| Multiple Linear Regression - Estimated Regression Equation |
| olieprijs[t] = -55.9227838874668 + 0.0102687293582253dowjones[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) | -55.9227838874668 | 14.489554 | -3.8595 | 0.000193 | 9.6e-05 |
| dowjones | 0.0102687293582253 | 0.001373 | 7.4785 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.582326771814317 |
| R-squared | 0.339104469171683 |
| Adjusted R-squared | 0.333041207420965 |
| F-TEST (value) | 55.9277305043773 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 109 |
| p-value | 2.02758920764268e-11 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21.5100723324371 |
| Sum Squared Residuals | 50432.4700803879 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 32.68 | 56.7033047787316 | -24.0233047787317 |
| 2 | 31.54 | 51.2166199953384 | -19.6766199953384 |
| 3 | 32.43 | 53.6012243269055 | -21.1712243269055 |
| 4 | 26.54 | 53.6107742452087 | -27.0707742452087 |
| 5 | 25.85 | 53.775381976821 | -27.9253819768210 |
| 6 | 27.6 | 54.7455715265862 | -27.1455715265862 |
| 7 | 25.71 | 47.3046448590289 | -21.5946448590289 |
| 8 | 25.38 | 48.9617097155657 | -23.5817097155657 |
| 9 | 28.57 | 52.3796562824510 | -23.8096562824510 |
| 10 | 27.64 | 54.6426788584168 | -27.0026788584168 |
| 11 | 25.36 | 51.3289598945174 | -25.9689598945174 |
| 12 | 25.9 | 49.9958734492326 | -24.0958734492326 |
| 13 | 26.29 | 36.932817458047 | -10.6428174580470 |
| 14 | 21.74 | 38.7626023423892 | -17.0226023423892 |
| 15 | 19.2 | 43.9081599365023 | -24.7081599365023 |
| 16 | 19.32 | 46.5440400754652 | -27.2240400754652 |
| 17 | 19.82 | 45.9821352049831 | -26.1621352049831 |
| 18 | 20.36 | 45.6612374125386 | -25.3012374125386 |
| 19 | 24.31 | 51.90893772867 | -27.59893772867 |
| 20 | 25.97 | 48.606206305184 | -22.636206305184 |
| 21 | 25.61 | 47.5909370335362 | -21.9809370335363 |
| 22 | 24.67 | 41.5525134217255 | -16.8825134217254 |
| 23 | 25.59 | 32.557619940388 | -6.96761994038798 |
| 24 | 26.09 | 33.2652380804633 | -7.17523808046329 |
| 25 | 28.37 | 27.8769277243217 | 0.493072275678275 |
| 26 | 27.34 | 26.7209768604663 | 0.619023139533698 |
| 27 | 24.46 | 32.8114629301233 | -8.3514629301233 |
| 28 | 27.46 | 31.6348719202579 | -4.17487192025785 |
| 29 | 30.23 | 31.0965851272997 | -0.866585127299676 |
| 30 | 32.33 | 25.3658126470613 | 6.9641873529387 |
| 31 | 29.87 | 25.9974421898857 | 3.87255781011425 |
| 32 | 24.87 | 29.6628651343043 | -4.79286513430427 |
| 33 | 25.48 | 32.628166111079 | -7.148166111079 |
| 34 | 27.28 | 37.5024238755478 | -10.2224238755478 |
| 35 | 28.24 | 38.0806560257095 | -9.84065602570947 |
| 36 | 29.58 | 39.4195956467285 | -9.83959564672846 |
| 37 | 26.95 | 41.5530268581934 | -14.6030268581934 |
| 38 | 29.08 | 43.502647814146 | -14.4226478141460 |
