| Multiple Linear Regression - Estimated Regression Equation |
| births[t] = + 9430.3111111111 + 286.706944444440difference[t] + 99.161855158722M1[t] -638.203273809523M2[t] -284.711259920635M3[t] -37.5551587301577M4[t] -920.277430555554M5[t] + 41.0002976190488M6[t] -338.555307539682M7[t] -164.444246031745M8[t] -214.333184523809M9[t] + 355.611210317461M10[t] + 228.722271825397M11[t] + 5.22227182539697t + 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) | 9430.3111111111 | 140.713171 | 67.018 | 0 | 0 |
| difference | 286.706944444440 | 134.583356 | 2.1303 | 0.037185 | 0.018593 |
| M1 | 99.161855158722 | 158.573874 | 0.6253 | 0.534083 | 0.267042 |
| M2 | -638.203273809523 | 158.462983 | -4.0275 | 0.000159 | 7.9e-05 |
| M3 | -284.711259920635 | 158.413321 | -1.7973 | 0.077243 | 0.038622 |
| M4 | -37.5551587301577 | 166.197782 | -0.226 | 0.821983 | 0.410991 |
| M5 | -920.277430555554 | 165.759024 | -5.5519 | 1e-06 | 0 |
| M6 | 41.0002976190488 | 165.377825 | 0.2479 | 0.80503 | 0.402515 |
| M7 | -338.555307539682 | 165.054585 | -2.0512 | 0.044552 | 0.022276 |
| M8 | -164.444246031745 | 164.789644 | -0.9979 | 0.322268 | 0.161134 |
| M9 | -214.333184523809 | 164.583284 | -1.3023 | 0.197717 | 0.098859 |
| M10 | 355.611210317461 | 164.435725 | 2.1626 | 0.034501 | 0.01725 |
| M11 | 228.722271825397 | 164.347126 | 1.3917 | 0.169067 | 0.084533 |
| t | 5.22227182539697 | 3.116074 | 1.6759 | 0.098874 | 0.049437 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.857999753809147 |
| R-squared | 0.736163577536557 |
| Adjusted R-squared | 0.67993614324107 |
| F-TEST (value) | 13.0926048246813 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 61 |
| p-value | 3.89466237038505e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 284.606401731326 |
| Sum Squared Residuals | 4941049.03829363 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9534.69523809529 | 165.304761904713 |
| 2 | 9081 | 8802.55238095238 | 278.447619047622 |
| 3 | 9084 | 9161.26666666666 | -77.2666666666633 |
| 4 | 9743 | 9413.64503968254 | 329.354960317462 |
| 5 | 8587 | 8536.14503968254 | 50.854960317464 |
| 6 | 9731 | 9502.64503968254 | 228.354960317463 |
| 7 | 9563 | 9128.3117063492 | 434.688293650796 |
| 8 | 9998 | 9307.64503968254 | 690.354960317463 |
| 9 | 9437 | 9262.97837301587 | 174.02162698413 |
| 10 | 10038 | 9838.14503968254 | 199.854960317462 |
| 11 | 9918 | 9716.47837301587 | 201.521626984129 |
| 12 | 9252 | 9492.97837301587 | -240.978373015871 |
| 13 | 9737 | 9597.36249999999 | 139.637500000010 |
| 14 | 9035 | 8865.21964285714 | 169.780357142859 |
| 15 | 9133 | 9223.93392857143 | -90.9339285714269 |
| 16 | 9487 | 9476.3123015873 | 10.6876984126990 |
| 17 | 8700 | 8598.8123015873 | 101.187698412698 |
| 18 | 9627 | 9565.3123015873 | 61.6876984126988 |
| 19 | 8947 | 9190.97896825397 | -243.978968253968 |
| 20 | 9283 | 9370.3123015873 | -87.312301587301 |
