| Multiple Linear Regression - Estimated Regression Equation |
| Apple[t] = -135.264627706655 -6.77815767354195e-07Volume[t] + 4.10342145389171Microsoft[t] + 0.027348992500557NASDAQ[t] -0.488752826704873Consumentenvertrouwen[t] + 1.68515979988809t + 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) | -135.264627706655 | 19.178931 | -7.0528 | 0 | 0 |
| Volume | -6.77815767354195e-07 | 0 | -2.7791 | 0.0063 | 0.00315 |
| Microsoft | 4.10342145389171 | 0.905561 | 4.5314 | 1.4e-05 | 7e-06 |
| NASDAQ | 0.027348992500557 | 0.006566 | 4.1654 | 5.8e-05 | 2.9e-05 |
| Consumentenvertrouwen | -0.488752826704873 | 0.162837 | -3.0015 | 0.003249 | 0.001625 |
| t | 1.68515979988809 | 0.124389 | 13.5475 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.940892489712407 |
| R-squared | 0.885278677197211 |
| Adjusted R-squared | 0.880652817406776 |
| F-TEST (value) | 191.376028955248 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 124 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 26.4769156006578 |
| Sum Squared Residuals | 86927.35540582 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 25.94 | 48.178485553421 | -22.2384855534210 |
| 2 | 28.66 | 65.2455866415472 | -36.5855866415473 |
| 3 | 33.95 | 92.8179938710718 | -58.8679938710718 |
| 4 | 31.01 | 12.9646676747204 | 18.0453323252796 |
| 5 | 21 | -13.0343873899839 | 34.0343873899839 |
| 6 | 26.19 | 37.4321047827792 | -11.2421047827792 |
| 7 | 25.41 | 17.2057380503468 | 8.20426194965317 |
| 8 | 30.47 | 32.752138344168 | -2.28213834416801 |
| 9 | 12.88 | -16.7582255253522 | 29.6382255253522 |
| 10 | 9.78 | -4.58146321440604 | 14.3614632144060 |
| 11 | 8.25 | -26.9521645619805 | 35.2021645619805 |
| 12 | 7.44 | -50.5439929038584 | 57.9839929038584 |
| 13 | 10.81 | -10.3956856539705 | 21.2056856539705 |
| 14 | 9.12 | -18.8710421871896 | 27.9910421871896 |
| 15 | 11.03 | -39.254193537013 | 50.284193537013 |
| 16 | 12.74 | -6.95973430776079 | 19.6997343077608 |
| 17 | 9.98 | -0.681752733822847 | 10.6617527338228 |
| 18 | 11.62 | 6.58807104935829 | 5.03192895064171 |
| 19 | 9.4 | -6.15594570855574 | 15.5559457085557 |
| 20 | 9.27 | -19.8073717903496 | 29.0773717903496 |
| 21 | 7.76 | -31.7317827966484 | 39.4917827966484 |
| 22 | 8.78 | -6.35728972695249 | 15.1372897269525 |
| 23 | 10.65 | 13.7570718856074 | -3.10707188560737 |
| 24 | 10.95 | 15.3367496977254 | -4.38674969772545 |
| 25 | 12.36 | 6.28031811034205 | 6.07968188965795 |
| 26 | 10.85 | -5.23931710607091 | 16.0893171060709 |
| 27 | 11.84 | -0.87293998652521 | 12.7129399865252 |
| 28 | 12.14 | -16.4713342340234 | 28.6113342340234 |
| 29 | 11.65 | -19.4660911739685 | 31.1160911739685 |
| 30 | 8.86 | -17.6486846324182 | 26.5086846324182 |
| 31 | 7.63 | -24.7508601572977 | 32.3808601572977 |
| 32 | 7.38 | -16.8161448520036 | 24.1961448520036 |
| 33 | 7.25 | -28.2377450331806 | 35.4877450331806 |
| 34 | 8.03 | 0.0777435765113541 | 7.95225642348865 |
| 35 | 7.75 | 11.7533176503373 | -4.00331765033733 |
| 36 | 7.16 | 1.97060781692436 | 5.18939218307564 |
| 37 | 7.18 | -4.69951075701846 | 11.8795107570185 |
| 38 | 7.51 | 6.31871938976005 | 1.19128061023995 |
| 39 | 7.07 | 11.9987940748728 | -4.92879407487285 |