| 39 | 28.76 | 44.3217843550517 | -15.5617843550517 |
| 40 | 29.59 | 48.0443014347019 | -18.4543014347019 |
| 41 | 30.7 | 52.3101369846959 | -21.6101369846959 |
| 42 | 30.52 | 52.9422799639882 | -22.4222799639882 |
| 43 | 32.67 | 50.0888054499246 | -17.4188054499246 |
| 44 | 33.19 | 51.0609460582677 | -17.8709460582678 |
| 45 | 37.13 | 47.7190907759269 | -10.5890907759269 |
| 46 | 35.54 | 50.5116717248963 | -14.9716717248963 |
| 47 | 37.75 | 48.3262807428788 | -10.5762807428788 |
| 48 | 41.84 | 47.1013240177361 | -5.26132401773606 |
| 49 | 42.94 | 48.8653890341856 | -5.9253890341856 |
| 50 | 49.14 | 46.7809396617594 | 2.35906033824055 |
| 51 | 44.61 | 50.9926590080356 | -6.38265900803556 |
| 52 | 40.22 | 53.679266670028 | -13.4592666700280 |
| 53 | 44.23 | 52.3045918708424 | -8.07459187084243 |
| 54 | 45.85 | 54.1968106296826 | -8.3468106296826 |
| 55 | 53.38 | 53.7683992408574 | -0.388399240857432 |
| 56 | 53.26 | 49.6725111617421 | 3.58748883825788 |
| 57 | 51.8 | 50.6376690341217 | 1.16233096587829 |
| 58 | 55.3 | 51.761684149673 | 3.53831585032695 |
| 59 | 57.81 | 52.3648693121752 | 5.44513068782481 |
| 60 | 63.96 | 52.4561583161698 | 11.5038416838302 |
| 61 | 63.77 | 52.2330188272156 | 11.5369811727844 |
| 62 | 59.15 | 50.0947613129523 | 9.05523868704767 |
| 63 | 56.12 | 53.9038437810924 | 2.21615621890757 |
| 64 | 57.42 | 55.2650665448188 | 2.15493345518123 |
| 65 | 63.52 | 55.7237706852507 | 7.7962293147493 |
| 66 | 61.71 | 56.7373969602011 | 4.97260303979887 |
| 67 | 63.01 | 58.5288794840371 | 4.48112051596289 |
| 68 | 68.18 | 59.4431044587999 | 8.7368955412001 |
| 69 | 72.03 | 60.4617624111359 | 11.5682375888641 |
| 70 | 69.75 | 57.0123935324144 | 12.7376064675856 |
| 71 | 74.41 | 57.4120524790365 | 16.9979475209635 |
| 72 | 74.33 | 59.6758965533509 | 14.6541034466491 |
| 73 | 64.24 | 62.512530351267 | 1.72746964873295 |
| 74 | 60.03 | 66.9232576725056 | -6.89325767250557 |
| 75 | 59.44 | 69.2032236519123 | -9.76322365191232 |
| 76 | 62.5 | 71.17964599149 | -8.67964599148996 |
| 77 | 55.04 | 72.5686970117771 | -17.5286970117771 |
| 78 | 58.34 | 73.786465626369 | -15.4464656263690 |
| 79 | 61.92 | 70.0594303058012 | -8.13943030580115 |
| 80 | 67.65 | 75.0528053308254 | -7.40280533082536 |
| 81 | 67.68 | 81.7577721652786 | -14.0777721652786 |
| 82 | 70.3 | 82.5018442945756 | -12.2018442945756 |
| 83 | 75.26 | 84.4844278717682 | -9.22442787176816 |
| 84 | 71.44 | 80.0322148839224 | -8.5922148839224 |
| 85 | 76.36 | 83.297465445251 | -6.93746544525089 |
| 86 | 81.71 | 86.8256981654435 | -5.11569816544353 |
| 87 | 92.6 | 79.630399504135 | 12.9696004958649 |
| 88 | 90.6 | 81.7497625563792 | 8.85023744362083 |
| 89 | 92.23 | 72.8277770534851 | 19.4022229465149 |
| 90 | 94.09 | 71.6104191880675 | 22.4795808119325 |
| 91 | 102.79 | 69.2928696592096 | 33.4971303407904 |
