| Multiple Linear Regression - Estimated Regression Equation |
| Births[t] = + 9330.6231884058 + 107.616287094544M1[t] -635.535541752933M2[t] -287.830227743271M3[t] + 8.73844030365812M4[t] -879.770531400966M5[t] + 75.7204968944103M6[t] -309.621808143547M7[t] -141.297446514838M8[t] -196.973084886128M9[t] + 367.351276742581M10[t] + 234.508971704624M11[t] + 11.0089717046239t + 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) | 9330.6231884058 | 136.438321 | 68.3871 | 0 | 0 |
| M1 | 107.616287094544 | 162.991916 | 0.6603 | 0.511536 | 0.255768 |
| M2 | -635.535541752933 | 162.923919 | -3.9008 | 0.000239 | 0.000119 |
| M3 | -287.830227743271 | 162.871013 | -1.7672 | 0.082111 | 0.041056 |
| M4 | 8.73844030365812 | 169.414367 | 0.0516 | 0.959029 | 0.479514 |
| M5 | -879.770531400966 | 169.305323 | -5.1964 | 2e-06 | 1e-06 |
| M6 | 75.7204968944103 | 169.210762 | 0.4475 | 0.656079 | 0.32804 |
| M7 | -309.621808143547 | 169.130707 | -1.8307 | 0.071957 | 0.035979 |
| M8 | -141.297446514838 | 169.065179 | -0.8358 | 0.406501 | 0.20325 |
| M9 | -196.973084886128 | 169.014195 | -1.1654 | 0.248312 | 0.124156 |
| M10 | 367.351276742581 | 168.977769 | 2.174 | 0.033534 | 0.016767 |
| M11 | 234.508971704624 | 168.95591 | 1.388 | 0.170108 | 0.085054 |
| t | 11.0089717046239 | 1.56919 | 7.0157 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.846476842937978 |
| R-squared | 0.716523045630245 |
| Adjusted R-squared | 0.661656538332874 |
| F-TEST (value) | 13.0593887040549 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 62 |
| p-value | 8.08797473439427e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 292.627597935097 |
| Sum Squared Residuals | 5309116.48654243 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 9700 | 9449.248447205 | 250.751552795006 |
| 2 | 9081 | 8717.10559006211 | 363.894409937889 |
| 3 | 9084 | 9075.8198757764 | 8.18012422360365 |
| 4 | 9743 | 9383.39751552795 | 359.602484472051 |
| 5 | 8587 | 8505.89751552795 | 81.1024844720503 |
| 6 | 9731 | 9472.39751552795 | 258.602484472051 |
| 7 | 9563 | 9098.06418219462 | 464.935817805384 |
| 8 | 9998 | 9277.39751552795 | 720.60248447205 |
| 9 | 9437 | 9232.73084886128 | 204.269151138717 |
| 10 | 10039 | 9808.06418219462 | 230.935817805384 |
| 11 | 9918 | 9686.23084886128 | 231.769151138717 |
| 12 | 9252 | 9462.73084886128 | -210.730848861283 |
| 13 | 9737 | 9581.35610766045 | 155.643892339550 |
| 14 | 9035 | 8849.2132505176 | 185.786749482402 |
| 15 | 9133 | 9207.92753623188 | -74.9275362318834 |
| 16 | 9487 | 9515.50517598344 | -28.5051759834363 |
| 17 | 8700 | 8638.00517598344 | 61.9948240165638 |
| 18 | 9627 | 9604.50517598344 | 22.4948240165637 |
| 19 | 8947 | 9230.1718426501 | -283.171842650103 |
| 20 | 9283 | 9409.50517598344 | -126.505175983436 |
| 21 | 8829 | 9364.83850931677 | -535.83850931677 |
| 22 | 9947 | 9940.1718426501 | 6.82815734989703 |
| 23 | 9628 | 9818.33850931677 | -190.338509316770 |
