| Multiple Linear Regression - Estimated Regression Equation |
| Births_per_month[t] = + 9330.58695652174 + 107.620600414077M1[t] -635.532091097308M2[t] -287.827639751553M3[t] + 8.74534161490679M4[t] -879.764492753623M5[t] + 75.7256728778466M6[t] -309.617494824017M7[t] -141.293995859213M8[t] -196.97049689441M9[t] + 367.186335403727M10[t] + 234.50983436853M11[t] + 11.00983436853t + 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) | 9330.58695652174 | 136.432397 | 68.3898 | 0 | 0 |
| M1 | 107.620600414077 | 162.984839 | 0.6603 | 0.5115 | 0.25575 |
| M2 | -635.532091097308 | 162.916845 | -3.901 | 0.000238 | 0.000119 |
| M3 | -287.827639751553 | 162.863941 | -1.7673 | 0.082101 | 0.04105 |
| M4 | 8.74534161490679 | 169.407011 | 0.0516 | 0.958995 | 0.479497 |
| M5 | -879.764492753623 | 169.297972 | -5.1965 | 2e-06 | 1e-06 |
| M6 | 75.7256728778466 | 169.203414 | 0.4475 | 0.656043 | 0.328022 |
| M7 | -309.617494824017 | 169.123363 | -1.8307 | 0.071949 | 0.035975 |
| M8 | -141.293995859213 | 169.057838 | -0.8358 | 0.406492 | 0.203246 |
| M9 | -196.97049689441 | 169.006856 | -1.1655 | 0.248298 | 0.124149 |
| M10 | 367.186335403727 | 168.970432 | 2.1731 | 0.033604 | 0.016802 |
| M11 | 234.50983436853 | 168.948573 | 1.3881 | 0.170088 | 0.085044 |
| t | 11.00983436853 | 1.569122 | 7.0166 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.846483642463992 |
| R-squared | 0.716534556959107 |
| Adjusted R-squared | 0.661670277660869 |
| F-TEST (value) | 13.0601288511253 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 62 |
| p-value | 8.07798272717264e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 292.614891203776 |
| Sum Squared Residuals | 5308655.42236025 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9449.21739130436 | 250.782608695645 |
| 2 | 9081 | 8717.07453416149 | 363.92546583851 |
| 3 | 9084 | 9075.78881987578 | 8.21118012422378 |
| 4 | 9743 | 9383.37163561077 | 359.628364389234 |
| 5 | 8587 | 8505.87163561077 | 81.128364389234 |
| 6 | 9731 | 9472.37163561077 | 258.628364389234 |
| 7 | 9563 | 9098.03830227743 | 464.961697722568 |
| 8 | 9998 | 9277.37163561077 | 720.628364389234 |
| 9 | 9437 | 9232.7049689441 | 204.295031055901 |
| 10 | 10038 | 9807.87163561077 | 230.128364389234 |
| 11 | 9918 | 9686.2049689441 | 231.795031055901 |
| 12 | 9252 | 9462.7049689441 | -210.704968944099 |
| 13 | 9737 | 9581.33540372671 | 155.664596273294 |
| 14 | 9035 | 8849.19254658385 | 185.807453416149 |
| 15 | 9133 | 9207.90683229814 | -74.9068322981364 |
| 16 | 9487 | 9515.48964803313 | -28.4896480331261 |
| 17 | 8700 | 8637.98964803313 | 62.010351966874 |
| 18 | 9627 | 9604.48964803313 | 22.510351966874 |
| 19 | 8947 | 9230.15631469979 | -283.156314699793 |
| 20 | 9283 | 9409.48964803313 | -126.489648033126 |
| 21 | 8829 | 9364.82298136646 | -535.82298136646 |
| 22 | 9947 | 9939.98964803313 | 7.01035196687387 |
| 23 | 9628 | 9818.32298136646 | -190.32298136646 |
