| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 952333.91111111 + 52432.9722222221X[t] -37833.4194444444M1[t] -209.672222221892M2[t] + 204791.075M3[t] + 372339.622222222M4[t] + 463427.569444444M5[t] + 475100.916666667M6[t] + 725201.263888889M7[t] + 617202.411111111M8[t] + 556696.158333333M9[t] + 394405.105555555M10[t] + 115945.252777778M11[t] + 3869.25277777778t + 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) | 952333.91111111 | 23528.996347 | 40.4749 | 0 | 0 |
| X | 52432.9722222221 | 21129.662477 | 2.4815 | 0.016799 | 0.008399 |
| M1 | -37833.4194444444 | 26228.315085 | -1.4425 | 0.155946 | 0.077973 |
| M2 | -209.672222221892 | 26078.945839 | -0.008 | 0.99362 | 0.49681 |
| M3 | 204791.075 | 25943.061198 | 7.8939 | 0 | 0 |
| M4 | 372339.622222222 | 25820.874055 | 14.4201 | 0 | 0 |
| M5 | 463427.569444444 | 25712.579684 | 18.0234 | 0 | 0 |
| M6 | 475100.916666667 | 25618.354269 | 18.5453 | 0 | 0 |
| M7 | 725201.263888889 | 25538.353535 | 28.3966 | 0 | 0 |
| M8 | 617202.411111111 | 25472.711507 | 24.2299 | 0 | 0 |
| M9 | 556696.158333333 | 25421.539413 | 21.8986 | 0 | 0 |
| M10 | 394405.105555555 | 25384.924762 | 15.537 | 0 | 0 |
| M11 | 115945.252777778 | 25362.930599 | 4.5714 | 3.6e-05 | 1.8e-05 |
| t | 3869.25277777778 | 609.960816 | 6.3434 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.991542565105353 |
| R-squared | 0.983156658415704 |
| Adjusted R-squared | 0.978396583620142 |
| F-TEST (value) | 206.542271002199 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 46 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 40090.7157698318 |
| Sum Squared Residuals | 73934212583.1223 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 921365 | 918369.744444445 | 2995.25555555506 |
| 2 | 987921 | 959862.744444444 | 28058.2555555558 |
| 3 | 1132614 | 1168732.74444444 | -36118.7444444446 |
| 4 | 1332224 | 1340150.54444445 | -7926.54444444494 |
| 5 | 1418133 | 1435107.74444444 | -16974.7444444443 |
| 6 | 1411549 | 1450650.34444445 | -39101.344444445 |
| 7 | 1695920 | 1704619.94444444 | -8699.94444444406 |
| 8 | 1636173 | 1600490.34444444 | 35682.6555555557 |
| 9 | 1539653 | 1543853.34444444 | -4200.34444444413 |
| 10 | 1395314 | 1385431.54444444 | 9882.45555555539 |
| 11 | 1127575 | 1110840.94444444 | 16734.0555555555 |
| 12 | 1036076 | 998764.944444444 | 37311.0555555556 |
| 13 | 989236 | 964800.777777778 | 24435.2222222224 |
| 14 | 1008380 | 1006293.77777778 | 2086.22222222239 |
| 15 | 1207763 | 1215163.77777778 | -7400.7777777777 |
| 16 | 1368839 | 1386581.57777778 | -17742.5777777776 |
| 17 | 1469798 | 1481538.77777778 | -11740.7777777778 |
| 18 | 1498721 | 1497081.37777778 | 1639.62222222239 |
| 19 | 1761769 | 1751050.97777778 | 10718.0222222222 |
| 20 | 1653214 | 1646921.37777778 | 6292.62222222226 |
| 21 | 1599104 | 1590284.37777778 | 8819.62222222224 |
| 22 | 1421179 | 1431862.57777778 | -10683.5777777777 |
| 23 | 1163995 | 1157271.97777778 | 6723.02222222223 |
| 24 | 1037735 | 1045195.97777778 | -7460.97777777782 |
| 25 | 1015407 | 1011231.81111111 | 4175.18888888893 |
| 26 | 1039210 | 1052724.81111111 | -13514.8111111112 |
| 27 | 1258049 | 1261594.81111111 | -3545.81111111111 |
| 28 | 1469445 | 1433012.61111111 | 36432.388888889 |
| 29 | 1552346 | 1527969.81111111 | 24376.1888888888 |
| 30 | 1549144 | 1543512.41111111 | 5631.58888888902 |
| 31 | 1785895 | 1797482.01111111 | -11587.0111111112 |
| 32 | 1662335 | 1693352.41111111 | -31017.4111111111 |
| 33 | 1629440 | 1636715.41111111 | -7275.41111111114 |
| 34 | 1467430 | 1478293.61111111 | -10863.6111111111 |
