| Multiple Linear Regression - Estimated Regression Equation |
| births[t] = + 9551.32375478927 + 483.352490421457difference[t] + 87.0966064586708M1[t] -645.046250684182M2[t] -286.331964969896M3[t] -79.3333333333332M4[t] -956.833333333333M5[t] + 9.66666666666673M6[t] -364.666666666667M7[t] -185.333333333333M8[t] -230M9[t] + 345.166666666667M10[t] + 223.5M11[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) | 9551.32375478927 | 122.522937 | 77.9554 | 0 | 0 |
| difference | 483.352490421457 | 66.87018 | 7.2282 | 0 | 0 |
| M1 | 87.0966064586708 | 160.704363 | 0.542 | 0.589783 | 0.294892 |
| M2 | -645.046250684182 | 160.704363 | -4.0139 | 0.000164 | 8.2e-05 |
| M3 | -286.331964969896 | 160.704363 | -1.7817 | 0.079691 | 0.039845 |
| M4 | -79.3333333333332 | 166.69712 | -0.4759 | 0.635809 | 0.317905 |
| M5 | -956.833333333333 | 166.69712 | -5.74 | 0 | 0 |
| M6 | 9.66666666666673 | 166.69712 | 0.058 | 0.953944 | 0.476972 |
| M7 | -364.666666666667 | 166.69712 | -2.1876 | 0.032478 | 0.016239 |
| M8 | -185.333333333333 | 166.69712 | -1.1118 | 0.270518 | 0.135259 |
| M9 | -230 | 166.69712 | -1.3797 | 0.17262 | 0.08631 |
| M10 | 345.166666666667 | 166.69712 | 2.0706 | 0.042564 | 0.021282 |
| M11 | 223.5 | 166.69712 | 1.3408 | 0.184892 | 0.092446 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.850890991214296 |
| R-squared | 0.724015478929646 |
| Adjusted R-squared | 0.670599120012804 |
| F-TEST (value) | 13.5541900198922 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 62 |
| p-value | 3.70481423317415e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 288.727881972289 |
| Sum Squared Residuals | 5168554.96934866 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9638.42036124798 | 61.5796387520246 |
| 2 | 9081 | 8906.27750410509 | 174.722495894910 |
| 3 | 9084 | 9264.99178981938 | -180.991789819376 |
| 4 | 9743 | 9471.99042145594 | 271.009578544062 |
| 5 | 8587 | 8594.49042145594 | -7.49042145593836 |
| 6 | 9731 | 9560.99042145594 | 170.009578544062 |
| 7 | 9563 | 9186.6570881226 | 376.342911877395 |
| 8 | 9998 | 9365.99042145594 | 632.009578544062 |
| 9 | 9437 | 9321.32375478927 | 115.676245210728 |
| 10 | 10038 | 9896.49042145594 | 141.509578544062 |
| 11 | 9918 | 9774.82375478927 | 143.176245210728 |
| 12 | 9252 | 9551.32375478927 | -299.323754789272 |
| 13 | 9737 | 9638.42036124794 | 98.5796387520576 |
| 14 | 9035 | 8906.27750410509 | 128.72249589491 |
| 15 | 9133 | 9264.99178981938 | -131.991789819376 |
| 16 | 9487 | 9471.99042145594 | 15.0095785440616 |
| 17 | 8700 | 8594.49042145594 | 105.509578544062 |
| 18 | 9627 | 9560.99042145594 | 66.0095785440617 |
| 19 | 8947 | 9186.6570881226 | -239.657088122605 |
| 20 | 9283 | 9365.99042145594 | -82.9904214559383 |
| 21 | 8829 | 9321.32375478927 | -492.323754789272 |
| 22 | 9947 | 9896.49042145594 | 50.5095785440617 |
| 23 | 9628 | 9774.82375478927 | -146.823754789272 |