| 92 | 109.65 | 74.0447241697284 | 35.6052758302716 |
| 93 | 124.05 | 75.6451056402078 | 48.4048943597922 |
| 94 | 132.69 | 67.8838973039675 | 64.8061026960325 |
| 95 | 135.81 | 60.3436720235163 | 75.4663279764837 |
| 96 | 116.07 | 62.4833671598897 | 53.5866328401103 |
| 97 | 101.42 | 58.2046956981979 | 43.2153043018021 |
| 98 | 75.73 | 38.3619165228313 | 37.3680834771687 |
| 99 | 55.48 | 32.537698605433 | 22.942301394567 |
| 100 | 43.8 | 32.3426954349203 | 11.4573045650797 |
| 101 | 45.29 | 30.2955215500645 | 14.9944784499355 |
| 102 | 44.01 | 23.0488792419649 | 20.9611207580351 |
| 103 | 47.48 | 18.3762993220917 | 29.1037006779083 |
| 104 | 51.07 | 26.1461333909928 | 24.9238666090072 |
| 105 | 57.84 | 30.3178046927719 | 27.5221953072281 |
| 106 | 69.04 | 32.3164074877633 | 36.7235925122367 |
| 107 | 65.61 | 33.2072197595893 | 32.4027802404107 |
| 108 | 72.87 | 40.3427544160329 | 32.5272455839671 |
| 109 | 68.41 | 43.0161154171533 | 25.3938845828467 |
| 110 | 73.25 | 45.2995727645419 | 27.9504272354581 |
| 111 | 77.43 | 49.2169903274112 | 28.2130096725888 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0076473633178198 | 0.0152947266356396 | 0.99235263668218 |
| 6 | 0.00139677209041784 | 0.00279354418083568 | 0.998603227909582 |
| 7 | 0.000218103298605027 | 0.000436206597210053 | 0.999781896701395 |
| 8 | 3.32870984615191e-05 | 6.65741969230383e-05 | 0.999966712901538 |
| 9 | 4.32657197371528e-06 | 8.65314394743056e-06 | 0.999995673428026 |
| 10 | 6.92490248508037e-07 | 1.38498049701607e-06 | 0.999999307509752 |
| 11 | 1.26088191084538e-07 | 2.52176382169077e-07 | 0.99999987391181 |
| 12 | 1.64548617706270e-08 | 3.29097235412541e-08 | 0.999999983545138 |
| 13 | 4.550569371878e-09 | 9.101138743756e-09 | 0.99999999544943 |
| 14 | 9.37401733802968e-10 | 1.87480346760594e-09 | 0.999999999062598 |
| 15 | 1.12902616565253e-09 | 2.25805233130505e-09 | 0.999999998870974 |
| 16 | 1.15807862414103e-09 | 2.31615724828206e-09 | 0.999999998841921 |
| 17 | 5.76541196062174e-10 | 1.15308239212435e-09 | 0.999999999423459 |
| 18 | 1.95853873718305e-10 | 3.91707747436610e-10 | 0.999999999804146 |
| 19 | 5.1722977849872e-11 | 1.03445955699744e-10 | 0.999999999948277 |
| 20 | 9.98217808795113e-12 | 1.99643561759023e-11 | 0.999999999990018 |
| 21 | 1.92118740985458e-12 | 3.84237481970915e-12 | 0.999999999998079 |
| 22 | 4.55409013107618e-13 | 9.10818026215236e-13 | 0.999999999999545 |
| 23 | 3.61328381794412e-13 | 7.22656763588824e-13 | 0.999999999999639 |
| 24 | 1.43009747196045e-13 | 2.8601949439209e-13 | 0.999999999999857 |
| 25 | 1.14679009239687e-13 | 2.29358018479374e-13 | 0.999999999999885 |
| 26 | 3.44480927679641e-14 | 6.88961855359282e-14 | 0.999999999999966 |
| 27 | 6.36734941660004e-15 | 1.27346988332001e-14 | 0.999999999999994 |
