| Multiple Linear Regression - Estimated Regression Equation |
| olieprijs[t] = -48.6979731359204 + 0.0070117197906449dowjones[t] -1.73792160184585M1[t] -3.42350501392251M2[t] -6.8636609608159M3[t] -10.1170751860686M4[t] -9.07662581132669M5[t] -8.08630606239669M6[t] -4.7462916723035M7[t] -4.60618584590421M8[t] -2.97025370798178M9[t] -0.815979678872401M10[t] + 1.47789919681228M11[t] + 0.55432711653647t + 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) | -48.6979731359204 | 9.563524 | -5.0921 | 2e-06 | 1e-06 |
| dowjones | 0.0070117197906449 | 0.00085 | 8.2465 | 0 | 0 |
| M1 | -1.73792160184585 | 5.870899 | -0.296 | 0.767845 | 0.383923 |
| M2 | -3.42350501392251 | 5.871413 | -0.5831 | 0.561192 | 0.280596 |
| M3 | -6.8636609608159 | 5.868961 | -1.1695 | 0.245074 | 0.122537 |
| M4 | -10.1170751860686 | 6.030358 | -1.6777 | 0.096627 | 0.048314 |
| M5 | -9.07662581132669 | 6.026867 | -1.506 | 0.13531 | 0.067655 |
| M6 | -8.08630606239669 | 6.024562 | -1.3422 | 0.182657 | 0.091328 |
| M7 | -4.7462916723035 | 6.024539 | -0.7878 | 0.432719 | 0.21636 |
| M8 | -4.60618584590421 | 6.022221 | -0.7649 | 0.446209 | 0.223104 |
| M9 | -2.97025370798178 | 6.023589 | -0.4931 | 0.623054 | 0.311527 |
| M10 | -0.815979678872401 | 6.021978 | -0.1355 | 0.892497 | 0.446249 |
| M11 | 1.47789919681228 | 6.020594 | 0.2455 | 0.806608 | 0.403304 |
| t | 0.55432711653647 | 0.039443 | 14.0538 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.890326724573104 |
| R-squared | 0.792681676489072 |
| Adjusted R-squared | 0.764896746534 |
| F-TEST (value) | 28.5291947026971 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 97 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 12.7709054395382 |
| Sum Squared Residuals | 15820.3144973258 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 32.68 | 27.0220635189905 | 5.65793648100946 |
| 2 | 31.54 | 22.1443752221109 | 9.3956247778891 |
| 3 | 32.43 | 20.8868079615376 | 11.5431920384624 |
| 4 | 26.54 | 18.1942417522267 | 8.34575824777331 |
| 5 | 25.85 | 19.9014161117491 | 5.9485838882509 |
| 6 | 27.6 | 22.1085302630357 | 5.49146973696429 |
| 7 | 25.71 | 20.9220393749683 | 4.78796062503172 |
| 8 | 25.38 | 22.7479535405204 | 2.63204645947958 |
| 9 | 28.57 | 27.2720637272954 | 1.29793627270456 |
| 10 | 27.64 | 31.5259076804036 | -3.88590768040363 |
| 11 | 25.36 | 32.1114316961837 | -6.75143169618366 |
| 12 | 25.9 | 30.2775981526863 | -4.37759815268633 |
| 13 | 26.29 | 20.1742546873017 | 6.11574531269826 |
| 14 | 21.74 | 20.2924167412566 | 1.44758325874341 |
| 15 | 19.2 | 20.9200905807939 | -1.72009058079394 |
| 16 | 19.32 | 20.0208418251383 | -0.700841825138296 |
| 17 | 19.82 | 21.2319370094726 | -1.41193700947263 |