| 35 | 1202209 | 1203703.01111111 | -1494.01111111119 |
| 36 | 1076982 | 1091627.01111111 | -14645.0111111112 |
| 37 | 1039367 | 1110095.81666667 | -70728.8166666665 |
| 38 | 1063449 | 1151588.81666667 | -88139.8166666668 |
| 39 | 1335135 | 1360458.81666667 | -25323.8166666666 |
| 40 | 1491602 | 1531876.61666667 | -40274.6166666665 |
| 41 | 1591972 | 1626833.81666667 | -34861.8166666667 |
| 42 | 1641248 | 1642376.41666667 | -1128.41666666652 |
| 43 | 1898849 | 1896346.01666667 | 2502.98333333320 |
| 44 | 1798580 | 1792216.41666667 | 6363.5833333333 |
| 45 | 1762444 | 1735579.41666667 | 26864.5833333332 |
| 46 | 1622044 | 1577157.61666667 | 44886.3833333334 |
| 47 | 1368955 | 1302567.01666667 | 66387.9833333334 |
| 48 | 1262973 | 1190491.01666667 | 72481.9833333334 |
| 49 | 1195650 | 1156526.85 | 39123.1500000001 |
| 50 | 1269530 | 1198019.85 | 71510.1499999999 |
| 51 | 1479279 | 1406889.85 | 72389.15 |
| 52 | 1607819 | 1578307.65 | 29511.3500000001 |
| 53 | 1712466 | 1673264.85 | 39201.1499999999 |
| 54 | 1721766 | 1688807.45 | 32958.5500000001 |
| 55 | 1949843 | 1942777.05 | 7065.9499999998 |
| 56 | 1821326 | 1838647.45 | -17321.4500000001 |
| 57 | 1757802 | 1782010.45 | -24208.4500000002 |
| 58 | 1590367 | 1623588.65 | -33221.65 |
| 59 | 1260647 | 1348998.05 | -88351.05 |
| 60 | 1149235 | 1236922.05 | -87687.05 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.0739122554076299 | 0.147824510815260 | 0.92608774459237 |
| 18 | 0.050540567873202 | 0.101081135746404 | 0.949459432126798 |
| 19 | 0.0181574157192374 | 0.0363148314384748 | 0.981842584280763 |
| 20 | 0.0154640491833394 | 0.0309280983666788 | 0.98453595081666 |
| 21 | 0.00549393608971369 | 0.0109878721794274 | 0.994506063910286 |
| 22 | 0.00282909992073826 | 0.00565819984147652 | 0.997170900079262 |
| 23 | 0.00104242204552191 | 0.00208484409104382 | 0.998957577954478 |
| 24 | 0.00125126120082128 | 0.00250252240164256 | 0.998748738799179 |
| 25 | 0.000440053005792219 | 0.000880106011584438 | 0.999559946994208 |
| 26 | 0.000216073609185294 | 0.000432147218370588 | 0.999783926390815 |
| 27 | 0.000109174461181898 | 0.000218348922363796 | 0.999890825538818 |
| 28 | 0.000222214201121020 | 0.000444428402242040 | 0.99977778579888 |
| 29 | 0.000157529950884210 | 0.000315059901768421 | 0.999842470049116 |
| 30 | 6.13886303523405e-05 | 0.000122777260704681 | 0.999938611369648 |
| 31 | 2.50468944862047e-05 | 5.00937889724094e-05 | 0.999974953105514 |
| 32 | 4.64012871780496e-05 | 9.28025743560991e-05 | 0.999953598712822 |
| 33 | 1.57694306437690e-05 | 3.15388612875379e-05 | 0.999984230569356 |
| 34 | 5.1540956779474e-06 | 1.03081913558948e-05 | 0.999994845904322 |
| 35 | 1.61897321064977e-06 | 3.23794642129954e-06 | 0.99999838102679 |
| 36 | 6.73548984820819e-07 | 1.34709796964164e-06 | 0.999999326451015 |
| 37 | 4.40564645005409e-07 | 8.81129290010818e-07 | 0.999999559435355 |
| 38 | 2.18226517834296e-06 | 4.36453035668591e-06 | 0.999997817734822 |
| 39 | 3.54583605312925e-05 | 7.0916721062585e-05 | 0.999964541639469 |
| 40 | 6.41198500359249e-05 | 0.000128239700071850 | 0.999935880149964 |
| 41 | 0.000422817609003540 | 0.000845635218007081 | 0.999577182390996 |
| 42 | 0.00379649812140028 | 0.00759299624280056 | 0.9962035018786 |
| 43 | 0.0153046039093696 | 0.0306092078187392 | 0.98469539609063 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 21 | 0.777777777777778 | NOK |
| 5% type I error level | 25 | 0.925925925925926 | NOK |
| 10% type I error level | 25 | 0.925925925925926 | NOK |
