| Multiple Linear Regression - Estimated Regression Equation |
| BEL_20[t] = -260.706690926404 + 0.0250525591118981Nikkei[t] + 0.102631890756772DJ_Indust[t] + 0.006957119094245Goudprijs[t] -10.2630504431514Conjunct_Seizoenzuiver[t] + 12.9959047466191Cons_vertrouw[t] -7.33394620617855Alg_consumptie_index_BE[t] -165.868025333682Gem_rente_kasbon_5j[t] + 0.806808871155089Y1[t] -0.114390996301673Y2[t] + 0.181991078938916Y3[t] -0.0730288844595162Y4[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) | -260.706690926404 | 157.937258 | -1.6507 | 0.101505 | 0.050753 |
| Nikkei | 0.0250525591118981 | 0.007214 | 3.4727 | 0.000725 | 0.000362 |
| DJ_Indust | 0.102631890756772 | 0.019485 | 5.2673 | 1e-06 | 0 |
| Goudprijs | 0.006957119094245 | 0.003585 | 1.9404 | 0.054758 | 0.027379 |
| Conjunct_Seizoenzuiver | -10.2630504431514 | 3.080988 | -3.3311 | 0.001161 | 0.00058 |
| Cons_vertrouw | 12.9959047466191 | 2.936731 | 4.4253 | 2.2e-05 | 1.1e-05 |
| Alg_consumptie_index_BE | -7.33394620617855 | 10.299251 | -0.7121 | 0.477842 | 0.238921 |
| Gem_rente_kasbon_5j | -165.868025333682 | 25.569328 | -6.487 | 0 | 0 |
| Y1 | 0.806808871155089 | 0.085344 | 9.4536 | 0 | 0 |
| Y2 | -0.114390996301673 | 0.112468 | -1.0171 | 0.311225 | 0.155613 |
| Y3 | 0.181991078938916 | 0.111477 | 1.6325 | 0.105276 | 0.052638 |
| Y4 | -0.0730288844595162 | 0.073509 | -0.9935 | 0.322547 | 0.161274 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.990305665787982 |
| R-squared | 0.980705311691779 |
| Adjusted R-squared | 0.978875642972896 |
| F-TEST (value) | 536.001573164823 |
| F-TEST (DF numerator) | 11 |
| F-TEST (DF denominator) | 116 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 110.643967300128 |
| Sum Squared Residuals | 1420082.14998977 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3173.95 | 3467.20395684971 | -293.253956849713 |
| 2 | 3165.26 | 3166.33400475918 | -1.07400475917596 |
| 3 | 3092.71 | 3253.24318993043 | -160.533189930426 |
| 4 | 3053.05 | 3097.78756228371 | -44.7375622837136 |
| 5 | 3181.96 | 3068.70449700179 | 113.255502998209 |
| 6 | 2999.93 | 3069.456961988 | -69.5269619880009 |
| 7 | 3249.57 | 3054.34084232542 | 195.229157674582 |
| 8 | 3210.52 | 3274.95114213856 | -64.431142138561 |
| 9 | 3030.29 | 3206.83415388342 | -176.544153883423 |
| 10 | 2803.47 | 3051.18046483841 | -247.710464838414 |
| 11 | 2767.63 | 2869.72876856238 | -102.098768562381 |
| 12 | 2882.6 | 2903.61905785664 | -21.0190578566352 |
| 13 | 2863.36 | 2847.09881908162 | 16.2611809183754 |
| 14 | 2897.06 | 2838.34280107637 | 58.7171989236346 |
| 15 | 3012.61 | 2894.63433382927 | 117.975666170726 |
| 16 | 3142.95 | 3017.40273750787 | 125.547262492127 |
| 17 | 3032.93 | 3022.07789545689 | 10.8521045431094 |
| 18 | 3045.78 | 2931.82647547135 | 113.953524528646 |
| 19 | 3110.52 | 3007.28256317961 | 103.237436820385 |
| 20 | 3013.24 | 3113.06577998169 | -99.8257799816897 |
| 21 | 2987.1 | 3041.88708251668 | -54.7870825166776 |
| 22 | 2995.55 | 2993.17053708436 | 2.37946291564232 |
| 23 | 2833.18 | 2925.48578054612 | -92.3057805461233 |
| 24 | 2848.96 | 2831.00156340159 | 17.9584365984119 |
| 25 | 2794.83 | 2891.44310757541 | -96.6131075754113 |
| 26 | 2845.26 | 2847.5657863162 | -2.30578631619529 |
| 27 | 2915.02 | 2869.74220681775 | 45.277793182248 |
| 28 | 2892.63 | 2834.95818618887 | 57.6718138111332 |
| 29 | 2604.42 | 2694.55960606494 | -90.1396060649419 |
| 30 | 2641.65 | 2440.86718632355 | 200.782813676453 |
| 31 | 2659.81 | 2537.94838063762 | 121.861619362381 |
| 32 | 2638.53 | 2556.12213401537 | 82.4078659846257 |