| 21 | 8829 | 9325.64563492063 | -496.645634920635 |
| 22 | 9947 | 9900.8123015873 | 46.1876984126991 |
| 23 | 9628 | 9779.14563492063 | -151.145634920634 |
| 24 | 9318 | 9555.64563492063 | -237.645634920634 |
| 25 | 9605 | 9660.02976190475 | -55.0297619047533 |
| 26 | 8640 | 8927.8869047619 | -287.886904761905 |
| 27 | 9214 | 9286.60119047619 | -72.6011904761905 |
| 28 | 9567 | 9538.97956349206 | 28.0204365079354 |
| 29 | 8547 | 8661.47956349206 | -114.479563492065 |
| 30 | 9185 | 9627.97956349206 | -442.979563492065 |
| 31 | 9470 | 9253.64623015873 | 216.353769841269 |
| 32 | 9123 | 9432.97956349206 | -309.979563492065 |
| 33 | 9278 | 9388.3128968254 | -110.312896825398 |
| 34 | 10170 | 9963.47956349206 | 206.520436507935 |
| 35 | 9434 | 9841.8128968254 | -407.812896825398 |
| 36 | 9655 | 9618.3128968254 | 36.6871031746021 |
| 37 | 9429 | 9722.69702380952 | -293.697023809517 |
| 38 | 8739 | 8990.55416666667 | -251.554166666668 |
| 39 | 9552 | 9349.26845238095 | 202.731547619046 |
| 40 | 9687 | 9888.35376984127 | -201.353769841269 |
| 41 | 9019 | 9010.85376984127 | 8.1462301587311 |
| 42 | 9672 | 9977.35376984127 | -305.353769841269 |
| 43 | 9206 | 9603.02043650794 | -397.020436507935 |
| 44 | 9069 | 9782.35376984127 | -713.353769841269 |
| 45 | 9788 | 9737.6871031746 | 50.3128968253978 |
| 46 | 10312 | 10312.8537698413 | -0.853769841268381 |
| 47 | 10105 | 10191.1871031746 | -86.187103174602 |
| 48 | 9863 | 9967.6871031746 | -104.687103174602 |
| 49 | 9656 | 10072.0712301587 | -416.071230158721 |
| 50 | 9295 | 9339.92837301587 | -44.9283730158724 |
| 51 | 9946 | 9698.64265873016 | 247.357341269842 |
| 52 | 9701 | 9951.02103174603 | -250.021031746032 |
| 53 | 9049 | 9073.52103174603 | -24.5210317460325 |
| 54 | 10190 | 10040.0210317460 | 149.978968253968 |
| 55 | 9706 | 9665.6876984127 | 40.3123015873011 |
| 56 | 9765 | 9845.02103174603 | -80.0210317460321 |
| 57 | 9893 | 9800.35436507937 | 92.6456349206342 |
| 58 | 9994 | 10375.5210317460 | -381.521031746032 |
| 59 | 10433 | 10253.8543650794 | 179.145634920634 |
| 60 | 10073 | 10030.3543650794 | 42.6456349206345 |
| 61 | 10112 | 10134.7384920635 | -22.7384920634845 |
| 62 | 9266 | 9402.59563492064 | -136.595634920636 |
| 63 | 9820 | 9761.30992063492 | 58.6900793650783 |
| 64 | 10097 | 10013.6882936508 | 83.3117063492042 |
| 65 | 9115 | 9136.1882936508 | -21.1882936507961 |
| 66 | 10411 | 10102.6882936508 | 308.311706349204 |
| 67 | 9678 | 9728.35496031746 | -50.3549603174625 |
| 68 | 10408 | 9907.6882936508 | 500.311706349204 |
| 69 | 10153 | 9863.02162698413 | 289.978373015871 |
| 70 | 10368 | 10438.1882936508 | -70.1882936507957 |
| 71 | 10581 | 10316.5216269841 | 264.478373015871 |
| 72 | 10597 | 10093.0216269841 | 503.97837301587 |
| 73 | 10680 | 10197.4057539682 | 482.594246031752 |
| 74 | 9738 | 9465.2628968254 | 272.737103174600 |