| 24 | 9318 | 9594.82298136646 | -276.82298136646 |
| 25 | 9605 | 9713.45341614907 | -108.453416149067 |
| 26 | 8640 | 8981.31055900621 | -341.310559006211 |
| 27 | 9214 | 9340.0248447205 | -126.024844720497 |
| 28 | 9567 | 9647.60766045549 | -80.6076604554865 |
| 29 | 8547 | 8770.10766045549 | -223.107660455486 |
| 30 | 9185 | 9736.60766045549 | -551.607660455487 |
| 31 | 9470 | 9362.27432712215 | 107.725672877847 |
| 32 | 9123 | 9541.60766045549 | -418.607660455486 |
| 33 | 9278 | 9496.94099378882 | -218.94099378882 |
| 34 | 10170 | 10072.1076604555 | 97.8923395445136 |
| 35 | 9434 | 9950.44099378882 | -516.44099378882 |
| 36 | 9655 | 9726.94099378882 | -71.9409937888199 |
| 37 | 9429 | 9845.57142857143 | -416.571428571427 |
| 38 | 8739 | 9113.42857142857 | -374.428571428571 |
| 39 | 9552 | 9472.14285714286 | 79.8571428571429 |
| 40 | 9687 | 9779.72567287785 | -92.7256728778469 |
| 41 | 9019 | 8902.22567287785 | 116.774327122153 |
| 42 | 9672 | 9868.72567287785 | -196.725672877847 |
| 43 | 9206 | 9494.39233954451 | -288.392339544514 |
| 44 | 9069 | 9673.72567287785 | -604.725672877847 |
| 45 | 9788 | 9629.05900621118 | 158.94099378882 |
| 46 | 10312 | 10204.2256728778 | 107.774327122153 |
| 47 | 10105 | 10082.5590062112 | 22.4409937888197 |
| 48 | 9863 | 9859.05900621118 | 3.94099378881965 |
| 49 | 9656 | 9977.68944099379 | -321.689440993788 |
| 50 | 9295 | 9245.54658385093 | 49.4534161490682 |
| 51 | 9946 | 9604.26086956522 | 341.739130434783 |
| 52 | 9701 | 9911.84368530021 | -210.843685300207 |
| 53 | 9049 | 9034.34368530021 | 14.6563146997928 |
| 54 | 10190 | 10000.8436853002 | 189.156314699793 |
| 55 | 9706 | 9626.51035196687 | 79.489648033126 |
| 56 | 9765 | 9805.84368530021 | -40.8436853002073 |
| 57 | 9893 | 9761.17701863354 | 131.822981366459 |
| 58 | 9994 | 10336.3436853002 | -342.343685300207 |
| 59 | 10433 | 10214.6770186335 | 218.32298136646 |
| 60 | 10073 | 9991.17701863354 | 81.8229813664593 |
| 61 | 10112 | 10109.8074534161 | 2.19254658385198 |
| 62 | 9266 | 9377.66459627329 | -111.664596273292 |
| 63 | 9820 | 9736.37888198758 | 83.6211180124221 |
| 64 | 10097 | 10043.9616977226 | 53.0383022774324 |
| 65 | 9115 | 9166.46169772257 | -51.4616977225677 |
| 66 | 10411 | 10132.9616977226 | 278.038302277433 |
| 67 | 9678 | 9758.62836438923 | -80.6283643892342 |
| 68 | 10408 | 9937.96169772257 | 470.038302277433 |
| 69 | 10153 | 9893.2950310559 | 259.704968944099 |
| 70 | 10368 | 10468.4616977226 | -100.461697722567 |
| 71 | 10581 | 10346.7950310559 | 234.204968944099 |
| 72 | 10597 | 10123.2950310559 | 473.704968944099 |
| 73 | 10680 | 10241.9254658385 | 438.074534161492 |
| 74 | 9738 | 9509.78260869565 | 228.217391304347 |
| 75 | 9556 | 9868.49689440994 | -312.496894409938 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0857950324780312 | 0.171590064956062 | 0.914204967521969 |
| 17 | 0.0524991423628487 | 0.104998284725697 | 0.947500857637151 |