| 33 | 2720.25 | 2612.97029490253 | 107.27970509747 |
| 34 | 2745.88 | 2670.9421193209 | 74.937880679098 |
| 35 | 2735.7 | 2703.55951123119 | 32.1404887688128 |
| 36 | 2811.7 | 2644.58139788928 | 167.118602110724 |
| 37 | 2799.43 | 2718.25634371398 | 81.1736562860207 |
| 38 | 2555.28 | 2635.76316212094 | -80.4831621209376 |
| 39 | 2304.98 | 2377.52624607223 | -72.546246072231 |
| 40 | 2214.95 | 2224.75260418944 | -9.80260418944235 |
| 41 | 2065.81 | 2111.78229724053 | -45.9722972405347 |
| 42 | 1940.49 | 1961.13332624318 | -20.6433262431819 |
| 43 | 2042 | 1916.43449107842 | 125.565508921578 |
| 44 | 1995.37 | 1942.15464530868 | 53.2153546913235 |
| 45 | 1946.81 | 1940.68266851602 | 6.12733148397533 |
| 46 | 1765.9 | 1861.52507793266 | -95.6250779326628 |
| 47 | 1635.25 | 1679.2992266262 | -44.0492266261958 |
| 48 | 1833.42 | 1684.40793861533 | 149.012061384672 |
| 49 | 1910.43 | 1960.85359447305 | -50.4235944730495 |
| 50 | 1959.67 | 2113.92544550314 | -154.255445503144 |
| 51 | 1969.6 | 2113.67604473085 | -144.07604473085 |
| 52 | 2061.41 | 2057.96091296613 | 3.44908703386985 |
| 53 | 2093.48 | 2222.85733855074 | -129.377338550744 |
| 54 | 2120.88 | 2084.87859936043 | 36.0014006395703 |
| 55 | 2174.56 | 2200.45878078965 | -25.8987807896495 |
| 56 | 2196.72 | 2272.17210730731 | -75.452107307312 |
| 57 | 2350.44 | 2363.07965422396 | -12.6396542239555 |
| 58 | 2440.25 | 2514.1510039829 | -73.9010039828977 |
| 59 | 2408.64 | 2551.04381936523 | -142.403819365229 |
| 60 | 2472.81 | 2554.96536232685 | -82.1553623268483 |
| 61 | 2407.6 | 2492.46870431742 | -84.8687043174208 |
| 62 | 2454.62 | 2541.96451296828 | -87.3445129682793 |
| 63 | 2448.05 | 2462.0851575135 | -14.0351575135041 |
| 64 | 2497.84 | 2486.10729206841 | 11.7327079315883 |
| 65 | 2645.64 | 2555.70179728264 | 89.9382027173589 |
| 66 | 2756.76 | 2577.8866697528 | 178.873330247205 |
| 67 | 2849.27 | 2719.98898167275 | 129.281018327251 |
| 68 | 2921.44 | 2875.68162076734 | 45.7583792326578 |
| 69 | 2981.85 | 2927.90536002629 | 53.9446399737078 |
| 70 | 3080.58 | 3083.64995305582 | -3.0699530558192 |
| 71 | 3106.22 | 3182.89048690123 | -76.6704869012327 |
| 72 | 3119.31 | 3141.57100875059 | -22.261008750592 |
| 73 | 3061.26 | 3105.43361308601 | -44.1736130860067 |
| 74 | 3097.31 | 3088.5267282131 | 8.78327178690254 |
| 75 | 3161.69 | 3159.25726362594 | 2.43273637405727 |
| 76 | 3257.16 | 3202.99522520012 | 54.1647747998809 |
| 77 | 3277.01 | 3216.61090476407 | 60.3990952359311 |
| 78 | 3295.32 | 3286.42053872432 | 8.89946127567834 |
| 79 | 3363.99 | 3330.06419902913 | 33.9258009708689 |
| 80 | 3494.17 | 3450.17288204795 | 43.9971179520542 |
| 81 | 3667.03 | 3607.03597959154 | 59.9940204084565 |
| 82 | 3813.06 | 3748.01786280001 | 65.0421371999933 |
| 83 | 3917.96 | 3827.02259176097 | 90.9374082390337 |
| 84 | 3895.51 | 3904.05484933636 | -8.54484933636026 |
| 85 | 3801.06 | 3825.15358404066 | -24.093584040661 |
| 86 | 3570.12 | 3726.30798898261 | -156.187988982612 |
| 87 | 3701.61 | 3522.69765525564 | 178.912344744364 |
| 88 | 3862.27 | 3684.16509310029 | 178.104906899715 |
| 89 | 3970.1 | 3818.89667219032 | 151.203327809679 |
| 90 | 4138.52 | 4021.74361967929 | 116.776380320708 |
| 91 | 4199.75 | 4184.15768023658 | 15.592319763425 |
| 92 | 4290.89 | 4124.76619869132 | 166.123801308677 |
| 93 | 4443.91 | 4317.89482363685 | 126.015176363151 |
| 94 | 4502.64 | 4447.52868376335 | 55.1113162366501 |
| 95 | 4356.98 | 4419.2951666984 | -62.3151666984014 |
| 96 | 4591.27 | 4398.5798222448 | 192.6901777552 |
