| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -1880.76580017901 + 0.192813678210668Nikkei[t] + 0.286352347829325DJ_Indust[t] + 0.0145348419797004Goudprijs[t] -10.0672478500057Conjunct_Seizoenzuiver[t] -2.30528030345926Cons_vertrouw[t] -18.3563447065875Rend_oblig_EUR[t] + 35.9956460531887Alg_consumptie_index_BE[t] -234.559373355687Gem_rente_kasbon_5j[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) | -1880.76580017901 | 273.254826 | -6.8828 | 0 | 0 |
| Nikkei | 0.192813678210668 | 0.015731 | 12.2568 | 0 | 0 |
| DJ_Indust | 0.286352347829325 | 0.034544 | 8.2895 | 0 | 0 |
| Goudprijs | 0.0145348419797004 | 0.008327 | 1.7454 | 0.085789 | 0.042894 |
| Conjunct_Seizoenzuiver | -10.0672478500057 | 6.08984 | -1.6531 | 0.103281 | 0.051641 |
| Cons_vertrouw | -2.30528030345926 | 7.758898 | -0.2971 | 0.767357 | 0.383678 |
| Rend_oblig_EUR | -18.3563447065875 | 81.447108 | -0.2254 | 0.822415 | 0.411208 |
| Alg_consumptie_index_BE | 35.9956460531887 | 19.585068 | 1.8379 | 0.070791 | 0.035396 |
| Gem_rente_kasbon_5j | -234.559373355687 | 109.529101 | -2.1415 | 0.036106 | 0.018053 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.983718731063487 |
| R-squared | 0.967702541845157 |
| Adjusted R-squared | 0.963601277317558 |
| F-TEST (value) | 235.952237494821 |
| F-TEST (DF numerator) | 8 |
| F-TEST (DF denominator) | 63 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 161.334860280945 |
| Sum Squared Residuals | 1639823.03993793 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2502.66 | 2715.11121737621 | -212.451217376205 |
| 2 | 2466.92 | 2525.04678792393 | -58.1267879239323 |
| 3 | 2513.17 | 2458.23207526742 | 54.937924732581 |
| 4 | 2443.27 | 2462.11526691126 | -18.8452669112567 |
| 5 | 2293.41 | 2420.37565727693 | -126.965657276927 |
| 6 | 2070.83 | 2097.57373016300 | -26.7437301629974 |
| 7 | 2029.6 | 2138.19060900769 | -108.590609007692 |
| 8 | 2052.02 | 2069.87463273278 | -17.8546327327776 |
| 9 | 1864.44 | 1920.80090928068 | -56.3609092806808 |
| 10 | 1670.07 | 1562.24769070221 | 107.822309297789 |
| 11 | 1810.99 | 1653.09716110496 | 157.892838895036 |
| 12 | 1905.41 | 1846.72884669622 | 58.6811533037796 |
| 13 | 1862.83 | 1908.92945799045 | -46.0994579904478 |
| 14 | 2014.45 | 1830.29235960961 | 184.157640390387 |
| 15 | 2197.82 | 1977.37911028682 | 220.440889713182 |
| 16 | 2962.34 | 3047.09957305382 | -84.7595730538206 |
| 17 | 3047.03 | 3194.64081645900 | -147.610816459004 |
| 18 | 3032.6 | 3202.0950925811 | -169.495092581102 |
| 19 | 3504.37 | 3659.56124244339 | -155.19124244339 |
| 20 | 3801.06 | 3948.66912136436 | -147.609121364356 |
| 21 | 3857.62 | 3830.83700857329 | 26.7829914267107 |
| 22 | 3674.4 | 3520.40647381457 | 153.993526185434 |
| 23 | 3720.98 | 3665.17605619967 | 55.803943800331 |
| 24 | 3844.49 | 3684.19213012148 | 160.297869878519 |
| 25 | 4116.68 | 4271.70370286783 | -155.023702867825 |
| 26 | 4105.18 | 4188.01448667954 | -82.8344866795445 |
| 27 | 4435.23 | 4574.11338074336 | -138.883380743356 |