| 18 | 0.023104396566747 | 0.0462087931334939 | 0.976895603433253 |
| 19 | 0.231495210219769 | 0.462990420439537 | 0.768504789780231 |
| 20 | 0.455792536295224 | 0.911585072590448 | 0.544207463704776 |
| 21 | 0.504624854768491 | 0.990750290463017 | 0.495375145231509 |
| 22 | 0.437677666203556 | 0.875355332407112 | 0.562322333796444 |
| 23 | 0.340351871668432 | 0.680703743336865 | 0.659648128331568 |
| 24 | 0.310855860228004 | 0.621711720456009 | 0.689144139771996 |
| 25 | 0.267236336881096 | 0.534472673762192 | 0.732763663118904 |
| 26 | 0.20684988325679 | 0.413699766513581 | 0.79315011674321 |
| 27 | 0.23991625264691 | 0.47983250529382 | 0.76008374735309 |
| 28 | 0.205631454710158 | 0.411262909420317 | 0.794368545289842 |
| 29 | 0.153268958573314 | 0.306537917146629 | 0.846731041426686 |
| 30 | 0.173008461432075 | 0.34601692286415 | 0.826991538567925 |
| 31 | 0.268002998181083 | 0.536005996362166 | 0.731997001818917 |
| 32 | 0.261416420975536 | 0.522832841951071 | 0.738583579024464 |
| 33 | 0.268458916033421 | 0.536917832066843 | 0.731541083966579 |
| 34 | 0.342995129165927 | 0.685990258331853 | 0.657004870834073 |
| 35 | 0.358773674727471 | 0.717547349454941 | 0.641226325272529 |
| 36 | 0.431905718587353 | 0.863811437174706 | 0.568094281412647 |
| 37 | 0.380362945006806 | 0.760725890013611 | 0.619637054993194 |
| 38 | 0.329100876838706 | 0.658201753677411 | 0.670899123161294 |
| 39 | 0.450505003315906 | 0.901010006631813 | 0.549494996684094 |
| 40 | 0.403190199995984 | 0.806380399991967 | 0.596809800004017 |
| 41 | 0.485094127735028 | 0.970188255470056 | 0.514905872264972 |
| 42 | 0.454317102071593 | 0.908634204143185 | 0.545682897928407 |
| 43 | 0.380756271864458 | 0.761512543728915 | 0.619243728135542 |
| 44 | 0.606126854145477 | 0.787746291709047 | 0.393873145854523 |
| 45 | 0.674996769060583 | 0.650006461878834 | 0.325003230939417 |
| 46 | 0.752290768263355 | 0.495418463473291 | 0.247709231736645 |
| 47 | 0.728811920081673 | 0.542376159836653 | 0.271188079918327 |
| 48 | 0.704138728110714 | 0.591722543778572 | 0.295861271889286 |
| 49 | 0.74712682558055 | 0.505746348838901 | 0.25287317441945 |
| 50 | 0.699421991351507 | 0.601156017296987 | 0.300578008648493 |
| 51 | 0.916224561685615 | 0.167550876628771 | 0.0837754383143854 |
| 52 | 0.872687059430543 | 0.254625881138913 | 0.127312940569457 |
| 53 | 0.8375866932 | 0.324826613600001 | 0.1624133068 |
| 54 | 0.791320712635808 | 0.417358574728383 | 0.208679287364191 |
| 55 | 0.789483857956299 | 0.421032284087401 | 0.210516142043701 |
| 56 | 0.775925335602774 | 0.448149328794452 | 0.224074664397226 |
| 57 | 0.673058641197512 | 0.653882717604975 | 0.326941358802487 |
| 58 | 0.53945230881435 | 0.9210953823713 | 0.46054769118565 |
| 59 | 0.416110442244623 | 0.832220884489246 | 0.583889557755377 |
| 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 | 1 | 0.0227272727272727 | OK |