| 24 | 9318 | 9551.32375478927 | -233.323754789272 |
| 25 | 9605 | 9638.42036124794 | -33.4203612479425 |
| 26 | 8640 | 8906.27750410509 | -266.27750410509 |
| 27 | 9214 | 9264.99178981938 | -50.9917898193758 |
| 28 | 9567 | 9471.99042145594 | 95.0095785440616 |
| 29 | 8547 | 8594.49042145594 | -47.4904214559383 |
| 30 | 9185 | 9560.99042145594 | -375.990421455938 |
| 31 | 9470 | 9186.6570881226 | 283.342911877395 |
| 32 | 9123 | 9365.99042145594 | -242.990421455938 |
| 33 | 9278 | 9321.32375478927 | -43.3237547892717 |
| 34 | 10170 | 9896.49042145594 | 273.509578544062 |
| 35 | 9434 | 9774.82375478927 | -340.823754789272 |
| 36 | 9655 | 9551.32375478927 | 103.676245210728 |
| 37 | 9429 | 9638.42036124794 | -209.420361247942 |
| 38 | 8739 | 8906.27750410509 | -167.277504105090 |
| 39 | 9552 | 9264.99178981938 | 287.008210180624 |
| 40 | 9687 | 9955.3429118774 | -268.342911877395 |
| 41 | 9019 | 9077.8429118774 | -58.8429118773951 |
| 42 | 9672 | 10044.3429118774 | -372.342911877395 |
| 43 | 9206 | 9670.00957854406 | -464.009578544062 |
| 44 | 9069 | 9849.3429118774 | -780.342911877395 |
| 45 | 9788 | 9804.67624521073 | -16.6762452107284 |
| 46 | 10312 | 10379.8429118774 | -67.842911877395 |
| 47 | 10105 | 10258.1762452107 | -153.176245210728 |
| 48 | 9863 | 10034.6762452107 | -171.676245210728 |
| 49 | 9656 | 10121.7728516694 | -465.772851669399 |
| 50 | 9295 | 9389.62999452655 | -94.6299945265467 |
| 51 | 9946 | 9748.34428024083 | 197.655719759168 |
| 52 | 9701 | 9955.3429118774 | -254.342911877395 |
| 53 | 9049 | 9077.8429118774 | -28.8429118773951 |
| 54 | 10190 | 10044.3429118774 | 145.657088122605 |
| 55 | 9706 | 9670.00957854406 | 35.9904214559383 |
| 56 | 9765 | 9849.3429118774 | -84.342911877395 |
| 57 | 9893 | 9804.67624521073 | 88.3237547892717 |
| 58 | 9994 | 10379.8429118774 | -385.842911877395 |
| 59 | 10433 | 10258.1762452107 | 174.823754789272 |
| 60 | 10073 | 10034.6762452107 | 38.3237547892717 |
| 61 | 10112 | 10121.7728516694 | -9.77285166939906 |
| 62 | 9266 | 9389.62999452655 | -123.629994526547 |
| 63 | 9820 | 9748.34428024083 | 71.6557197591676 |
| 64 | 10097 | 9955.3429118774 | 141.657088122605 |
| 65 | 9115 | 9077.8429118774 | 37.157088122605 |
| 66 | 10411 | 10044.3429118774 | 366.657088122605 |
| 67 | 9678 | 9670.00957854406 | 7.99042145593837 |
| 68 | 10408 | 9849.3429118774 | 558.657088122605 |
| 69 | 10153 | 9804.67624521073 | 348.323754789272 |
| 70 | 10368 | 10379.8429118774 | -11.8429118773950 |
| 71 | 10581 | 10258.1762452107 | 322.823754789272 |
| 72 | 10597 | 10034.6762452107 | 562.323754789272 |
| 73 | 10680 | 10121.7728516694 | 558.227148330601 |
| 74 | 9738 | 9389.62999452655 | 348.370005473453 |
| 75 | 9556 | 9748.34428024083 | -192.344280240832 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0628864086217765 | 0.125772817243553 | 0.937113591378224 |
| 17 | 0.0252538380525609 | 0.0505076761051218 | 0.97474616194744 |