| 28 | 4296.49 | 4296.48693981688 | 0.00306018311966483 |
| 29 | 4202.52 | 4205.90718229782 | -3.38718229781947 |
| 30 | 4562.84 | 4589.98746184695 | -27.1474618469506 |
| 31 | 4621.4 | 4562.66660732138 | 58.7333926786242 |
| 32 | 4696.96 | 4566.91792302561 | 130.042076974394 |
| 33 | 4591.27 | 4377.72025694618 | 213.549743053825 |
| 34 | 4356.98 | 4195.95741884186 | 161.022581158144 |
| 35 | 4502.64 | 4406.82482368066 | 95.8151763193443 |
| 36 | 4443.91 | 4332.6346476118 | 111.275352388198 |
| 37 | 4290.89 | 4232.51989786714 | 58.3701021328598 |
| 38 | 4199.75 | 4043.98047642233 | 155.769523577667 |
| 39 | 4138.52 | 4018.02623632452 | 120.493763675484 |
| 40 | 3970.1 | 3811.40438107579 | 158.695618924211 |
| 41 | 3862.27 | 3696.03820748375 | 166.231792516251 |
| 42 | 3701.61 | 3505.66041887935 | 195.949581120654 |
| 43 | 3570.12 | 3503.17358467137 | 66.9464153286269 |
| 44 | 3801.06 | 3922.97674055146 | -121.916740551459 |
| 45 | 3895.51 | 4073.91399629707 | -178.403996297075 |
| 46 | 3917.96 | 3931.52329307046 | -13.5632930704627 |
| 47 | 3813.06 | 3910.48894529271 | -97.4289452927083 |
| 48 | 3667.03 | 3858.52945154261 | -191.499451542606 |
| 49 | 3494.17 | 3791.34559426302 | -297.175594263016 |
| 50 | 3363.99 | 3532.12246397146 | -168.132463971461 |
| 51 | 3295.32 | 3273.35752520006 | 21.96247479994 |
| 52 | 3277.01 | 3309.00481489556 | -31.9948148955643 |
| 53 | 3257.16 | 3174.07846882506 | 83.0815311749384 |
| 54 | 3161.69 | 3103.55342279670 | 58.1365772033041 |
| 55 | 3097.31 | 2991.46234121307 | 105.847658786932 |
| 56 | 3061.26 | 2850.41400538995 | 210.845994610050 |
| 57 | 3119.31 | 2858.82228946229 | 260.487710537713 |
| 58 | 3106.22 | 3019.84507318781 | 86.3749268121896 |
| 59 | 3080.58 | 2957.54148305236 | 123.038516947640 |
| 60 | 2981.85 | 2812.99259262929 | 168.857407370712 |
| 61 | 2921.44 | 2781.20598750142 | 140.234012498581 |
| 62 | 2849.27 | 2670.49488108333 | 178.775118916669 |
| 63 | 2756.76 | 2535.57989216804 | 221.180107831961 |
| 64 | 2645.64 | 2570.32042246488 | 75.319577535124 |
| 65 | 2497.84 | 2517.17044876234 | -19.3304487623408 |
| 66 | 2448.05 | 2581.48762006692 | -133.437620066922 |
| 67 | 2454.62 | 2726.19854089696 | -271.578540896956 |
| 68 | 2407.6 | 2579.49381485465 | -171.893814854649 |
| 69 | 2472.81 | 2869.19278930997 | -396.382789309974 |
| 70 | 2408.64 | 2693.30659962385 | -284.666599623851 |
| 71 | 2440.25 | 2590.90190935628 | -150.651909356276 |
| 72 | 2350.44 | 2646.2535309255 | -295.813530925502 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 12 | 0.0295705876302805 | 0.0591411752605609 | 0.97042941236972 |
| 13 | 0.00717844974521512 | 0.0143568994904302 | 0.992821550254785 |
| 14 | 0.0435359161531321 | 0.0870718323062642 | 0.956464083846868 |
| 15 | 0.0268057658008719 | 0.0536115316017438 | 0.973194234199128 |
| 16 | 0.0188968297021226 | 0.0377936594042452 | 0.981103170297877 |
| 17 | 0.00880785448045581 | 0.0176157089609116 | 0.991192145519544 |
| 18 | 0.00363552676402688 | 0.00727105352805377 | 0.996364473235973 |