| 40 | 7.11 | 7.39334991482251 | -0.283349914822512 |
| 41 | 8.98 | 4.83417174391928 | 4.14582825608072 |
| 42 | 9.53 | 16.3104560719259 | -6.78045607192589 |
| 43 | 10.54 | 27.9742580726626 | -17.4342580726626 |
| 44 | 11.31 | 30.5992926827847 | -19.2892926827847 |
| 45 | 10.36 | 36.9407336498574 | -26.5807336498574 |
| 46 | 11.44 | 34.1904168829836 | -22.7504168829836 |
| 47 | 10.45 | 31.1330765380166 | -20.6830765380166 |
| 48 | 10.69 | 40.1281408273606 | -29.4381408273606 |
| 49 | 11.28 | 38.550062417357 | -27.270062417357 |
| 50 | 11.96 | 42.320148104994 | -30.360148104994 |
| 51 | 13.52 | 31.9588739559964 | -18.4388739559964 |
| 52 | 12.89 | 35.2150934122132 | -22.3250934122132 |
| 53 | 14.03 | 43.2362206602436 | -29.2062206602436 |
| 54 | 16.27 | 46.2472004379849 | -29.9772004379849 |
| 55 | 16.17 | 40.3373119130283 | -24.1673119130283 |
| 56 | 17.25 | 42.6726688073329 | -25.4226688073329 |
| 57 | 19.38 | 47.9848972643424 | -28.6048972643424 |
| 58 | 26.2 | 44.5803588710128 | -18.3803588710128 |
| 59 | 33.53 | 54.3017221318908 | -20.7717221318908 |
| 60 | 32.2 | 56.3061317155998 | -24.1061317155998 |
| 61 | 38.45 | 36.7895944503496 | 1.66040554965040 |
| 62 | 44.86 | 39.660840872117 | 5.19915912788298 |
| 63 | 41.67 | 48.2111183459934 | -6.5411183459934 |
| 64 | 36.06 | 48.4285626169065 | -12.3685626169065 |
| 65 | 39.76 | 61.340004805694 | -21.5800048056940 |
| 66 | 36.81 | 59.9961225741562 | -23.1861225741562 |
| 67 | 42.65 | 69.3475785377138 | -26.6975785377138 |
| 68 | 46.89 | 78.6821490239058 | -31.7921490239058 |
| 69 | 53.61 | 78.4706396928341 | -24.8606396928341 |
| 70 | 57.59 | 72.569278062371 | -14.9792780623710 |
| 71 | 67.82 | 85.0207464490563 | -17.2007464490563 |
| 72 | 71.89 | 77.9401074249624 | -6.0501074249624 |
| 73 | 75.51 | 76.6091575212 | -1.09915752120007 |
| 74 | 68.49 | 77.2272524293938 | -8.73725242939383 |
| 75 | 62.72 | 79.6857544919912 | -16.9657544919912 |
| 76 | 70.39 | 66.9510915701674 | 3.43890842983263 |
| 77 | 59.77 | 69.8821421863585 | -10.1121421863585 |
| 78 | 57.27 | 71.3890333027405 | -14.1190333027405 |
| 79 | 67.96 | 71.41897909899 | -3.45897909899003 |
| 80 | 67.85 | 88.322986969919 | -20.4729869699190 |
| 81 | 76.98 | 92.9925372751243 | -16.0125372751243 |
| 82 | 81.08 | 108.757906315931 | -27.6779063159307 |
| 83 | 91.66 | 114.387992192707 | -22.7279921927065 |
| 84 | 84.84 | 110.458228276817 | -25.6182282768172 |
| 85 | 85.73 | 104.92785294832 | -19.1978529483201 |
| 86 | 84.61 | 110.284764178585 | -25.6747641785849 |
| 87 | 92.91 | 112.915501662618 | -20.0055016626176 |
| 88 | 99.8 | 127.417353473631 | -27.6173534736308 |
| 89 | 121.19 | 129.944100025998 | -8.75410002599787 |
| 90 | 122.04 | 120.867878238308 | 1.17212176169202 |
| 91 | 131.76 | 114.351076350367 | 17.4089236496335 |
| 92 | 138.48 | 123.025822550719 | 15.4541774492809 |
| 93 | 153.47 | 132.512964352385 | 20.9570356476149 |
| 94 | 189.95 | 170.914809724386 | 19.0351902756140 |
| 95 | 182.22 | 152.718847807530 | 29.5011521924698 |
| 96 | 198.08 | 170.532218788816 | 27.5477812111839 |
| 97 | 135.36 | 134.225746519343 | 1.13425348065748 |
| 98 | 125.02 | 128.339813119608 | -3.31981311960778 |
