| Multiple Linear Regression - Estimated Regression Equation |
| x[t] = + 49.8477598332706 + 0.199099762966021y[t] + 0.456711187033412z[t] + 0.166158579526877t + 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) | 49.8477598332706 | 11.422293 | 4.3641 | 5.5e-05 | 2.8e-05 |
| y | 0.199099762966021 | 0.063757 | 3.1228 | 0.002834 | 0.001417 |
| z | 0.456711187033412 | 0.108296 | 4.2172 | 9.1e-05 | 4.6e-05 |
| t | 0.166158579526877 | 0.021415 | 7.7589 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.981353702016435 |
| R-squared | 0.963055088461362 |
| Adjusted R-squared | 0.961075896771792 |
| F-TEST (value) | 486.590103190381 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 56 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.783395793075165 |
| Sum Squared Residuals | 34.3677022420405 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 114 | 113.880719203709 | 0.119280796290517 |
| 2 | 113.8 | 114.043383095092 | -0.243383095092458 |
| 3 | 113.6 | 113.369908039629 | 0.230091960371214 |
| 4 | 113.7 | 113.860477406011 | -0.160477406011423 |
| 5 | 114.2 | 114.491554816648 | -0.291554816648046 |
| 6 | 114.8 | 114.686969226726 | 0.113030773274386 |
| 7 | 115.2 | 115.155272138845 | 0.0447278611545424 |
| 8 | 115.3 | 115.403427101525 | -0.103427101524943 |
| 9 | 114.9 | 115.160902090688 | -0.260902090687929 |
| 10 | 115.1 | 115.082289788545 | 0.0177102114545427 |
| 11 | 116 | 115.859726409546 | 0.140273590453826 |
| 12 | 116 | 115.972006226293 | 0.0279937737066145 |
| 13 | 116 | 116.084286043041 | -0.0842860430405909 |
| 14 | 115.9 | 116.036147839237 | -0.136147839237224 |
| 15 | 115.6 | 115.624997163773 | -0.0249971637733318 |
| 16 | 116.6 | 116.244372242190 | 0.355627757810326 |
| 17 | 116.9 | 116.573305320233 | 0.326694679766697 |
| 18 | 117.9 | 117.087279351057 | 0.8127206489435 |
| 19 | 117.9 | 117.458388859660 | 0.441611140340468 |
| 20 | 117.7 | 117.354015415110 | 0.345984584889692 |
| 21 | 117.4 | 116.888985976867 | 0.511014023133263 |
| 22 | 117.3 | 116.593720413428 | 0.706279586572172 |
| 23 | 119 | 117.749446584064 | 1.25055341593601 |
| 24 | 119.1 | 117.919099851735 | 1.18090014826518 |
| 25 | 119 | 118.222271787372 | 0.777728212628285 |
| 26 | 118.5 | 118.328700438009 | 0.171299561991213 |
| 27 | 117 | 117.677491836808 | -0.677491836807904 |
| 28 | 117.5 | 118.490115512080 | -0.99011551208013 |
| 29 | 118.2 | 119.269908611047 | -1.06990861104704 |
| 30 | 118.2 | 119.470035977057 | -1.27003597705699 |
| 31 | 118.3 | 119.490973556398 | -1.19097355639751 |
| 32 | 118.2 | 119.665339780001 | -1.46533978000072 |
| 33 | 117.9 | 119.518869962503 | -1.61886996250278 |
| 34 | 117.8 | 119.480077612954 | -1.68007761295350 |
| 35 | 118.6 | 120.114649711734 | -1.51464971173407 |
| 36 | 118.9 | 120.007919789219 | -1.10791978921864 |
| 37 | 120.8 | 120.735052393194 | 0.0649476068056636 |
| 38 | 121.8 | 120.875449830314 | 0.924550169685530 |
| 39 | 121.3 | 120.159798344291 | 1.1402016557086 |
| 40 | 121.9 | 121.043854280674 | 0.856145719326299 |
| 41 | 122 | 121.808450359276 | 0.191549640723596 |
| 42 | 121.9 | 122.031982389727 | -0.131982389726888 |
| 43 | 122 | 122.701741542779 | -0.701741542778957 |
| 44 | 122.2 | 122.243701480823 | -0.0437014808232769 |
| 45 | 123 | 122.633582755545 | 0.366417244454835 |
| 46 | 123.1 | 122.463628215996 | 0.636371784004002 |
| 47 | 124.9 | 123.382791149039 | 1.51720885096088 |
| 48 | 125.4 | 123.640291965973 | 1.75970803402733 |
| 49 | 124.7 | 123.706900664017 | 0.993099335983456 |
| 50 | 124.4 | 123.994875579289 | 0.405124420710774 |
| 51 | 124 | 123.467759734190 | 0.532240265810336 |
| 52 | 125 | 124.910433217055 | 0.0895667829454147 |
| 53 | 125.1 | 125.413843125835 | -0.313843125835268 |
| 54 | 125.4 | 125.609257535913 | -0.209257535912820 |
| 55 | 125.7 | 126.191169139702 | -0.491169139702152 |
