| Multiple Linear Regression - Estimated Regression Equation |
| Olieprijzen[t] = -2393.44635741823 + 1530.92424367196PeriodegemiddeldeEUR[t] + 977.515418385255PeriodegemiddeldeUS[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) | -2393.44635741823 | 493.701744 | -4.848 | 1e-05 | 5e-06 |
| PeriodegemiddeldeEUR | 1530.92424367196 | 335.211966 | 4.567 | 2.7e-05 | 1.3e-05 |
| PeriodegemiddeldeUS | 977.515418385255 | 180.916131 | 5.4031 | 1e-06 | 1e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.833503259517036 |
| R-squared | 0.694727683625524 |
| Adjusted R-squared | 0.684016374279051 |
| F-TEST (value) | 64.8592680085644 |
| F-TEST (DF numerator) | 2 |
| F-TEST (DF denominator) | 57 |
| p-value | 2.1094237467878e-15 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12.3394914909879 |
| Sum Squared Residuals | 8678.99386460131 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 35.16 | 55.9077174730628 | -20.7477174730628 |
| 2 | 41.54 | 55.0589896786029 | -13.5189896786029 |
| 3 | 45.07 | 56.674417610038 | -11.604417610038 |
| 4 | 46.84 | 54.5404645348103 | -7.70046453481026 |
| 5 | 45.2 | 53.4340298144444 | -8.23402981444441 |
| 6 | 46.65 | 54.1668050730911 | -7.51680507309109 |
| 7 | 52.55 | 55.03794745594 | -2.48794745594007 |
| 8 | 55.05 | 53.5791112850779 | 1.47088871492212 |
| 9 | 60.75 | 53.7189647212669 | 7.0310352787331 |
| 10 | 55.99 | 55.2159493101176 | 0.774050689882439 |
| 11 | 53.39 | 57.5874221735147 | -4.19742217351468 |
| 12 | 49.42 | 56.7616305656584 | -7.34163056565844 |
| 13 | 55.12 | 54.5529314692051 | 0.56706853079489 |
| 14 | 59.84 | 55.9070819285822 | 3.93291807141779 |
| 15 | 55.98 | 55.1750072309997 | 0.804992769000288 |
| 16 | 61.27 | 53.658906377904 | 7.61109362209598 |
| 17 | 66.94 | 53.6846432155944 | 13.2553567844056 |
| 18 | 64.67 | 53.3276944012104 | 11.3423055987896 |
| 19 | 67.74 | 53.4072183513793 | 14.3327816486207 |
| 20 | 69.79 | 53.855960276332 | 15.934039723668 |
| 21 | 64.49 | 53.5321524652938 | 10.9578475347062 |
| 22 | 54.92 | 53.2584940452859 | 1.66150595471406 |
| 23 | 53.32 | 54.2043875633725 | -0.884387563372523 |
| 24 | 56.13 | 56.7941602324538 | -0.664160232453843 |
| 25 | 54.63 | 54.9506463551622 | -0.320646355162208 |
| 26 | 52.11 | 55.5260433057271 | -3.4160433057271 |
| 27 | 57.83 | 57.0922134740067 | 0.73778652599326 |
| 28 | 64.93 | 60.4392166913885 | 4.4907833086115 |
| 29 | 63.4 | 60.369932224962 | 3.03006777503796 |
| 30 | 65.37 | 59.1446999882094 | 6.22530001179062 |
| 31 | 69.91 | 63.4739143183605 | 6.43608568163953 |
| 32 | 73.81 | 61.9873492554529 | 11.8226507445471 |
| 33 | 71.42 | 66.6111432920572 | 4.80885670794278 |
| 34 | 75.57 | 73.3346390288095 | 2.23536097119046 |
| 35 | 86.02 | 84.5165948944477 | 1.5034051055523 |
| 36 | 85.91 | 81.5312144193839 | 4.37878558061614 |
| 37 | 92.93 | 85.4320034816617 | 7.49799651833829 |
| 38 | 88.71 | 86.248812432063 | 2.46118756793702 |
| 39 | 98.01 | 110.316751678798 | -12.3067516787977 |
| 40 | 98.39 | 118.191361902836 | -19.8013619028358 |
| 41 | 110.21 | 111.347890023313 | -1.13789002331287 |
| 42 | 121.36 | 111.211017280408 | 10.1489827195919 |
| 43 | 137.11 | 118.877484151359 | 18.2325158486412 |
| 44 | 121.29 | 92.7035730529478 | 28.5864269470522 |
| 45 | 106.41 | 76.6042944272333 | 29.8057055727667 |
| 46 | 93.38 | 57.9695953760365 | 35.4104046239635 |
| 47 | 58.66 | 53.5493855074356 | 5.11061449256436 |
| 48 | 43.12 | 59.5328501503823 | -16.4128501503823 |
| 49 | 34.57 | 57.0607468941592 | -22.4907468941591 |
| 50 | 41.77 | 53.7455278874814 | -11.9755278874814 |
| 51 | 42.85 | 55.3340167124489 | -12.4840167124489 |
| 52 | 48.09 | 56.5666947718148 | -8.47669477181476 |
| 53 | 48.91 | 62.4188205159615 | -13.5088205159615 |
| 54 | 65.62 | 68.9077731231737 | -3.28777312317366 |
| 55 | 68.47 | 70.3641343431196 | -1.89413434311956 |
| 56 | 71.52 | 74.2499852719717 | -2.72998527197168 |