| 18 | 0.00970958652843406 | 0.0194191730568681 | 0.990290413471566 |
| 19 | 0.148579319870377 | 0.297158639740754 | 0.851420680129623 |
| 20 | 0.375555160510833 | 0.751110321021666 | 0.624444839489167 |
| 21 | 0.508910414703815 | 0.98217917059237 | 0.491089585296185 |
| 22 | 0.406094554376384 | 0.812189108752768 | 0.593905445623616 |
| 23 | 0.346973812461059 | 0.693947624922119 | 0.653026187538941 |
| 24 | 0.272384861908357 | 0.544769723816715 | 0.727615138091643 |
| 25 | 0.201453921323331 | 0.402907842646662 | 0.798546078676669 |
| 26 | 0.220629084902142 | 0.441258169804285 | 0.779370915097858 |
| 27 | 0.162010428414125 | 0.324020856828250 | 0.837989571585875 |
| 28 | 0.117628050260768 | 0.235256100521536 | 0.882371949739232 |
| 29 | 0.0802646370649753 | 0.160529274129951 | 0.919735362935025 |
| 30 | 0.116285925472923 | 0.232571850945845 | 0.883714074527077 |
| 31 | 0.107301041391532 | 0.214602082783063 | 0.892698958608468 |
| 32 | 0.134188895600302 | 0.268377791200604 | 0.865811104399698 |
| 33 | 0.09905893413577 | 0.19811786827154 | 0.90094106586423 |
| 34 | 0.0947900699005712 | 0.189580139801142 | 0.905209930099429 |
| 35 | 0.0951337328751895 | 0.190267465750379 | 0.90486626712481 |
| 36 | 0.086249305825813 | 0.172498611651626 | 0.913750694174187 |
| 37 | 0.0712702639584215 | 0.142540527916843 | 0.928729736041578 |
| 38 | 0.0589649249372218 | 0.117929849874444 | 0.941035075062778 |
| 39 | 0.0571857836021641 | 0.114371567204328 | 0.942814216397836 |
| 40 | 0.0393145980716531 | 0.0786291961433063 | 0.960685401928347 |
| 41 | 0.0282828166572107 | 0.0565656333144214 | 0.97171718334279 |
| 42 | 0.0314177911054975 | 0.062835582210995 | 0.968582208894503 |
| 43 | 0.0347914111105862 | 0.0695828222211725 | 0.965208588889414 |
| 44 | 0.176210807685340 | 0.352421615370679 | 0.82378919231466 |
| 45 | 0.201813126610689 | 0.403626253221378 | 0.798186873389311 |
| 46 | 0.154250353596875 | 0.308500707193749 | 0.845749646403125 |
| 47 | 0.158510708037767 | 0.317021416075535 | 0.841489291962233 |
| 48 | 0.179424776637648 | 0.358849553275295 | 0.820575223362352 |
| 49 | 0.350709779801318 | 0.701419559602636 | 0.649290220198682 |
| 50 | 0.303553555207902 | 0.607107110415804 | 0.696446444792098 |
| 51 | 0.310627320986465 | 0.62125464197293 | 0.689372679013535 |
| 52 | 0.295266014005051 | 0.590532028010103 | 0.704733985994949 |
| 53 | 0.219145807559674 | 0.438291615119348 | 0.780854192440326 |
| 54 | 0.194213920440546 | 0.388427840881093 | 0.805786079559454 |
| 55 | 0.132094428020570 | 0.264188856041139 | 0.86790557197943 |
| 56 | 0.207467473951453 | 0.414934947902906 | 0.792532526048547 |
| 57 | 0.16515156893878 | 0.33030313787756 | 0.83484843106122 |
| 58 | 0.151190529244099 | 0.302381058488199 | 0.8488094707559 |
| 59 | 0.0957868379932259 | 0.191573675986452 | 0.904213162006774 |
| 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 |