| 18 | 20.36 | 22.5574676314814 | -2.19746763148144 |
| 19 | 24.31 | 30.7178796931353 | -6.40787969313527 |
| 20 | 25.97 | 29.1571331998059 | -3.18713319980592 |
| 21 | 25.61 | 30.6541437185638 | -5.04414371856375 |
| 22 | 24.67 | 29.2395731585188 | -4.56957315851878 |
| 23 | 25.59 | 25.9458632001245 | -0.355863200124529 |
| 24 | 26.09 | 25.5054687306220 | 0.584531269377953 |
| 25 | 28.37 | 20.6426145195676 | 7.72738548043242 |
| 26 | 27.34 | 18.7220489271945 | 8.61795107280552 |
| 27 | 24.46 | 19.9949412218670 | 4.46505877813303 |
| 28 | 27.46 | 16.4924512595386 | 10.9675487404614 |
| 29 | 30.23 | 17.7196733993914 | 12.5103266006086 |
| 30 | 32.33 | 15.3512196840948 | 16.9787803159052 |
| 31 | 29.87 | 19.676852075047 | 10.1931479249530 |
| 32 | 24.87 | 22.8741183972535 | 1.99588160274654 |
| 33 | 25.48 | 27.0891519756569 | -1.60915197565690 |
| 34 | 27.28 | 33.1260061543282 | -5.84600615432817 |
| 35 | 28.24 | 36.3690420879605 | -8.12904208796053 |
| 36 | 29.58 | 36.3597281511869 | -6.7797281511869 |
| 37 | 26.95 | 36.6328885695819 | -9.6828885695819 |
| 38 | 29.08 | 36.8328773934935 | -7.75287739349355 |
| 39 | 28.76 | 34.5063734508364 | -5.7463734508364 |
| 40 | 29.59 | 34.3491048834268 | -4.75910488342678 |
| 41 | 30.7 | 38.8566900101349 | -8.15669001013491 |
| 42 | 30.52 | 40.8329783459135 | -10.3129783459135 |
| 43 | 32.67 | 42.7789031571187 | -10.1089031571187 |
| 44 | 33.19 | 44.1371356126349 | -10.9471356126349 |
| 45 | 37.13 | 44.0455007784263 | -6.91550077842627 |
| 46 | 35.54 | 48.660939121138 | -13.1209391211380 |
| 47 | 37.75 | 50.0169109075141 | -12.2669109075141 |
| 48 | 41.84 | 48.2569107734123 | -6.41691077341226 |
| 49 | 42.94 | 48.2778596309378 | -5.33785963093778 |
| 50 | 49.14 | 45.7232943350946 | 3.41670566490543 |
| 51 | 44.61 | 45.7133223768707 | -1.10332237687068 |
| 52 | 40.22 | 44.8487115169808 | -4.62871151698081 |
| 53 | 44.23 | 45.5048290798856 | -1.27482907988561 |
| 54 | 45.85 | 48.3415255511742 | -2.49152555117422 |
| 55 | 53.38 | 51.9433381081382 | 1.43666189186183 |
| 56 | 53.26 | 49.8410063781794 | 3.41899362182060 |
| 57 | 51.8 | 52.690297175761 | -0.89029717576102 |
| 58 | 55.3 | 56.1664011696909 | -0.86640116969086 |
| 59 | 57.81 | 59.4264755824145 | -1.61647558241448 |
| 60 | 63.96 | 58.5652376910775 | 5.39476230892249 |
| 61 | 63.77 | 57.2292785347174 | 6.54072146528258 |
| 62 | 59.15 | 54.6379718271712 | 4.51202817282878 |
| 63 | 56.12 | 54.3530703359561 | 1.76692966404385 |
| 64 | 57.42 | 52.5834568026877 | 4.83654319731226 |
| 65 | 63.52 | 54.4914468170143 | 9.02855318298573 |
| 66 | 61.71 | 56.7282205430153 | 4.98177945698469 |
| 67 | 63.01 | 61.8458266843209 | 1.16417331567912 |
| 68 | 68.18 | 63.1645130402177 | 5.01548695978226 |