| 57 | 68.07 | 81.3263605245398 | -13.2563605245398 |
| 58 | 65 | 88.1316810307755 | -23.1316810307755 |
| 59 | 76.34 | 90.9216831102657 | -14.5816831102657 |
| 60 | 76.18 | 82.6678618486089 | -6.48786184860892 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 6 | 0.0807699925858095 | 0.161539985171619 | 0.91923000741419 |
| 7 | 0.0335523684603659 | 0.0671047369207318 | 0.966447631539634 |
| 8 | 0.0218843380336745 | 0.0437686760673491 | 0.978115661966325 |
| 9 | 0.0287350534325526 | 0.0574701068651051 | 0.971264946567447 |
| 10 | 0.0119986919086722 | 0.0239973838173443 | 0.988001308091328 |
| 11 | 0.00463078994849895 | 0.0092615798969979 | 0.9953692100515 |
| 12 | 0.00229450653383979 | 0.00458901306767959 | 0.99770549346616 |
| 13 | 0.000847451382229283 | 0.00169490276445857 | 0.99915254861777 |
| 14 | 0.000583259719951104 | 0.00116651943990221 | 0.999416740280049 |
| 15 | 0.000213619650345421 | 0.000427239300690842 | 0.999786380349655 |
| 16 | 0.000184994579390121 | 0.000369989158780243 | 0.99981500542061 |
| 17 | 0.00248883056365491 | 0.00497766112730983 | 0.997511169436345 |
| 18 | 0.00280506592287483 | 0.00561013184574967 | 0.997194934077125 |
| 19 | 0.00438905097209481 | 0.00877810194418962 | 0.995610949027905 |
| 20 | 0.0107065395260413 | 0.0214130790520825 | 0.989293460473959 |
| 21 | 0.00845210836196781 | 0.0169042167239356 | 0.991547891638032 |
| 22 | 0.00527463515225548 | 0.010549270304511 | 0.994725364847745 |
| 23 | 0.0027593684275241 | 0.00551873685504821 | 0.997240631572476 |
| 24 | 0.00363496967677163 | 0.00726993935354326 | 0.996365030323228 |
| 25 | 0.00196630092587536 | 0.00393260185175071 | 0.998033699074125 |
| 26 | 0.00100971666678705 | 0.00201943333357411 | 0.998990283333213 |
| 27 | 0.0010316447867273 | 0.00206328957345459 | 0.998968355213273 |
| 28 | 0.00279358928564804 | 0.00558717857129608 | 0.997206410714352 |
| 29 | 0.00225548499931896 | 0.00451096999863791 | 0.99774451500068 |
| 30 | 0.00176583471244225 | 0.00353166942488449 | 0.998234165287558 |
| 31 | 0.00139516164588892 | 0.00279032329177784 | 0.99860483835411 |
| 32 | 0.00143537913892482 | 0.00287075827784964 | 0.998564620861075 |
| 33 | 0.000789913434571762 | 0.00157982686914352 | 0.999210086565428 |
| 34 | 0.000399006271863093 | 0.000798012543726185 | 0.999600993728137 |
| 35 | 0.000193348869936288 | 0.000386697739872576 | 0.999806651130064 |
| 36 | 9.41350849712153e-05 | 0.000188270169942431 | 0.999905864915029 |
| 37 | 5.03020977425496e-05 | 0.000100604195485099 | 0.999949697902257 |
| 38 | 2.26256656377323e-05 | 4.52513312754646e-05 | 0.999977374334362 |
| 39 | 2.5556591179626e-05 | 5.11131823592519e-05 | 0.99997444340882 |
| 40 | 6.60312590718342e-05 | 0.000132062518143668 | 0.999933968740928 |
| 41 | 4.32933070512838e-05 | 8.65866141025676e-05 | 0.99995670669295 |
| 42 | 4.75846398765785e-05 | 9.5169279753157e-05 | 0.999952415360123 |
| 43 | 0.000100127865396253 | 0.000200255730792507 | 0.999899872134604 |
| 44 | 0.00291662625863259 | 0.00583325251726518 | 0.997083373741367 |
| 45 | 0.0581644190558304 | 0.116328838111661 | 0.94183558094417 |
| 46 | 0.849295088530697 | 0.301409822938606 | 0.150704911469303 |
| 47 | 0.954382948617727 | 0.0912341027645455 | 0.0456170513822727 |
| 48 | 0.956495719715067 | 0.0870085605698655 | 0.0435042802849327 |
| 49 | 0.989715263232747 | 0.0205694735345058 | 0.0102847367672529 |
| 50 | 0.984260694743792 | 0.0314786105124154 | 0.0157393052562077 |
| 51 | 0.965800809466144 | 0.0683983810677113 | 0.0341991905338556 |
| 52 | 0.974601340968821 | 0.0507973180623574 | 0.0253986590311787 |
| 53 | 0.949204525195798 | 0.101590949608404 | 0.050795474804202 |
| 54 | 0.876037785470484 | 0.247924429059031 | 0.123962214529516 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 31 | 0.63265306122449 | NOK |
| 5% type I error level | 38 | 0.775510204081633 | NOK |
| 10% type I error level | 44 | 0.897959183673469 | NOK |
