086 | 5.08870274914004 |
| 68 | 10408 | 9852.2446305842 | 555.755369415807 |
| 69 | 10153 | 9807.57796391753 | 345.422036082474 |
| 70 | 10368 | 10382.7446305842 | -14.7446305841933 |
| 71 | 10581 | 10261.0779639175 | 319.922036082474 |
| 72 | 10597 | 10037.5779639175 | 559.422036082473 |
| 73 | 10680 | 10125.0891016200 | 554.910898379979 |
| 74 | 9738 | 9392.94624447717 | 345.053755522827 |
| 75 | 9556 | 9751.66053019146 | -195.660530191459 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0630388211182975 | 0.126077642236595 | 0.936961178881702 |
| 17 | 0.0253237597126573 | 0.0506475194253147 | 0.974676240287343 |
| 18 | 0.00973707430190853 | 0.0194741486038171 | 0.990262925698091 |
| 19 | 0.149017374937020 | 0.298034749874040 | 0.85098262506298 |
| 20 | 0.376322610958729 | 0.752645221917459 | 0.62367738904127 |
| 21 | 0.510518424652707 | 0.978963150694586 | 0.489481575347293 |
| 22 | 0.407513451231753 | 0.815026902463506 | 0.592486548768247 |
| 23 | 0.348488695967874 | 0.696977391935748 | 0.651511304032126 |
| 24 | 0.274190031051132 | 0.548380062102263 | 0.725809968948868 |
| 25 | 0.202970665839589 | 0.405941331679177 | 0.797029334160411 |
| 26 | 0.222576847717770 | 0.445153695435541 | 0.77742315228223 |
| 27 | 0.163762367280227 | 0.327524734560454 | 0.836237632719773 |
| 28 | 0.113492226028674 | 0.226984452057348 | 0.886507773971326 |
| 29 | 0.0770729718031561 | 0.154145943606312 | 0.922927028196844 |
| 30 | 0.113714303277493 | 0.227428606554985 | 0.886285696722507 |
| 31 | 0.102195838290823 | 0.204391676581647 | 0.897804161709177 |
| 32 | 0.128764138444980 | 0.257528276889959 | 0.87123586155502 |
| 33 | 0.095711507530766 | 0.191423015061532 | 0.904288492469234 |
| 34 | 0.086717737251797 | 0.173435474503594 | 0.913282262748203 |
| 35 | 0.0912570712313378 | 0.182514142462676 | 0.908742928768662 |
| 36 | 0.0827898217903253 | 0.165579643580651 | 0.917210178209675 |
| 37 | 0.0715029755211217 | 0.143005951042243 | 0.928497024478878 |
| 38 | 0.0621059092356678 | 0.124211818471336 | 0.937894090764332 |
| 39 | 0.0602771004790983 | 0.120554200958197 | 0.939722899520902 |
| 40 | 0.0400478875032021 | 0.0800957750064042 | 0.959952112496798 |
| 41 | 0.0253437719950878 | 0.0506875439901756 | 0.974656228004912 |
| 42 | 0.0300904208643591 | 0.0601808417287181 | 0.96990957913564 |
| 43 | 0.0351980890433704 | 0.0703961780867408 | 0.96480191095663 |
| 44 | 0.176960482957353 | 0.353920965914706 | 0.823039517042647 |
| 45 | 0.203300678468998 | 0.406601356937996 | 0.796699321531002 |
| 46 | 0.155090652972055 | 0.310181305944110 | 0.844909347027945 |
| 47 | 0.158106321827903 | 0.316212643655805 | 0.841893678172097 |
| 48 | 0.177541106156011 | 0.355082212312021 | 0.82245889384399 |
| 49 | 0.349503971848223 | 0.699007943696447 | 0.650496028151777 |
| 50 | 0.301108124559651 | 0.602216249119303 | 0.698891875440349 |
| 51 | 0.305339001260655 | 0.610678002521309 | 0.694660998739345 |
| 52 | 0.295185361245224 | 0.590370722490447 | 0.704814638754776 |
| 53 | 0.218853314793356 | 0.437706629586712 | 0.781146685206644 |
| 54 | 0.193341917338099 | 0.386683834676199 | 0.8066580826619 |
| 55 | 0.131213342801170 | 0.262426685602339 | 0.86878665719883 |
| 56 | 0.206155423921493 | 0.412310847842985 | 0.793844576078507 |
| 57 | 0.163711540232966 | 0.327423080465931 | 0.836288459767034 |
| 58 | 0.15032322418632 | 0.30064644837264 | 0.84967677581368 |
| 59 | 0.0949625925667216 | 0.189925185133443 | 0.905037407433278 |
| 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 | 1 | 0.0227272727272727 | OK |
| 10% type I error level | 6 | 0.136363636363636 | NOK |
