| Multiple Linear Regression - Estimated Regression Equation |
| wkl[t] = + 477.993760890492 + 0.000337047508224897bvg[t] -8.15082618449848M1[t] -20.0515922400293M2[t] -13.4216469414095M3[t] -8.84333732104988M4[t] -8.88767330186228M5[t] -11.9050494733973M6[t] -13.1368512782844M7[t] -17.0475856182171M8[t] -15.2677929888212M9[t] + 6.19349772806338M10[t] + 8.45229429338714M11[t] -1.03850630532863t + 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) | 477.993760890492 | 31.666012 | 15.0949 | 0 | 0 |
| bvg | 0.000337047508224897 | 0.011353 | 0.0297 | 0.976442 | 0.488221 |
| M1 | -8.15082618449848 | 12.732764 | -0.6401 | 0.525186 | 0.262593 |
| M2 | -20.0515922400293 | 13.754834 | -1.4578 | 0.15155 | 0.075775 |
| M3 | -13.4216469414095 | 13.595873 | -0.9872 | 0.328607 | 0.164303 |
| M4 | -8.84333732104988 | 12.950613 | -0.6829 | 0.498053 | 0.249027 |
| M5 | -8.88767330186228 | 14.304897 | -0.6213 | 0.537402 | 0.268701 |
| M6 | -11.9050494733973 | 13.475594 | -0.8835 | 0.381489 | 0.190744 |
| M7 | -13.1368512782844 | 12.801573 | -1.0262 | 0.310055 | 0.155027 |
| M8 | -17.0475856182171 | 13.184982 | -1.293 | 0.202346 | 0.101173 |
| M9 | -15.2677929888212 | 12.714327 | -1.2008 | 0.235833 | 0.117916 |
| M10 | 6.19349772806338 | 12.827693 | 0.4828 | 0.631463 | 0.315732 |
| M11 | 8.45229429338714 | 12.956477 | 0.6524 | 0.517347 | 0.258673 |
| t | -1.03850630532863 | 0.172032 | -6.0367 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.741731690526168 |
| R-squared | 0.550165900730807 |
| Adjusted R-squared | 0.425743703060604 |
| F-TEST (value) | 4.42176646155290 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 47 |
| p-value | 7.76836363377553e-05 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 19.8705683838929 |
| Sum Squared Residuals | 18557.4559312513 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 462 | 469.451222568948 | -7.45122256894819 |
| 2 | 455 | 456.509253828024 | -1.50925382802365 |
| 3 | 461 | 462.086873873477 | -1.08687387347749 |
| 4 | 461 | 465.759136859241 | -4.75913685924094 |
| 5 | 463 | 464.520915671808 | -1.52091567180823 |
| 6 | 462 | 460.485593092946 | 1.51440690705374 |
| 7 | 456 | 458.257752968767 | -2.25775296876687 |
| 8 | 455 | 453.378618205216 | 1.62138179478368 |
| 9 | 456 | 454.191358601027 | 1.8086413989728 |
| 10 | 472 | 474.645488430848 | -2.64548843084813 |
| 11 | 472 | 475.896450014092 | -3.89645001409176 |
| 12 | 471 | 466.407334652917 | 4.59266534708293 |
| 13 | 465 | 457.034311271107 | 7.9656887288926 |
| 14 | 459 | 444.148966511564 | 14.8510334884360 |
| 15 | 465 | 449.748831692561 | 15.2511683074393 |
| 16 | 468 | 453.329417756087 | 14.6705822439131 |
| 17 | 467 | 452.176469588235 | 14.8235304117649 |
| 18 | 463 | 448.229453456528 | 14.7705465434719 |
| 19 | 460 | 446.163059088788 | 13.8369409112116 |
| 20 | 462 | 440.955303004719 | 21.0446969952814 |
| 21 | 461 | 441.781862348367 | 19.2181376516333 |
| 22 | 476 | 462.004777587545 | 13.9952224124546 |
| 23 | 476 | 463.397636171752 | 12.6023638282484 |
| 24 | 471 | 453.811788175716 | 17.1882118242836 |
| 25 | 453 | 444.60526626297 | 8.39473373703014 |
| 26 | 443 | 431.607010588171 | 11.3929894118289 |
| 27 | 442 | 437.210583291758 | 4.78941670824174 |
| 28 | 444 | 440.784765452628 | 3.21523454737176 |
| 29 | 438 | 439.586652918674 | -1.58665291867430 |
| 30 | 427 | 435.593124230832 | -8.5931242308322 |
| 31 | 424 | 433.360902489046 | -9.36090248904592 |
| 32 | 416 | 428.384698043127 | -12.3846980431266 |
| 33 | 406 | 429.190697488773 | -23.190697488773 |
| 34 | 431 | 449.554835633898 | -18.5548356338979 |