| 69 | 72.03 | 66.0503348979086 | 5.97966510209137 |
| 70 | 69.75 | 66.403629248679 | 3.34637075132105 |
| 71 | 74.41 | 69.524731375152 | 4.885268624848 |
| 72 | 74.33 | 70.1469630399218 | 4.18303696007824 |
| 73 | 64.24 | 70.9002860295801 | -6.66028602958013 |
| 74 | 60.03 | 72.7807737357156 | -12.7507737357156 |
| 75 | 59.44 | 71.4517570504756 | -12.0117570504756 |
| 76 | 62.5 | 70.1022156498648 | -7.60221564986477 |
| 77 | 55.04 | 72.6454674772237 | -17.6054674772237 |
| 78 | 58.34 | 75.0216341926628 | -16.6816341926628 |
| 79 | 61.92 | 76.3710720012779 | -14.4510720012779 |
| 80 | 67.65 | 80.4750939268105 | -12.8250939268105 |
| 81 | 67.68 | 87.243655618571 | -19.563655618571 |
| 82 | 70.3 | 90.460325980247 | -20.1603259802470 |
| 83 | 75.26 | 94.662284712448 | -19.4022847124480 |
| 84 | 71.44 | 90.6986412825422 | -19.2586412825422 |
| 85 | 76.36 | 91.7446334562621 | -15.3846334562621 |
| 86 | 81.71 | 93.0225339635896 | -11.3125339635896 |
| 87 | 92.6 | 85.2235930759278 | 7.37640692407218 |
| 88 | 90.6 | 83.9716548148027 | 6.62834518519726 |
| 89 | 92.23 | 79.4742985659793 | 12.7557014340207 |
| 90 | 94.09 | 80.1877060502648 | 13.9022939497352 |
| 91 | 102.79 | 82.4995725173439 | 20.2904274826562 |
| 92 | 109.65 | 86.4386787934005 | 23.2113212065995 |
| 93 | 124.05 | 89.7217145772315 | 34.3282854227685 |
| 94 | 132.69 | 87.13078778791 | 45.55921221209 |
| 95 | 135.81 | 84.8303580550585 | 50.9796419449415 |
| 96 | 116.07 | 85.3678180275594 | 30.7021819724406 |
| 97 | 101.42 | 81.262650257082 | 20.1573497429180 |
| 98 | 75.73 | 66.5822972240891 | 9.1477027759109 |
| 99 | 55.48 | 59.7195611628742 | -4.23956116287422 |
| 100 | 43.8 | 56.8873214953336 | -13.0873214953336 |
| 101 | 45.29 | 57.084241529149 | -11.7942415291490 |
| 102 | 44.01 | 53.6807177383574 | -9.67071773835743 |
| 103 | 47.48 | 54.3845163886499 | -6.90451638864992 |
| 104 | 51.07 | 60.3843671111771 | -9.31436711117714 |
| 105 | 57.84 | 65.4231375305855 | -7.58313753058552 |
| 106 | 69.04 | 69.4964296990846 | -0.456429699084604 |
| 107 | 65.61 | 72.9529023831442 | -7.34290238314422 |
| 108 | 72.87 | 76.9016341509917 | -4.03163415099168 |
| 109 | 68.41 | 77.5434707959788 | -9.13347079597883 |
| 110 | 73.25 | 77.9714106302843 | -4.72141063028433 |
| 111 | 77.43 | 77.7604827828605 | -0.330482782860549 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00748027114777157 | 0.0149605422955431 | 0.992519728852228 |
| 18 | 0.00117286362300805 | 0.00234572724601610 | 0.998827136376992 |
| 19 | 0.000422764280358312 | 0.000845528560716625 | 0.999577235719642 |
| 20 | 0.000174883677174151 | 0.000349767354348302 | 0.999825116322826 |
| 21 | 3.44347882798642e-05 | 6.88695765597284e-05 | 0.99996556521172 |