| 19 | 0.0126834364079223 | 0.0253668728158446 | 0.987316563592078 |
| 20 | 0.0098312905236135 | 0.019662581047227 | 0.990168709476386 |
| 21 | 0.0085423274210427 | 0.0170846548420854 | 0.991457672578957 |
| 22 | 0.00964141881242596 | 0.0192828376248519 | 0.990358581187574 |
| 23 | 0.0101725478974864 | 0.0203450957949727 | 0.989827452102514 |
| 24 | 0.0486182409202005 | 0.0972364818404011 | 0.9513817590798 |
| 25 | 0.0358083590016406 | 0.0716167180032811 | 0.96419164099836 |
| 26 | 0.0571690072494385 | 0.114338014498877 | 0.942830992750561 |
| 27 | 0.066124279114496 | 0.132248558228992 | 0.933875720885504 |
| 28 | 0.115146615030104 | 0.230293230060208 | 0.884853384969896 |
| 29 | 0.11635616463503 | 0.23271232927006 | 0.88364383536497 |
| 30 | 0.116926248968341 | 0.233852497936681 | 0.88307375103166 |
| 31 | 0.101026985907348 | 0.202053971814697 | 0.898973014092652 |
| 32 | 0.0906935725684602 | 0.181387145136920 | 0.90930642743154 |
| 33 | 0.0811686440175722 | 0.162337288035144 | 0.918831355982428 |
| 34 | 0.066509819209235 | 0.13301963841847 | 0.933490180790765 |
| 35 | 0.04608417567395 | 0.0921683513479 | 0.95391582432605 |
| 36 | 0.0393803364857196 | 0.078760672971439 | 0.96061966351428 |
| 37 | 0.0257989522192675 | 0.051597904438535 | 0.974201047780733 |
| 38 | 0.0253574831125675 | 0.050714966225135 | 0.974642516887432 |
| 39 | 0.0255022671100953 | 0.0510045342201906 | 0.974497732889905 |
| 40 | 0.0306257244213581 | 0.0612514488427163 | 0.969374275578642 |
| 41 | 0.0296845535815120 | 0.0593691071630239 | 0.970315446418488 |
| 42 | 0.0217074982347763 | 0.0434149964695527 | 0.978292501765224 |
| 43 | 0.0262362903043584 | 0.0524725806087169 | 0.973763709695642 |
| 44 | 0.0509025446656283 | 0.101805089331257 | 0.949097455334372 |
| 45 | 0.0659967776606105 | 0.131993555321221 | 0.93400322233939 |
| 46 | 0.323763953998365 | 0.647527907996731 | 0.676236046001635 |
| 47 | 0.44756834105966 | 0.89513668211932 | 0.55243165894034 |
| 48 | 0.418157337423533 | 0.836314674847066 | 0.581842662576467 |
| 49 | 0.383416001052739 | 0.766832002105477 | 0.616583998947261 |
| 50 | 0.582636506925018 | 0.834726986149965 | 0.417363493074982 |
| 51 | 0.720832151855975 | 0.558335696288051 | 0.279167848144025 |
| 52 | 0.684592371163764 | 0.630815257672472 | 0.315407628836236 |
| 53 | 0.625380418285328 | 0.749239163429343 | 0.374619581714672 |
| 54 | 0.558957749436368 | 0.882084501127265 | 0.441042250563632 |
| 55 | 0.864147598744966 | 0.271704802510068 | 0.135852401255034 |
| 56 | 0.79014390877989 | 0.419712182440221 | 0.209856091220110 |
| 57 | 0.801865467746379 | 0.396269064507242 | 0.198134532253621 |
| 58 | 0.735939661979597 | 0.528120676040805 | 0.264060338020403 |
| 59 | 0.623104086239145 | 0.753791827521709 | 0.376895913760855 |
| 60 | 0.473003261752936 | 0.946006523505872 | 0.526996738247064 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 1 | 0.0204081632653061 | NOK |
| 5% type I error level | 10 | 0.204081632653061 | NOK |
| 10% type I error level | 23 | 0.469387755102041 | NOK |