| 28 | 1.53534694571255e-15 | 3.07069389142509e-15 | 0.999999999999998 |
| 29 | 7.46472522238545e-16 | 1.49294504447709e-15 | 1 |
| 30 | 6.25466533341625e-16 | 1.25093306668325e-15 | 1 |
| 31 | 1.62785444003324e-16 | 3.25570888006649e-16 | 1 |
| 32 | 3.40522949395136e-17 | 6.81045898790272e-17 | 1 |
| 33 | 6.78905287725539e-18 | 1.35781057545108e-17 | 1 |
| 34 | 1.41447291898268e-18 | 2.82894583796535e-18 | 1 |
| 35 | 3.26386693957087e-19 | 6.52773387914173e-19 | 1 |
| 36 | 9.85942924229823e-20 | 1.97188584845965e-19 | 1 |
| 37 | 2.28736224777857e-20 | 4.57472449555714e-20 | 1 |
| 38 | 7.11322538701448e-21 | 1.42264507740290e-20 | 1 |
| 39 | 2.19129109195900e-21 | 4.38258218391801e-21 | 1 |
| 40 | 9.10430135843322e-22 | 1.82086027168664e-21 | 1 |
| 41 | 5.9031628504441e-22 | 1.18063257008882e-21 | 1 |
| 42 | 3.72804978087277e-22 | 7.45609956174554e-22 | 1 |
| 43 | 4.44116319768361e-22 | 8.88232639536722e-22 | 1 |
| 44 | 6.19926696783512e-22 | 1.23985339356702e-21 | 1 |
| 45 | 5.07095772714657e-21 | 1.01419154542931e-20 | 1 |
| 46 | 1.28548559514558e-20 | 2.57097119029116e-20 | 1 |
| 47 | 7.096191835121e-20 | 1.4192383670242e-19 | 1 |
| 48 | 2.06176048572089e-18 | 4.12352097144179e-18 | 1 |
| 49 | 4.14401562304348e-17 | 8.28803124608696e-17 | 1 |
| 50 | 6.78394683087695e-15 | 1.35678936617539e-14 | 0.999999999999993 |
| 51 | 4.48667893932478e-14 | 8.97335787864956e-14 | 0.999999999999955 |
| 52 | 8.38379644382117e-14 | 1.67675928876423e-13 | 0.999999999999916 |
| 53 | 3.07761764994792e-13 | 6.15523529989584e-13 | 0.999999999999692 |
| 54 | 1.21855543953909e-12 | 2.43711087907819e-12 | 0.999999999998781 |
| 55 | 2.12614648342259e-11 | 4.25229296684519e-11 | 0.999999999978739 |
| 56 | 2.20552249924672e-10 | 4.41104499849344e-10 | 0.999999999779448 |
| 57 | 9.90749169876725e-10 | 1.98149833975345e-09 | 0.99999999900925 |
| 58 | 5.57508166833243e-09 | 1.11501633366649e-08 | 0.999999994424918 |
| 59 | 3.06670519974533e-08 | 6.13341039949066e-08 | 0.999999969332948 |
| 60 | 2.90637534814009e-07 | 5.81275069628017e-07 | 0.999999709362465 |
| 61 | 1.47339520884296e-06 | 2.94679041768592e-06 | 0.999998526604791 |
| 62 | 3.45383644486776e-06 | 6.90767288973552e-06 | 0.999996546163555 |
| 63 | 4.83369788890461e-06 | 9.66739577780923e-06 | 0.999995166302111 |
| 64 | 6.49759962382277e-06 | 1.29951992476455e-05 | 0.999993502400376 |
| 65 | 1.14785785513790e-05 | 2.29571571027580e-05 | 0.999988521421449 |
| 66 | 1.52170140278202e-05 | 3.04340280556403e-05 | 0.999984782985972 |
| 67 | 1.84803065523026e-05 | 3.69606131046052e-05 | 0.999981519693448 |
| 68 | 2.58928908964950e-05 | 5.17857817929899e-05 | 0.999974107109104 |
| 69 | 3.82430394317363e-05 | 7.64860788634726e-05 | 0.999961756960568 |
| 70 | 5.19461668422504e-05 | 0.000103892333684501 | 0.999948053833158 |