| 99 | 143.5 | 142.897610200019 | 0.602389799981412 |
| 100 | 173.95 | 152.885254917168 | 21.064745082832 |
| 101 | 188.75 | 163.894935060509 | 24.8550649394914 |
| 102 | 167.44 | 158.357081011564 | 9.08291898843592 |
| 103 | 158.95 | 154.068229902799 | 4.88177009720097 |
| 104 | 169.53 | 166.816641752092 | 2.71335824790794 |
| 105 | 113.66 | 143.363418163676 | -29.7034181636756 |
| 106 | 107.59 | 113.233153703027 | -5.64315370302663 |
| 107 | 92.67 | 114.027267493110 | -21.3572674931099 |
| 108 | 85.35 | 124.450843499766 | -39.1008434997655 |
| 109 | 90.13 | 131.315761246626 | -41.1857612466257 |
| 110 | 89.31 | 120.700582249832 | -31.3905822498319 |
| 111 | 105.12 | 135.478213328747 | -30.3582133287469 |
| 112 | 125.83 | 146.395363505359 | -20.5653635053587 |
| 113 | 135.81 | 148.036926548736 | -12.2269265487360 |
| 114 | 142.43 | 163.093091892054 | -20.6630918920535 |
| 115 | 163.39 | 170.565799446791 | -7.17579944679118 |
| 116 | 168.21 | 177.397709892225 | -9.18770989222488 |
| 117 | 185.35 | 184.622354185872 | 0.727645814127707 |
| 118 | 188.5 | 191.624364689813 | -3.12436468981265 |
| 119 | 199.91 | 206.662931137023 | -6.75293113702316 |
| 120 | 210.73 | 212.419462191432 | -1.68946219143215 |
| 121 | 192.06 | 192.134425475708 | -0.0744254757083966 |
| 122 | 204.62 | 210.283651493891 | -5.66365149389066 |
| 123 | 235 | 217.086080815919 | 17.9139191840807 |
| 124 | 261.09 | 221.272619962765 | 39.8173800372346 |
| 125 | 256.88 | 188.281649578984 | 68.5983504210164 |
| 126 | 251.53 | 182.455131241217 | 69.0748687587832 |
| 127 | 257.25 | 201.650799348650 | 55.5992006513505 |
| 128 | 243.1 | 196.983927379366 | 46.1160726206341 |
| 129 | 283.75 | 208.601073973491 | 75.1489260265087 |
| 130 | 300.98 | 222.230056208288 | 78.7499437917124 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.00227065435729663 | 0.00454130871459326 | 0.997729345642703 |
| 10 | 0.000783668561400259 | 0.00156733712280052 | 0.9992163314386 |
| 11 | 0.000262233170977136 | 0.000524466341954271 | 0.999737766829023 |
| 12 | 4.54089428549818e-05 | 9.08178857099635e-05 | 0.999954591057145 |
| 13 | 7.84540046768715e-06 | 1.56908009353743e-05 | 0.999992154599532 |
| 14 | 1.12921531753865e-06 | 2.25843063507730e-06 | 0.999998870784683 |
| 15 | 1.18892874298638e-06 | 2.37785748597277e-06 | 0.999998811071257 |
| 16 | 3.37602263715364e-07 | 6.75204527430727e-07 | 0.999999662397736 |
| 17 | 5.35765536330916e-08 | 1.07153107266183e-07 | 0.999999946423446 |
| 18 | 7.90976768039436e-09 | 1.58195353607887e-08 | 0.999999992090232 |
| 19 | 1.1202588850449e-09 | 2.2405177700898e-09 | 0.999999998879741 |
| 20 | 1.70308949751608e-10 | 3.40617899503216e-10 | 0.999999999829691 |
| 21 | 3.54943522992144e-11 | 7.09887045984289e-11 | 0.999999999964506 |
| 22 | 4.88324897661246e-12 | 9.76649795322493e-12 | 0.999999999995117 |
| 23 | 6.47237807003038e-13 | 1.29447561400608e-12 | 0.999999999999353 |
| 24 | 7.88800772346634e-14 | 1.57760154469327e-13 | 0.99999999999992 |
| 25 | 2.41924680798591e-14 | 4.83849361597182e-14 | 0.999999999999976 |
| 26 | 6.45610225334389e-15 | 1.29122045066878e-14 | 0.999999999999994 |
| 27 | 9.79422379477627e-16 | 1.95884475895525e-15 | 0.999999999999999 |