| 22 | 1.37833369746501e-05 | 2.75666739493002e-05 | 0.999986216663025 |
| 23 | 1.7705925185213e-05 | 3.5411850370426e-05 | 0.999982294074815 |
| 24 | 8.4900684745096e-06 | 1.69801369490192e-05 | 0.999991509931526 |
| 25 | 4.60809323565757e-06 | 9.21618647131514e-06 | 0.999995391906764 |
| 26 | 2.87900832969180e-06 | 5.75801665938359e-06 | 0.99999712099167 |
| 27 | 8.77472223482334e-07 | 1.75494444696467e-06 | 0.999999122527776 |
| 28 | 1.14399247489017e-06 | 2.28798494978034e-06 | 0.999998856007525 |
| 29 | 2.22392175306121e-06 | 4.44784350612242e-06 | 0.999997776078247 |
| 30 | 2.68677828932563e-06 | 5.37355657865125e-06 | 0.99999731322171 |
| 31 | 1.17773898249539e-06 | 2.35547796499079e-06 | 0.999998822261017 |
| 32 | 3.58172832224542e-07 | 7.16345664449084e-07 | 0.999999641827168 |
| 33 | 1.03027761958555e-07 | 2.06055523917111e-07 | 0.999999896972238 |
| 34 | 3.5115035498484e-08 | 7.0230070996968e-08 | 0.999999964884964 |
| 35 | 1.69922453518528e-08 | 3.39844907037057e-08 | 0.999999983007755 |
| 36 | 7.3325498653776e-09 | 1.46650997307552e-08 | 0.99999999266745 |
| 37 | 1.95668424511597e-09 | 3.91336849023194e-09 | 0.999999998043316 |
| 38 | 6.47345202154582e-10 | 1.29469040430916e-09 | 0.999999999352655 |
| 39 | 2.13199764205663e-10 | 4.26399528411327e-10 | 0.9999999997868 |
| 40 | 8.0940413291743e-11 | 1.61880826583486e-10 | 0.99999999991906 |
| 41 | 2.61490466442464e-11 | 5.22980932884928e-11 | 0.99999999997385 |
| 42 | 6.5888666333416e-12 | 1.31777332666832e-11 | 0.999999999993411 |
| 43 | 2.05462938480733e-12 | 4.10925876961467e-12 | 0.999999999997945 |
| 44 | 8.1063920801105e-13 | 1.6212784160221e-12 | 0.99999999999919 |
| 45 | 6.33514549189135e-13 | 1.26702909837827e-12 | 0.999999999999367 |
| 46 | 3.04477836346505e-13 | 6.0895567269301e-13 | 0.999999999999696 |
| 47 | 2.15258131735338e-13 | 4.30516263470677e-13 | 0.999999999999785 |
| 48 | 3.16777760324955e-13 | 6.3355552064991e-13 | 0.999999999999683 |
| 49 | 1.93750167211857e-13 | 3.87500334423714e-13 | 0.999999999999806 |
| 50 | 1.33109026240231e-12 | 2.66218052480461e-12 | 0.999999999998669 |
| 51 | 1.2171285881172e-12 | 2.4342571762344e-12 | 0.999999999998783 |
| 52 | 4.12507100121560e-13 | 8.25014200243119e-13 | 0.999999999999587 |
| 53 | 2.43374841701112e-13 | 4.86749683402224e-13 | 0.999999999999757 |
| 54 | 1.18815604551350e-13 | 2.37631209102701e-13 | 0.999999999999881 |
| 55 | 3.17623350286591e-13 | 6.35246700573181e-13 | 0.999999999999682 |
| 56 | 1.08984283062346e-12 | 2.17968566124691e-12 | 0.99999999999891 |
| 57 | 9.6049646407843e-13 | 1.92099292815686e-12 | 0.99999999999904 |
| 58 | 1.86282926813895e-12 | 3.72565853627789e-12 | 0.999999999998137 |
| 59 | 3.10299089673166e-12 | 6.20598179346332e-12 | 0.999999999996897 |