| 24 | 9318 | 9594.83850931677 | -276.838509316770 |
| 25 | 9605 | 9713.46376811594 | -108.463768115937 |
| 26 | 8640 | 8981.32091097309 | -341.320910973085 |
| 27 | 9214 | 9340.03519668737 | -126.035196687370 |
| 28 | 9567 | 9647.61283643892 | -80.6128364389232 |
| 29 | 8547 | 8770.11283643892 | -223.112836438923 |
| 30 | 9185 | 9736.61283643892 | -551.612836438923 |
| 31 | 9470 | 9362.27950310559 | 107.720496894410 |
| 32 | 9123 | 9541.61283643892 | -418.612836438923 |
| 33 | 9278 | 9496.94616977226 | -218.946169772257 |
| 34 | 10170 | 10072.2795031056 | 97.7204968944101 |
| 35 | 9434 | 9950.44616977226 | -516.446169772257 |
| 36 | 9655 | 9726.94616977226 | -71.9461697722564 |
| 37 | 9429 | 9845.57142857142 | -416.571428571424 |
| 38 | 8739 | 9113.42857142857 | -374.428571428571 |
| 39 | 9552 | 9472.14285714286 | 79.8571428571428 |
| 40 | 9687 | 9779.7204968944 | -92.7204968944101 |
| 41 | 9019 | 8902.22049689441 | 116.77950310559 |
| 42 | 9672 | 9868.7204968944 | -196.72049689441 |
| 43 | 9206 | 9494.38716356108 | -288.387163561077 |
| 44 | 9069 | 9673.72049689441 | -604.72049689441 |
| 45 | 9788 | 9629.05383022774 | 158.946169772256 |
| 46 | 10312 | 10204.3871635611 | 107.612836438923 |
| 47 | 10105 | 10082.5538302277 | 22.4461697722565 |
| 48 | 9863 | 9859.05383022774 | 3.94616977225661 |
| 49 | 9656 | 9977.67908902691 | -321.679089026911 |
| 50 | 9295 | 9245.53623188406 | 49.4637681159416 |
| 51 | 9946 | 9604.25051759834 | 341.749482401656 |
| 52 | 9701 | 9911.8281573499 | -210.828157349897 |
| 53 | 9049 | 9034.3281573499 | 14.6718426501029 |
| 54 | 10190 | 10000.8281573499 | 189.171842650103 |
| 55 | 9706 | 9626.49482401656 | 79.5051759834362 |
| 56 | 9765 | 9805.8281573499 | -40.8281573498971 |
| 57 | 9893 | 9761.16149068323 | 131.838509316770 |
| 58 | 9994 | 10336.4948240166 | -342.494824016564 |
| 59 | 10433 | 10214.6614906832 | 218.338509316770 |
| 60 | 10073 | 9991.16149068323 | 81.8385093167697 |
| 61 | 10112 | 10109.7867494824 | 2.21325051760193 |
| 62 | 9266 | 9377.64389233955 | -111.643892339545 |
| 63 | 9820 | 9736.35817805383 | 83.6418219461689 |
| 64 | 10097 | 10043.9358178054 | 53.064182194616 |
| 65 | 9115 | 9166.43581780538 | -51.4358178053838 |
| 66 | 10411 | 10132.9358178054 | 278.064182194616 |
| 67 | 9678 | 9758.60248447205 | -80.6024844720507 |
| 68 | 10408 | 9937.93581780538 | 470.064182194616 |
| 69 | 10153 | 9893.26915113872 | 259.730848861283 |
| 70 | 10368 | 10468.6024844721 | -100.602484472051 |
| 71 | 10581 | 10346.7691511387 | 234.230848861283 |
| 72 | 10597 | 10123.2691511387 | 473.730848861283 |
| 73 | 10680 | 10241.8944099379 | 438.105590062115 |
| 74 | 9738 | 9509.75155279503 | 228.248447204968 |
| 75 | 9556 | 9868.46583850932 | -312.465838509318 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0857950324780317 | 0.171590064956063 | 0.914204967521968 |
