| Multiple Linear Regression - Estimated Regression Equation |
| Bel20[t] = + 4765.30342448302 -0.081675043345911Goudprijs[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) | 4765.30342448302 | 301.416177 | 15.8097 | 0 | 0 |
| Goudprijs | -0.081675043345911 | 0.015442 | -5.2892 | 1e-06 | 1e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.539896177404536 |
| R-squared | 0.29148788237603 |
| Adjusted R-squared | 0.281068586528619 |
| F-TEST (value) | 27.9757755845325 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 68 |
| p-value | 1.41125002617315e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 719.60904727157 |
| Sum Squared Residuals | 35212928.3022266 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2649.2 | 2227.08810242213 | 422.111897577871 |
| 2 | 2579.4 | 2209.44629305942 | 369.953706940576 |
| 3 | 2504.6 | 2295.77681387605 | 208.823186123949 |
| 4 | 2462.3 | 2301.98411717034 | 160.315882829660 |
| 5 | 2467.4 | 2116.09171851505 | 351.308281484953 |
| 6 | 2446.7 | 2258.28796898028 | 188.412031019722 |
| 7 | 2656.3 | 2517.19785638682 | 139.102143613184 |
| 8 | 2626.2 | 2606.30532867721 | 19.8946713227949 |
| 9 | 2482.6 | 2663.06948380261 | -180.469483802613 |
| 10 | 2539.9 | 2706.76563199268 | -166.865631992675 |
| 11 | 2502.7 | 2725.30586683220 | -222.605866832197 |
| 12 | 2466.9 | 2778.96637031046 | -312.066370310461 |
| 13 | 2513.2 | 2912.91344139775 | -399.713441397755 |
| 14 | 2443.3 | 2964.20536861899 | -520.905368618987 |
| 15 | 2293.4 | 3011.98526897634 | -718.585268976345 |
| 16 | 2070.8 | 3018.8459726174 | -948.045972617401 |
| 17 | 2029.6 | 2986.66600553911 | -957.066005539113 |
| 18 | 2052 | 2974.33307399388 | -922.33307399388 |
| 19 | 1864.4 | 2983.64402893531 | -1119.24402893531 |
| 20 | 1670.1 | 2891.92295525786 | -1221.82295525786 |
| 21 | 1811 | 2838.18077673625 | -1027.18077673625 |
| 22 | 1905.4 | 3064.01227158769 | -1158.61227158769 |
| 23 | 1862.8 | 3160.38882273587 | -1297.58882273587 |
| 24 | 2014.5 | 3197.55096745825 | -1183.05096745825 |
| 25 | 2197.8 | 3160.87887299594 | -963.07887299594 |
| 26 | 2962.3 | 3255.70359832054 | -293.403598320543 |
| 27 | 3047 | 3288.70031583229 | -241.700315832291 |
| 28 | 3032.6 | 3198.93944319514 | -166.339443195135 |
| 29 | 3504.4 | 3263.21770230837 | 241.182297691633 |
| 30 | 3801.1 | 3259.13395014107 | 541.966049858928 |
| 31 | 3857.6 | 3247.45441894261 | 610.145581057394 |
| 32 | 3674.4 | 3122.98165288344 | 551.418347116562 |
| 33 | 3721 | 3119.7146511496 | 601.285348850399 |
| 34 | 3844.5 | 3181.29763383242 | 663.202366167582 |
| 35 | 4116.7 | 3315.97978030983 | 800.720219690174 |
| 36 | 4105.2 | 3319.98185743378 | 785.218142566225 |
| 37 | 4435.2 | 3374.21408621546 | 1060.98591378454 |
| 38 | 4296.5 | 3422.72906196293 | 873.770938037069 |
| 39 | 4202.5 | 3484.39371968909 | 718.106280310906 |
| 40 | 4562.8 | 3491.66279854688 | 1071.13720145312 |
| 41 | 4621.4 | 3481.94346838872 | 1139.45653161128 |
| 42 | 4697 | 3463.64825867923 | 1233.35174132077 |
| 43 | 4591.3 | 3444.53629853629 | 1146.76370146371 |