| 75 | 9556 | 9823.97718253969 | -267.977182539686 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.128704094160690 | 0.257408188321380 | 0.87129590583931 |
| 18 | 0.058526104950631 | 0.117052209901262 | 0.941473895049369 |
| 19 | 0.332367614469385 | 0.66473522893877 | 0.667632385530615 |
| 20 | 0.550884107448716 | 0.898231785102568 | 0.449115892551284 |
| 21 | 0.586756671353634 | 0.826486657292732 | 0.413243328646366 |
| 22 | 0.513449018504325 | 0.97310196299135 | 0.486550981495675 |
| 23 | 0.407871981551802 | 0.815743963103603 | 0.592128018448198 |
| 24 | 0.370593804769151 | 0.741187609538303 | 0.629406195230849 |
| 25 | 0.319036561008133 | 0.638073122016266 | 0.680963438991867 |
| 26 | 0.249508717541666 | 0.499017435083332 | 0.750491282458334 |
| 27 | 0.280486322768490 | 0.560972645536981 | 0.71951367723151 |
| 28 | 0.242372334677351 | 0.484744669354702 | 0.757627665322649 |
| 29 | 0.182497335099524 | 0.364994670199047 | 0.817502664900476 |
| 30 | 0.197747143157021 | 0.395494286314041 | 0.80225285684298 |
| 31 | 0.299959030274243 | 0.599918060548485 | 0.700040969725757 |
| 32 | 0.287707852601751 | 0.575415705203503 | 0.712292147398249 |
| 33 | 0.288768577780515 | 0.57753715556103 | 0.711231422219485 |
| 34 | 0.382424533003743 | 0.764849066007487 | 0.617575466996257 |
| 35 | 0.374207099953586 | 0.748414199907172 | 0.625792900046414 |
| 36 | 0.44291566149623 | 0.88583132299246 | 0.55708433850377 |
| 37 | 0.384864629026903 | 0.769729258053805 | 0.615135370973097 |
| 38 | 0.359014037214079 | 0.718028074428158 | 0.640985962785921 |
| 39 | 0.446307393782848 | 0.892614787565697 | 0.553692606217152 |
| 40 | 0.375181631546514 | 0.750363263093028 | 0.624818368453486 |
| 41 | 0.364361540384441 | 0.728723080768882 | 0.635638459615559 |
| 42 | 0.316459530508156 | 0.632919061016311 | 0.683540469491844 |
| 43 | 0.282369215667827 | 0.564738431335654 | 0.717630784332173 |
| 44 | 0.5455371596092 | 0.9089256807816 | 0.4544628403908 |
| 45 | 0.562852318887968 | 0.874295362224064 | 0.437147681112032 |
| 46 | 0.627185925495232 | 0.745628149009536 | 0.372814074504768 |
| 47 | 0.564436560349907 | 0.871126879300186 | 0.435563439650093 |
| 48 | 0.503167450735586 | 0.993665098528827 | 0.496832549264414 |
| 49 | 0.559425109492356 | 0.881149781015288 | 0.440574890507644 |
| 50 | 0.48379018640313 | 0.96758037280626 | 0.51620981359687 |
| 51 | 0.783017429210445 | 0.43396514157911 | 0.216982570789555 |
| 52 | 0.705302666891452 | 0.589394666217095 | 0.294697333108548 |
| 53 | 0.648188520995924 | 0.703622958008152 | 0.351811479004076 |
| 54 | 0.584657412834871 | 0.830685174330258 | 0.415342587165129 |
| 55 | 0.580366115387948 | 0.839267769224104 | 0.419633884612052 |
| 56 | 0.558480063448771 | 0.883039873102457 | 0.441519936551229 |
| 57 | 0.429348480632675 | 0.85869696126535 | 0.570651519367325 |
| 58 | 0.29345967342011 | 0.58691934684022 | 0.70654032657989 |
| 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 |