| 28 | 3.11140778748183e-16 | 6.22281557496367e-16 | 1 |
| 29 | 8.21383320983268e-17 | 1.64276664196654e-16 | 1 |
| 30 | 1.70527951000045e-17 | 3.41055902000091e-17 | 1 |
| 31 | 4.40047318458629e-18 | 8.80094636917258e-18 | 1 |
| 32 | 1.01098881447753e-18 | 2.02197762895506e-18 | 1 |
| 33 | 5.18862923003446e-19 | 1.03772584600689e-18 | 1 |
| 34 | 9.67472902857229e-20 | 1.93494580571446e-19 | 1 |
| 35 | 2.60499498487988e-20 | 5.20998996975975e-20 | 1 |
| 36 | 6.96000222125746e-21 | 1.39200044425149e-20 | 1 |
| 37 | 2.57922389884548e-21 | 5.15844779769096e-21 | 1 |
| 38 | 6.66907861830183e-22 | 1.33381572366037e-21 | 1 |
| 39 | 1.80271097390945e-22 | 3.6054219478189e-22 | 1 |
| 40 | 8.29864029079795e-23 | 1.65972805815959e-22 | 1 |
| 41 | 5.75110656464839e-23 | 1.15022131292968e-22 | 1 |
| 42 | 2.63740100989436e-23 | 5.27480201978871e-23 | 1 |
| 43 | 6.46709755248152e-24 | 1.29341951049630e-23 | 1 |
| 44 | 1.49012390153578e-24 | 2.98024780307156e-24 | 1 |
| 45 | 3.36250086907328e-25 | 6.72500173814657e-25 | 1 |
| 46 | 5.16653603550891e-26 | 1.03330720710178e-25 | 1 |
| 47 | 1.29005361019737e-26 | 2.58010722039473e-26 | 1 |
| 48 | 2.88024098481495e-27 | 5.76048196962991e-27 | 1 |
| 49 | 3.86270370455062e-28 | 7.72540740910124e-28 | 1 |
| 50 | 5.1658044062612e-29 | 1.03316088125224e-28 | 1 |
| 51 | 2.78882917668439e-29 | 5.57765835336878e-29 | 1 |
| 52 | 6.45605459224193e-30 | 1.29121091844839e-29 | 1 |
| 53 | 8.66558766648855e-31 | 1.73311753329771e-30 | 1 |
| 54 | 2.16591986304775e-31 | 4.33183972609549e-31 | 1 |
| 55 | 1.34029399104026e-31 | 2.68058798208052e-31 | 1 |
| 56 | 1.02572369387912e-31 | 2.05144738775824e-31 | 1 |
| 57 | 1.27699197340272e-31 | 2.55398394680545e-31 | 1 |
| 58 | 1.70020616053307e-27 | 3.40041232106614e-27 | 1 |
| 59 | 7.37590853004726e-24 | 1.47518170600945e-23 | 1 |
| 60 | 3.88795743629668e-23 | 7.77591487259337e-23 | 1 |
| 61 | 2.91270842056247e-21 | 5.82541684112493e-21 | 1 |
| 62 | 1.61786901565852e-18 | 3.23573803131703e-18 | 1 |
| 63 | 1.28848215709782e-16 | 2.57696431419565e-16 | 1 |
| 64 | 1.00382595309837e-15 | 2.00765190619675e-15 | 0.999999999999999 |
| 65 | 3.74199454501944e-15 | 7.48398909003887e-15 | 0.999999999999996 |
| 66 | 5.48047793527659e-15 | 1.09609558705532e-14 | 0.999999999999994 |
| 67 | 9.19165264595268e-15 | 1.83833052919054e-14 | 0.99999999999999 |
| 68 | 3.64622072127117e-14 | 7.29244144254234e-14 | 0.999999999999964 |
| 69 | 2.08540147123569e-12 | 4.17080294247139e-12 | 0.999999999997915 |
| 70 | 1.23889246662059e-10 | 2.47778493324118e-10 | 0.99999999987611 |
| 71 | 2.09618494802648e-08 | 4.19236989605296e-08 | 0.99999997903815 |
| 72 | 4.51088677832015e-06 | 9.02177355664029e-06 | 0.999995489113222 |
| 73 | 7.07393671053924e-05 | 0.000141478734210785 | 0.999929260632895 |
| 74 | 0.000205825396529211 | 0.000411650793058423 | 0.999794174603471 |
| 75 | 0.000157868499977219 | 0.000315736999954437 | 0.999842131500023 |
| 76 | 0.000200471330016404 | 0.000400942660032808 | 0.999799528669984 |
| 77 | 0.000220615370467109 | 0.000441230740934219 | 0.999779384629533 |
| 78 | 0.000185758073985888 | 0.000371516147971777 | 0.999814241926014 |
| 79 | 0.00151703595391136 | 0.00303407190782272 | 0.998482964046089 |