| 44 | 4357 | 3464.38333406935 | 892.616665930654 |
| 45 | 4502.6 | 3430.07981586406 | 1072.52018413594 |
| 46 | 4443.9 | 3492.88792419707 | 951.01207580293 |
| 47 | 4290.9 | 3515.26688607385 | 775.633113926151 |
| 48 | 4199.8 | 3487.2523462062 | 712.5476537938 |
| 49 | 4138.5 | 3543.93482628826 | 594.565173711737 |
| 50 | 3970.1 | 3528.98829335596 | 441.111706644038 |
| 51 | 3862.3 | 3471.65241292713 | 390.647587072868 |
| 52 | 3701.6 | 3454.41897878114 | 247.181021218855 |
| 53 | 3570.12 | 3526.45636701224 | 43.6636329877617 |
| 54 | 3801.06 | 3371.60048482839 | 429.459515171609 |
| 55 | 3895.51 | 3458.09435573171 | 437.415644268290 |
| 56 | 3917.96 | 3549.48872923579 | 368.471270764215 |
| 57 | 3813.06 | 3545.81335228522 | 267.246647714781 |
| 58 | 3667.03 | 3577.42159406009 | 89.6084059399136 |
| 59 | 3494.17 | 3637.20772578929 | -143.037725789293 |
| 60 | 3364 | 3700.99593464245 | -336.99593464245 |
| 61 | 3295.3 | 3738.32142945153 | -443.021429451531 |
| 62 | 3277 | 3788.14320589254 | -511.143205892537 |
| 63 | 3257.2 | 3830.04250312899 | -572.84250312899 |
| 64 | 3161.7 | 3838.61838268031 | -676.91838268031 |
| 65 | 3097.3 | 3838.04665737689 | -740.746657376889 |
| 66 | 3061.3 | 3891.21711059508 | -829.917110595077 |
| 67 | 3119.3 | 3895.79091302245 | -776.490913022448 |
| 68 | 3106.22 | 3903.14166692358 | -796.92166692358 |
| 69 | 3080.58 | 3910.73744595475 | -830.15744595475 |
| 70 | 2981.85 | 3915.31124838212 | -933.46124838212 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.00271782252297893 | 0.00543564504595785 | 0.997282177477021 |
| 6 | 0.000415089198144224 | 0.000830178396288449 | 0.999584910801856 |
| 7 | 6.68518771421995e-05 | 0.000133703754284399 | 0.999933148122858 |
| 8 | 6.89900309341026e-06 | 1.37980061868205e-05 | 0.999993100996907 |
| 9 | 2.22126770705098e-06 | 4.44253541410196e-06 | 0.999997778732293 |
| 10 | 2.53784292155581e-07 | 5.07568584311163e-07 | 0.999999746215708 |
| 11 | 3.24732413134827e-08 | 6.49464826269653e-08 | 0.999999967526759 |
| 12 | 4.9143344232158e-09 | 9.8286688464316e-09 | 0.999999995085666 |
| 13 | 4.81655077028751e-10 | 9.63310154057503e-10 | 0.999999999518345 |
| 14 | 6.98408639029019e-11 | 1.39681727805804e-10 | 0.99999999993016 |
| 15 | 8.25195391093207e-11 | 1.65039078218641e-10 | 0.99999999991748 |
| 16 | 1.87646094775231e-09 | 3.75292189550463e-09 | 0.99999999812354 |
| 17 | 6.24599451275262e-09 | 1.24919890255052e-08 | 0.999999993754006 |
| 18 | 6.3583802258866e-09 | 1.27167604517732e-08 | 0.99999999364162 |
| 19 | 3.11472950128520e-08 | 6.22945900257039e-08 | 0.999999968852705 |
| 20 | 7.9197403583946e-07 | 1.58394807167892e-06 | 0.999999208025964 |
| 21 | 2.76752853902068e-06 | 5.53505707804136e-06 | 0.999997232471461 |
| 22 | 3.89737589362887e-06 | 7.79475178725774e-06 | 0.999996102624106 |
| 23 | 8.86779339765293e-06 | 1.77355867953059e-05 | 0.999991132206602 |
| 24 | 2.5134035825225e-05 | 5.026807165045e-05 | 0.999974865964175 |
| 25 | 0.000154690071026657 | 0.000309380142053315 | 0.999845309928973 |