| 17 | 0.0524991423628487 | 0.104998284725697 | 0.947500857637151 |
| 18 | 0.0231043965667466 | 0.0462087931334933 | 0.976895603433253 |
| 19 | 0.231495210219771 | 0.462990420439541 | 0.76850478978023 |
| 20 | 0.455792536295226 | 0.911585072590453 | 0.544207463704774 |
| 21 | 0.504624854768493 | 0.990750290463014 | 0.495375145231507 |
| 22 | 0.437456128742004 | 0.874912257484009 | 0.562543871257996 |
| 23 | 0.340133745453152 | 0.680267490906304 | 0.659866254546848 |
| 24 | 0.310692455296403 | 0.621384910592806 | 0.689307544703597 |
| 25 | 0.267120809636914 | 0.534241619273828 | 0.732879190363086 |
| 26 | 0.206731687361517 | 0.413463374723033 | 0.793268312638483 |
| 27 | 0.239844142132692 | 0.479688284265384 | 0.760155857867308 |
| 28 | 0.205581894907057 | 0.411163789814114 | 0.794418105092943 |
| 29 | 0.153234914208051 | 0.306469828416101 | 0.84676508579195 |
| 30 | 0.172957135267870 | 0.345914270535741 | 0.82704286473213 |
| 31 | 0.267970244265079 | 0.535940488530159 | 0.73202975573492 |
| 32 | 0.26137013599641 | 0.52274027199282 | 0.73862986400359 |
| 33 | 0.268430672150749 | 0.536861344301499 | 0.73156932784925 |
| 34 | 0.342786019861389 | 0.685572039722779 | 0.65721398013861 |
| 35 | 0.358549701599177 | 0.717099403198355 | 0.641450298400823 |
| 36 | 0.431739198587508 | 0.863478397175016 | 0.568260801412492 |
| 37 | 0.380196293293068 | 0.760392586586136 | 0.619803706706932 |
| 38 | 0.328943489855802 | 0.657886979711604 | 0.671056510144198 |
| 39 | 0.450397184889652 | 0.900794369779304 | 0.549602815110348 |
| 40 | 0.403099124692339 | 0.806198249384678 | 0.596900875307661 |
| 41 | 0.485034456755899 | 0.970068913511797 | 0.514965543244101 |
| 42 | 0.454268641179832 | 0.908537282359664 | 0.545731358820168 |
| 43 | 0.380707848314169 | 0.761415696628338 | 0.619292151685831 |
| 44 | 0.606071238392927 | 0.787857523214147 | 0.393928761607073 |
| 45 | 0.674969372556427 | 0.650061254887147 | 0.325030627443573 |
| 46 | 0.752228437215017 | 0.495543125569966 | 0.247771562784983 |
| 47 | 0.728763241613885 | 0.542473516772231 | 0.271236758386115 |
| 48 | 0.704101815787326 | 0.591796368425348 | 0.295898184212674 |
| 49 | 0.747094349261184 | 0.505811301477633 | 0.252905650738816 |
| 50 | 0.699397735368026 | 0.601204529263948 | 0.300602264631974 |
| 51 | 0.916220847455845 | 0.167558305088310 | 0.0837791525441551 |
| 52 | 0.872681982634765 | 0.254636034730471 | 0.127318017365235 |
| 53 | 0.837583282163457 | 0.324833435673085 | 0.162416717836543 |
| 54 | 0.79132209024671 | 0.417355819506579 | 0.208677909753290 |
| 55 | 0.789487349144987 | 0.421025301710025 | 0.210512650855013 |
| 56 | 0.77593043117339 | 0.44813913765322 | 0.22406956882661 |
| 57 | 0.673067406242274 | 0.653865187515451 | 0.326932593757726 |
| 58 | 0.539475400383979 | 0.921049199232042 | 0.460524599616021 |
| 59 | 0.416134471360841 | 0.832268942721682 | 0.583865528639159 |
| 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 |