| 56 | 126.4 | 126.280044292009 | 0.119955707991190 |
| 57 | 125.7 | 126.043370447282 | -0.343370447281944 |
| 58 | 125.4 | 125.742253717733 | -0.342253717732886 |
| 59 | 126.4 | 126.724641267810 | -0.324641267809769 |
| 60 | 126.2 | 126.578091392701 | -0.378091392701150 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.00333073989334265 | 0.0066614797866853 | 0.996669260106657 |
| 8 | 0.000420127998039443 | 0.000840255996078886 | 0.99957987200196 |
| 9 | 0.000173656921383911 | 0.000347313842767821 | 0.999826343078616 |
| 10 | 9.68204327802015e-05 | 0.000193640865560403 | 0.99990317956722 |
| 11 | 1.56311650853392e-05 | 3.12623301706783e-05 | 0.999984368834915 |
| 12 | 7.85246446315106e-06 | 1.57049289263021e-05 | 0.999992147535537 |
| 13 | 5.63820355499963e-06 | 1.12764071099993e-05 | 0.999994361796445 |
| 14 | 2.15561747366569e-06 | 4.31123494733138e-06 | 0.999997844382526 |
| 15 | 3.84756534675376e-07 | 7.69513069350752e-07 | 0.999999615243465 |
| 16 | 5.71733412890327e-07 | 1.14346682578065e-06 | 0.999999428266587 |
| 17 | 2.57476373656807e-07 | 5.14952747313614e-07 | 0.999999742523626 |
| 18 | 3.12560078184292e-06 | 6.25120156368584e-06 | 0.999996874399218 |
| 19 | 1.00419154292086e-06 | 2.00838308584172e-06 | 0.999998995808457 |
| 20 | 2.69834164790103e-07 | 5.39668329580205e-07 | 0.999999730165835 |
| 21 | 8.80993241492482e-08 | 1.76198648298496e-07 | 0.999999911900676 |
| 22 | 3.64897345920761e-08 | 7.29794691841521e-08 | 0.999999963510265 |
| 23 | 5.89768451677386e-07 | 1.17953690335477e-06 | 0.999999410231548 |
| 24 | 1.47729237574290e-06 | 2.95458475148580e-06 | 0.999998522707624 |
| 25 | 1.66518748057375e-06 | 3.33037496114750e-06 | 0.99999833481252 |
| 26 | 1.14260623403192e-05 | 2.28521246806384e-05 | 0.99998857393766 |
| 27 | 0.000580618617633538 | 0.00116123723526708 | 0.999419381382366 |
| 28 | 0.00483128226353624 | 0.00966256452707249 | 0.995168717736464 |
| 29 | 0.0125330434795475 | 0.025066086959095 | 0.987466956520452 |
| 30 | 0.0183059278566079 | 0.0366118557132158 | 0.981694072143392 |
| 31 | 0.0205760662504206 | 0.0411521325008411 | 0.97942393374958 |
| 32 | 0.0257183847822968 | 0.0514367695645936 | 0.974281615217703 |
| 33 | 0.038163710477163 | 0.076327420954326 | 0.961836289522837 |
| 34 | 0.123031856092509 | 0.246063712185018 | 0.87696814390749 |
| 35 | 0.262649294710555 | 0.525298589421111 | 0.737350705289445 |
| 36 | 0.498439707730293 | 0.996879415460587 | 0.501560292269707 |
| 37 | 0.545240727707036 | 0.909518544585929 | 0.454759272292964 |
| 38 | 0.680888750668807 | 0.638222498662386 | 0.319111249331193 |
| 39 | 0.746833370321693 | 0.506333259356613 | 0.253166629678307 |
| 40 | 0.788473274542078 | 0.423053450915845 | 0.211526725457922 |
| 41 | 0.762207206860107 | 0.475585586279785 | 0.237792793139893 |
| 42 | 0.739420523838982 | 0.521158952322037 | 0.260579476161018 |
| 43 | 0.8848529099706 | 0.230294180058802 | 0.115147090029401 |
| 44 | 0.974866832453922 | 0.0502663350921559 | 0.0251331675460780 |
| 45 | 0.98468571530503 | 0.0306285693899397 | 0.0153142846949698 |
| 46 | 0.99162935601279 | 0.01674128797442 | 0.00837064398721 |
| 47 | 0.990561823814605 | 0.0188763523707910 | 0.00943817618539552 |
| 48 | 0.999308761427698 | 0.00138247714460367 | 0.000691238572301833 |
| 49 | 0.999343907799846 | 0.00131218440030848 | 0.000656092200154239 |
| 50 | 0.997618946876975 | 0.00476210624604997 | 0.00238105312302499 |
| 51 | 0.99490674376383 | 0.0101865124723415 | 0.00509325623617073 |
| 52 | 0.988206104200814 | 0.0235877915983726 | 0.0117938957991863 |
| 53 | 0.95738745057707 | 0.0852250988458595 | 0.0426125494229297 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 25 | 0.531914893617021 | NOK |
| 5% type I error level | 33 | 0.702127659574468 | NOK |
| 10% type I error level | 37 | 0.787234042553192 | NOK |