| 35 | 434 | 450.744117523136 | -16.7441175231363 |
| 36 | 418 | 441.415436775877 | -23.4154367758767 |
| 37 | 412 | 432.130719841222 | -20.1307198412219 |
| 38 | 404 | 419.078199517599 | -15.0781995175990 |
| 39 | 409 | 424.623463002263 | -15.6234630022632 |
| 40 | 412 | 428.346957209277 | -16.3469572092768 |
| 41 | 406 | 427.124914302239 | -21.1249143022389 |
| 42 | 398 | 423.073076395474 | -25.0730763954739 |
| 43 | 397 | 420.948372808811 | -23.9483728088114 |
| 44 | 385 | 415.977561123024 | -30.9775611230237 |
| 45 | 390 | 416.631889189969 | -26.6318891899689 |
| 46 | 413 | 437.250161156295 | -24.2501611562953 |
| 47 | 413 | 438.240585015681 | -25.2405850156811 |
| 48 | 401 | 428.923363883701 | -27.9233638837011 |
| 49 | 397 | 419.64741018426 | -22.6474101842602 |
| 50 | 397 | 406.656569554642 | -9.65656955464235 |
| 51 | 409 | 412.33024813994 | -3.33024813994032 |
| 52 | 419 | 415.779722722767 | 3.22027727723292 |
| 53 | 424 | 414.591047519043 | 9.40895248095656 |
| 54 | 428 | 410.618752824219 | 17.3812471757805 |
| 55 | 430 | 408.269912644587 | 21.7300873554126 |
| 56 | 424 | 403.303819623915 | 20.6961803760852 |
| 57 | 433 | 404.204192371864 | 28.7958076281358 |
| 58 | 456 | 424.544737191413 | 31.4552628085867 |
| 59 | 459 | 425.721211275339 | 33.2787887246608 |
| 60 | 446 | 416.442076511789 | 29.5579234882113 |
| 61 | 441 | 407.131069871492 | 33.8689301285076 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.000140542605976049 | 0.000281085211952099 | 0.999859457394024 |
| 18 | 6.48173427370901e-06 | 1.29634685474180e-05 | 0.999993518265726 |
| 19 | 1.61445512218299e-06 | 3.22891024436599e-06 | 0.999998385544878 |
| 20 | 2.20281459475342e-07 | 4.40562918950683e-07 | 0.99999977971854 |
| 21 | 1.73875548978238e-08 | 3.47751097956477e-08 | 0.999999982612445 |
| 22 | 1.79774390630517e-09 | 3.59548781261034e-09 | 0.999999998202256 |
| 23 | 2.33694707305671e-10 | 4.67389414611341e-10 | 0.999999999766305 |
| 24 | 2.56239171090847e-10 | 5.12478342181695e-10 | 0.99999999974376 |
| 25 | 1.28150305251415e-06 | 2.56300610502830e-06 | 0.999998718496947 |
| 26 | 1.74606830111757e-05 | 3.49213660223515e-05 | 0.999982539316989 |
| 27 | 0.000209810673788679 | 0.000419621347577358 | 0.999790189326211 |
| 28 | 0.000480106583197835 | 0.00096021316639567 | 0.999519893416802 |
| 29 | 0.00168792518371605 | 0.0033758503674321 | 0.998312074816284 |
| 30 | 0.00788951582167657 | 0.0157790316433531 | 0.992110484178323 |
| 31 | 0.0118890966004893 | 0.0237781932009785 | 0.98811090339951 |
| 32 | 0.0427406864877315 | 0.085481372975463 | 0.957259313512268 |
| 33 | 0.107495216589976 | 0.214990433179951 | 0.892504783410024 |
| 34 | 0.110411558583316 | 0.220823117166631 | 0.889588441416684 |
| 35 | 0.126462765741363 | 0.252925531482725 | 0.873537234258637 |
| 36 | 0.280944330542163 | 0.561888661084326 | 0.719055669457837 |
| 37 | 0.459069373584128 | 0.918138747168255 | 0.540930626415872 |
| 38 | 0.607602022651323 | 0.784795954697353 | 0.392397977348677 |
| 39 | 0.726063589978342 | 0.547872820043315 | 0.273936410021658 |
| 40 | 0.929509464952723 | 0.140981070094554 | 0.0704905350472768 |
| 41 | 0.990095563521964 | 0.0198088729560722 | 0.00990443647803609 |
| 42 | 0.998149949780456 | 0.00370010043908806 | 0.00185005021954403 |
| 43 | 0.999359456908612 | 0.00128108618277606 | 0.000640543091388029 |
| 44 | 0.999160920919032 | 0.00167815816193583 | 0.000839079080967915 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 16 | 0.571428571428571 | NOK |
| 5% type I error level | 19 | 0.678571428571429 | NOK |
| 10% type I error level | 20 | 0.714285714285714 | NOK |