| 80 | 0.00335693186973702 | 0.00671386373947405 | 0.996643068130263 |
| 81 | 0.00900195386329636 | 0.0180039077265927 | 0.990998046136704 |
| 82 | 0.0136716678443468 | 0.0273433356886936 | 0.986328332155653 |
| 83 | 0.0284441286097502 | 0.0568882572195003 | 0.97155587139025 |
| 84 | 0.0255214851179051 | 0.0510429702358103 | 0.974478514882095 |
| 85 | 0.0200296514052098 | 0.0400593028104196 | 0.97997034859479 |
| 86 | 0.0163657460466244 | 0.0327314920932488 | 0.983634253953376 |
| 87 | 0.0176874943440083 | 0.0353749886880167 | 0.982312505655992 |
| 88 | 0.0256935350408176 | 0.0513870700816351 | 0.974306464959182 |
| 89 | 0.0681820476756125 | 0.136364095351225 | 0.931817952324387 |
| 90 | 0.164204649901271 | 0.328409299802543 | 0.835795350098729 |
| 91 | 0.269982519646002 | 0.539965039292004 | 0.730017480353998 |
| 92 | 0.475724247224613 | 0.951448494449225 | 0.524275752775387 |
| 93 | 0.824946083740823 | 0.350107832518353 | 0.175053916259177 |
| 94 | 0.946022672306675 | 0.107954655386650 | 0.0539773276933249 |
| 95 | 0.975073980706578 | 0.0498520385868444 | 0.0249260192934222 |
| 96 | 0.999669446876487 | 0.000661106247025361 | 0.000330553123512681 |
| 97 | 0.999398939141464 | 0.00120212171707268 | 0.000601060858536341 |
| 98 | 0.999305945423068 | 0.00138810915386385 | 0.000694054576931923 |
| 99 | 0.999012623305296 | 0.00197475338940889 | 0.000987376694704446 |
| 100 | 0.999472547136667 | 0.00105490572666614 | 0.000527452863333069 |
| 101 | 0.99969143232711 | 0.000617135345779361 | 0.000308567672889680 |
| 102 | 0.999943587909488 | 0.000112824181024662 | 5.64120905123308e-05 |
| 103 | 0.999892931118658 | 0.000214137762683155 | 0.000107068881341577 |
| 104 | 0.999985930271678 | 2.81394566438669e-05 | 1.40697283219335e-05 |
| 105 | 0.999983142940273 | 3.37141194534049e-05 | 1.68570597267025e-05 |
| 106 | 0.999965346637842 | 6.93067243169453e-05 | 3.46533621584727e-05 |
| 107 | 0.999944483851323 | 0.000111032297353433 | 5.55161486767166e-05 |
| 108 | 0.999916378375824 | 0.000167243248352207 | 8.36216241761036e-05 |
| 109 | 0.999802263684607 | 0.000395472630785408 | 0.000197736315392704 |
| 110 | 0.99953411200284 | 0.000931775994319226 | 0.000465887997159613 |
| 111 | 0.999002884984767 | 0.00199423003046700 | 0.000997115015233502 |
| 112 | 0.997812236318194 | 0.0043755273636129 | 0.00218776368180645 |
| 113 | 0.9954363166532 | 0.00912736669359867 | 0.00456368334679933 |
| 114 | 0.99015969042232 | 0.0196806191553603 | 0.00984030957768015 |
| 115 | 0.980665602566502 | 0.0386687948669965 | 0.0193343974334983 |
| 116 | 0.966198162260553 | 0.0676036754788937 | 0.0338018377394469 |
| 117 | 0.970955724920936 | 0.0580885501581285 | 0.0290442750790643 |
| 118 | 0.955982179227945 | 0.0880356415441107 | 0.0440178207720554 |
| 119 | 0.9684313656718 | 0.0631372686564009 | 0.0315686343282005 |
| 120 | 0.965841492380531 | 0.068317015238938 | 0.034158507619469 |
| 121 | 0.957549373727507 | 0.0849012525449852 | 0.0424506262724926 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 90 | 0.79646017699115 | NOK |
| 5% type I error level | 98 | 0.867256637168142 | NOK |
| 10% type I error level | 107 | 0.946902654867257 | NOK |