| 60 | 1.13246084396079e-11 | 2.26492168792159e-11 | 0.999999999988675 |
| 61 | 1.53375767526321e-11 | 3.06751535052642e-11 | 0.999999999984662 |
| 62 | 9.50255529793055e-12 | 1.90051105958611e-11 | 0.999999999990497 |
| 63 | 4.37277533661982e-12 | 8.74555067323964e-12 | 0.999999999995627 |
| 64 | 3.06596046164466e-12 | 6.13192092328932e-12 | 0.999999999996934 |
| 65 | 5.43046032634346e-12 | 1.08609206526869e-11 | 0.99999999999457 |
| 66 | 4.07954425146939e-12 | 8.15908850293877e-12 | 0.99999999999592 |
| 67 | 1.86171900402458e-12 | 3.72343800804915e-12 | 0.999999999998138 |
| 68 | 1.83466651513025e-12 | 3.6693330302605e-12 | 0.999999999998165 |
| 69 | 2.61853916250356e-12 | 5.23707832500713e-12 | 0.999999999997381 |
| 70 | 2.45967080070759e-12 | 4.91934160141519e-12 | 0.99999999999754 |
| 71 | 3.36784700134852e-12 | 6.73569400269705e-12 | 0.999999999996632 |
| 72 | 4.19054072309947e-12 | 8.38108144619894e-12 | 0.99999999999581 |
| 73 | 3.97358753717037e-12 | 7.94717507434075e-12 | 0.999999999996026 |
| 74 | 5.75682874275299e-12 | 1.15136574855060e-11 | 0.999999999994243 |
| 75 | 4.58141141670885e-12 | 9.1628228334177e-12 | 0.999999999995419 |
| 76 | 2.62868663773777e-12 | 5.25737327547554e-12 | 0.999999999997371 |
| 77 | 3.15864417049744e-12 | 6.31728834099489e-12 | 0.999999999996841 |
| 78 | 2.42015839886178e-12 | 4.84031679772355e-12 | 0.99999999999758 |
| 79 | 1.24885595339557e-12 | 2.49771190679114e-12 | 0.999999999998751 |
| 80 | 4.67668385176018e-13 | 9.35336770352037e-13 | 0.999999999999532 |
| 81 | 6.77820197227502e-13 | 1.35564039445500e-12 | 0.999999999999322 |
| 82 | 7.79957618070229e-12 | 1.55991523614046e-11 | 0.9999999999922 |
| 83 | 6.97666569229903e-10 | 1.39533313845981e-09 | 0.999999999302333 |
| 84 | 3.68472948182127e-08 | 7.36945896364253e-08 | 0.999999963152705 |
| 85 | 2.16892253999585e-06 | 4.3378450799917e-06 | 0.99999783107746 |
| 86 | 0.00161424998133087 | 0.00322849996266173 | 0.99838575001867 |
| 87 | 0.0301469341578051 | 0.0602938683156101 | 0.969853065842195 |
| 88 | 0.0534373034941395 | 0.106874606988279 | 0.94656269650586 |
| 89 | 0.068311428182464 | 0.136622856364928 | 0.931688571817536 |
| 90 | 0.129241801030599 | 0.258483602061198 | 0.8707581989694 |
| 91 | 0.309252599596736 | 0.618505199193472 | 0.690747400403264 |
| 92 | 0.586919271167388 | 0.826161457665225 | 0.413080728832612 |
| 93 | 0.807050667964522 | 0.385898664070955 | 0.192949332035478 |
| 94 | 0.830673835494471 | 0.338652329011058 | 0.169326164505529 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 69 | 0.884615384615385 | NOK |
| 5% type I error level | 70 | 0.897435897435897 | NOK |
| 10% type I error level | 71 | 0.91025641025641 | NOK |