| 26 | 0.010872838392084 | 0.021745676784168 | 0.989127161607916 |
| 27 | 0.0932399037851689 | 0.186479807570338 | 0.906760096214831 |
| 28 | 0.329169012007137 | 0.658338024014275 | 0.670830987992863 |
| 29 | 0.70350127626752 | 0.59299744746496 | 0.29649872373248 |
| 30 | 0.914434304614233 | 0.171131390771533 | 0.0855656953857666 |
| 31 | 0.973694889238028 | 0.0526102215239438 | 0.0263051107619719 |
| 32 | 0.995222638774283 | 0.00955472245143393 | 0.00477736122571697 |
| 33 | 0.999688296482678 | 0.000623407034644084 | 0.000311703517322042 |
| 34 | 0.999988174220698 | 2.36515586048543e-05 | 1.18257793024272e-05 |
| 35 | 0.999996632441126 | 6.7351177476962e-06 | 3.3675588738481e-06 |
| 36 | 0.99999890515189 | 2.18969622156121e-06 | 1.09484811078060e-06 |
| 37 | 0.999999272321587 | 1.45535682619666e-06 | 7.27678413098331e-07 |
| 38 | 0.999999125301375 | 1.74939725070256e-06 | 8.74698625351279e-07 |
| 39 | 0.999998570914354 | 2.85817129294742e-06 | 1.42908564647371e-06 |
| 40 | 0.999999349304193 | 1.30139161501156e-06 | 6.50695807505778e-07 |
| 41 | 0.999999786133657 | 4.27732686701193e-07 | 2.13866343350597e-07 |
| 42 | 0.999999962682362 | 7.4635276161619e-08 | 3.73176380808095e-08 |
| 43 | 0.99999998594877 | 2.81024586127777e-08 | 1.40512293063889e-08 |
| 44 | 0.999999982891823 | 3.42163538686300e-08 | 1.71081769343150e-08 |
| 45 | 0.999999990677896 | 1.86442086833993e-08 | 9.32210434169965e-09 |
| 46 | 0.999999998748654 | 2.50269238949582e-09 | 1.25134619474791e-09 |
| 47 | 0.999999999800752 | 3.98495372887314e-10 | 1.99247686443657e-10 |
| 48 | 0.999999999917193 | 1.65613181862986e-10 | 8.2806590931493e-11 |
| 49 | 0.999999999997135 | 5.73107512732147e-12 | 2.86553756366074e-12 |
| 50 | 0.99999999999879 | 2.4199652667224e-12 | 1.2099826333612e-12 |
| 51 | 0.99999999999293 | 1.41415934540421e-11 | 7.07079672702105e-12 |
| 52 | 0.999999999975129 | 4.97425056713071e-11 | 2.48712528356536e-11 |
| 53 | 0.999999999945206 | 1.09587845250076e-10 | 5.47939226250381e-11 |
| 54 | 0.99999999999377 | 1.24601356693217e-11 | 6.23006783466084e-12 |
| 55 | 0.99999999994904 | 1.01919167268810e-10 | 5.09595836344052e-11 |
| 56 | 0.999999999984359 | 3.12830561633148e-11 | 1.56415280816574e-11 |
| 57 | 0.999999999980774 | 3.84528040195124e-11 | 1.92264020097562e-11 |
| 58 | 0.999999999906154 | 1.87692099076313e-10 | 9.38460495381565e-11 |
| 59 | 0.999999998782952 | 2.43409558434155e-09 | 1.21704779217078e-09 |
| 60 | 0.99999998461159 | 3.07768201524078e-08 | 1.53884100762039e-08 |
| 61 | 0.999999855797429 | 2.88405142925528e-07 | 1.44202571462764e-07 |
| 62 | 0.999998304116465 | 3.39176707099134e-06 | 1.69588353549567e-06 |
| 63 | 0.999994542429673 | 1.09151406548946e-05 | 5.45757032744732e-06 |
| 64 | 0.999939549651601 | 0.000120900696797492 | 6.0450348398746e-05 |
| 65 | 0.999457515169032 | 0.00108496966193609 | 0.000542484830968046 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 55 | 0.901639344262295 | NOK |
| 5% type I error level | 56 | 0.918032786885246 | NOK |
| 10% type I error level | 57 | 0.934426229508197 | NOK |
