| Multiple Linear Regression - Estimated Regression Equation |
| gk[t] = + 15.8797850467290 + 4.89964485981308cr[t] + 1.47280373831776M1[t] + 0.922803738317753M2[t] + 0.662303738317755M3[t] + 0.946553738317755M4[t] + 0.657553738317754M5[t] + 1.23780373831775M6[t] + 1.03880373831775M7[t] + 1.36005373831776M8[t] + 1.65080373831776M9[t] + 0.482053738317755M10[t] -0.476696261682245M11[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) | 15.8797850467290 | 1.018703 | 15.5882 | 0 | 0 |
| cr | 4.89964485981308 | 0.580146 | 8.4455 | 0 | 0 |
| M1 | 1.47280373831776 | 1.323996 | 1.1124 | 0.273773 | 0.136886 |
| M2 | 0.922803738317753 | 1.323996 | 0.697 | 0.490551 | 0.245276 |
| M3 | 0.662303738317755 | 1.323996 | 0.5002 | 0.620135 | 0.310067 |
| M4 | 0.946553738317755 | 1.323996 | 0.7149 | 0.479538 | 0.239769 |
| M5 | 0.657553738317754 | 1.323996 | 0.4966 | 0.622637 | 0.311318 |
| M6 | 1.23780373831775 | 1.323996 | 0.9349 | 0.356433 | 0.178216 |
| M7 | 1.03880373831775 | 1.323996 | 0.7846 | 0.438122 | 0.219061 |
| M8 | 1.36005373831776 | 1.323996 | 1.0272 | 0.311563 | 0.155782 |
| M9 | 1.65080373831776 | 1.323996 | 1.2468 | 0.22098 | 0.11049 |
| M10 | 0.482053738317755 | 1.323996 | 0.3641 | 0.718045 | 0.359023 |
| M11 | -0.476696261682245 | 1.323996 | -0.36 | 0.721041 | 0.360521 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.831416003623353 |
| R-squared | 0.691252571081027 |
| Adjusted R-squared | 0.582282890286095 |
| F-TEST (value) | 6.34353121013436 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 34 |
| p-value | 9.94366698381377e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.73236122050102 |
| Sum Squared Residuals | 102.036563542056 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 22.68 | 22.2522336448598 | 0.427766355140204 |
| 2 | 22.052 | 21.7022336448598 | 0.349766355140177 |
| 3 | 21.467 | 21.4417336448598 | 0.0252663551401843 |
| 4 | 21.383 | 21.7259836448598 | -0.342983644859815 |
| 5 | 21.777 | 21.4369836448598 | 0.340016355140188 |
| 6 | 21.928 | 22.0172336448598 | -0.0892336448598124 |
| 7 | 21.814 | 21.8182336448598 | -0.00423364485981282 |
| 8 | 22.937 | 22.1394836448598 | 0.797516355140187 |
| 9 | 23.595 | 22.4302336448598 | 1.16476635514019 |
| 10 | 20.83 | 21.2614836448598 | -0.431483644859814 |
| 11 | 19.65 | 20.3027336448598 | -0.652733644859815 |
| 12 | 19.195 | 20.7794299065421 | -1.58442990654206 |
| 13 | 19.644 | 17.3525887850467 | 2.29141121495327 |
| 14 | 18.483 | 16.8025887850467 | 1.68041121495327 |
| 15 | 18.079 | 16.5420887850467 | 1.53691121495327 |
| 16 | 19.178 | 16.8263387850467 | 2.35166121495327 |
| 17 | 18.391 | 16.5373387850467 | 1.85366121495327 |
| 18 | 18.441 | 17.1175887850467 | 1.32341121495327 |
| 19 | 18.584 | 16.9185887850467 | 1.66541121495327 |
| 20 | 20.108 | 17.2398387850467 | 2.86816121495327 |
| 21 | 20.148 | 17.5305887850467 | 2.61741121495327 |
| 22 | 19.394 | 16.3618387850467 | 3.03216121495327 |
| 23 | 17.745 | 15.4030887850467 | 2.34191121495327 |
| 24 | 17.696 | 15.8797850467290 | 1.81621495327103 |
| 25 | 17.032 | 17.3525887850467 | -0.320588785046736 |
| 26 | 16.438 | 16.8025887850467 | -0.364588785046727 |
| 27 | 15.683 | 16.5420887850467 | -0.859088785046729 |
| 28 | 15.594 | 16.8263387850467 | -1.23233878504673 |
| 29 | 15.713 | 16.5373387850467 | -0.82433878504673 |
| 30 | 15.937 | 17.1175887850467 | -1.18058878504673 |
| 31 | 16.171 | 16.9185887850467 | -0.74758878504673 |
| 32 | 15.928 | 17.2398387850467 | -1.31183878504673 |
| 33 | 16.348 | 17.5305887850467 | -1.18258878504673 |
| 34 | 15.579 | 16.3618387850467 | -0.782838785046727 |
| 35 | 15.305 | 15.4030887850467 | -0.0980887850467276 |
| 36 | 15.648 | 15.8797850467290 | -0.231785046728974 |
| 37 | 14.954 | 17.3525887850467 | -2.39858878504673 |
| 38 | 15.137 | 16.8025887850467 | -1.66558878504673 |
| 39 | 15.839 | 16.5420887850467 | -0.703088785046728 |
| 40 | 16.05 | 16.8263387850467 | -0.776338785046728 |
| 41 | 15.168 | 16.5373387850467 | -1.36933878504673 |
| 42 | 17.064 | 17.1175887850467 | -0.0535887850467288 |
| 43 | 16.005 | 16.9185887850467 | -0.91358878504673 |
| 44 | 14.886 | 17.2398387850467 | -2.35383878504673 |
| 45 | 14.931 | 17.5305887850467 | -2.59958878504673 |
| 46 | 14.544 | 16.3618387850467 | -1.81783878504673 |
| 47 | 13.812 | 15.4030887850467 | -1.59108878504673 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0142006076382903 | 0.0284012152765806 | 0.98579939236171 |
| 17 | 0.00331858970101251 | 0.00663717940202502 | 0.996681410298987 |
| 18 | 0.000738097515788324 | 0.00147619503157665 | 0.999261902484212 |
| 19 | 0.000139991188941082 | 0.000279982377882164 | 0.999860008811059 |
| 20 | 7.32207682626125e-05 | 0.000146441536525225 | 0.999926779231737 |
| 21 | 6.32176817919617e-05 | 0.000126435363583923 | 0.999936782318208 |
| 22 | 0.00694134151904918 | 0.0138826830380984 | 0.99305865848095 |
| 23 | 0.0405469112272844 | 0.0810938224545688 | 0.959453088772716 |
| 24 | 0.106071407858608 | 0.212142815717215 | 0.893928592141392 |
| 25 | 0.635534331607374 | 0.728931336785253 | 0.364465668392626 |
| 26 | 0.796318387598945 | 0.407363224802109 | 0.203681612401055 |
| 27 | 0.817655840169544 | 0.364688319660911 | 0.182344159830456 |
| 28 | 0.838526441298317 | 0.322947117403366 | 0.161473558701683 |
| 29 | 0.80617970836341 | 0.38764058327318 | 0.19382029163659 |
| 30 | 0.781451080445735 | 0.437097839108530 | 0.218548919554265 |
| 31 | 0.65182362264326 | 0.696352754713479 | 0.348176377356740 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 5 | 0.3125 | NOK |
| 5% type I error level | 7 | 0.4375 | NOK |
| 10% type I error level | 8 | 0.5 | NOK |