| 71 | 8.2816094917897e-05 | 0.000165632189835794 | 0.999917183905082 |
| 72 | 0.000100291923631035 | 0.000200583847262071 | 0.999899708076369 |
| 73 | 7.70807049668336e-05 | 0.000154161409933667 | 0.999922919295033 |
| 74 | 6.33865769926826e-05 | 0.000126773153985365 | 0.999936613423007 |
| 75 | 5.78810847324065e-05 | 0.000115762169464813 | 0.999942118915268 |
| 76 | 5.08308886367328e-05 | 0.000101661777273466 | 0.999949169111363 |
| 77 | 8.07681623927217e-05 | 0.000161536324785443 | 0.999919231837607 |
| 78 | 0.000118622957190525 | 0.000237245914381051 | 0.99988137704281 |
| 79 | 0.000133251220305663 | 0.000266502440611325 | 0.999866748779694 |
| 80 | 0.00014322679343419 | 0.00028645358686838 | 0.999856773206566 |
| 81 | 0.000236850066513689 | 0.000473700133027377 | 0.999763149933486 |
| 82 | 0.000421011365266578 | 0.000842022730533156 | 0.999578988634733 |
| 83 | 0.000765332798712077 | 0.00153066559742415 | 0.999234667201288 |
| 84 | 0.0019286646575156 | 0.0038573293150312 | 0.998071335342484 |
| 85 | 0.00624262306377481 | 0.0124852461275496 | 0.993757376936225 |
| 86 | 0.0308153422426565 | 0.0616306844853129 | 0.969184657757344 |
| 87 | 0.0621753813976319 | 0.124350762795264 | 0.937824618602368 |
| 88 | 0.203766778858362 | 0.407533557716724 | 0.796233221141638 |
| 89 | 0.374561990793369 | 0.749123981586739 | 0.62543800920663 |
| 90 | 0.605430942304534 | 0.789138115390932 | 0.394569057695466 |
| 91 | 0.732707323770796 | 0.534585352458409 | 0.267292676229205 |
| 92 | 0.873792629852052 | 0.252414740295897 | 0.126207370147948 |
| 93 | 0.933114472959905 | 0.133771054080189 | 0.0668855270400947 |
| 94 | 0.962492506699994 | 0.0750149866000112 | 0.0375074933000056 |
| 95 | 0.999244725490263 | 0.00151054901947450 | 0.000755274509737249 |
| 96 | 0.999619218630353 | 0.000761562739294844 | 0.000380781369647422 |
| 97 | 0.999593499838218 | 0.000813000323564021 | 0.000406500161782011 |
| 98 | 0.999637467824319 | 0.000725064351362889 | 0.000362532175681444 |
| 99 | 0.99913115878141 | 0.00173768243718269 | 0.000868841218591343 |
| 100 | 0.999711540572145 | 0.000576918855710372 | 0.000288459427855186 |
| 101 | 0.999916042509363 | 0.000167914981273365 | 8.39574906366826e-05 |
| 102 | 0.99991262266919 | 0.000174754661621746 | 8.7377330810873e-05 |
| 103 | 0.999598346838513 | 0.000803306322973919 | 0.000401653161486959 |
| 104 | 0.999428550778122 | 0.00114289844375523 | 0.000571449221877614 |
| 105 | 0.999375255999146 | 0.00124948800170849 | 0.000624744000854243 |
| 106 | 0.997119369433465 | 0.00576126113307057 | 0.00288063056653528 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 91 | 0.892156862745098 | NOK |
| 5% type I error level | 93 | 0.911764705882353 | NOK |
| 10% type I error level | 95 | 0.931372549019608 | NOK |