| 97 | 4696.96 | 4671.32137790449 | 25.638622095512 |
| 98 | 4621.4 | 4629.46956744007 | -8.06956744006972 |
| 99 | 4562.84 | 4584.77454273744 | -21.9345427374353 |
| 100 | 4202.52 | 4488.22698001557 | -285.706980015571 |
| 101 | 4296.49 | 4225.08075205745 | 71.4092479425464 |
| 102 | 4435.23 | 4422.28089135067 | 12.9491086493269 |
| 103 | 4105.18 | 4281.92776215144 | -176.747762151443 |
| 104 | 4116.68 | 4145.17490964838 | -28.4949096483841 |
| 105 | 3844.49 | 4025.45204593649 | -180.962045936491 |
| 106 | 3720.98 | 3789.66113769446 | -68.6811376944588 |
| 107 | 3674.4 | 3746.02102646824 | -71.6210264682444 |
| 108 | 3857.62 | 3730.77000425409 | 126.849995745909 |
| 109 | 3801.06 | 3811.2136841969 | -10.1536841968965 |
| 110 | 3504.37 | 3569.6541459628 | -65.2841459627997 |
| 111 | 3032.6 | 3196.51429632775 | -163.914296327754 |
| 112 | 3047.03 | 2863.23668579991 | 183.79331420009 |
| 113 | 2962.34 | 2955.67556438988 | 6.66443561011828 |
| 114 | 2197.82 | 2520.05182648897 | -322.231826488974 |
| 115 | 2014.45 | 1967.53999366548 | 46.9100063345203 |
| 116 | 1862.83 | 1940.45550701668 | -77.6255070166772 |
| 117 | 1905.41 | 1767.08456288793 | 138.325437112074 |
| 118 | 1810.99 | 1801.85855741938 | 9.13144258061918 |
| 119 | 1670.07 | 1725.45280795337 | -55.382807953366 |
| 120 | 1864.44 | 1732.7451791336 | 131.694820866399 |
| 121 | 2052.02 | 1959.21478275693 | 92.8052172430666 |
| 122 | 2029.6 | 2068.29470960025 | -38.6947096002482 |
| 123 | 2070.83 | 2080.140736216 | -9.31073621600352 |
| 124 | 2293.41 | 2253.81642931338 | 39.5935706866216 |
| 125 | 2443.27 | 2435.66568786687 | 7.60431213312592 |
| 126 | 2513.17 | 2506.78981830183 | 6.38018169816949 |
| 127 | 2466.92 | 2617.09648544227 | -150.17648544227 |
| 128 | 2502.66 | 2545.26478975177 | -42.6047897517722 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 15 | 0.800234918979488 | 0.399530162041024 | 0.199765081020512 |
| 16 | 0.823051761176634 | 0.353896477646733 | 0.176948238823366 |
| 17 | 0.732092649661197 | 0.535814700677606 | 0.267907350338803 |
| 18 | 0.645530426197792 | 0.708939147604415 | 0.354469573802208 |
| 19 | 0.556525169993537 | 0.886949660012927 | 0.443474830006463 |
| 20 | 0.621360135088531 | 0.757279729822938 | 0.378639864911469 |
| 21 | 0.851579884392403 | 0.296840231215195 | 0.148420115607598 |
| 22 | 0.849503734649504 | 0.300992530700991 | 0.150496265350496 |
| 23 | 0.853531494387146 | 0.292937011225709 | 0.146468505612854 |
| 24 | 0.805461517894422 | 0.389076964211157 | 0.194538482105578 |
| 25 | 0.790243436157216 | 0.419513127685568 | 0.209756563842784 |
| 26 | 0.738309825706358 | 0.523380348587284 | 0.261690174293642 |
| 27 | 0.68291693836554 | 0.63416612326892 | 0.31708306163446 |
| 28 | 0.613516650781789 | 0.772966698436422 | 0.386483349218211 |
| 29 | 0.561817216988133 | 0.876365566023734 | 0.438182783011867 |
| 30 | 0.544205104426856 | 0.911589791146287 | 0.455794895573144 |
| 31 | 0.493916554220293 | 0.987833108440586 | 0.506083445779707 |
| 32 | 0.441078290806547 | 0.882156581613095 | 0.558921709193453 |
| 33 | 0.403345603944057 | 0.806691207888114 | 0.596654396055943 |
| 34 | 0.373918652356706 | 0.747837304713412 | 0.626081347643294 |
| 35 | 0.363777786776246 | 0.727555573552492 | 0.636222213223754 |
| 36 | 0.380631613254466 | 0.761263226508931 | 0.619368386745534 |
| 37 | 0.356711551565587 | 0.713423103131173 | 0.643288448434413 |
| 38 | 0.375614734690629 | 0.751229469381258 | 0.624385265309371 |
| 39 | 0.407152803411803 | 0.814305606823607 | 0.592847196588197 |
| 40 | 0.370514333778512 | 0.741028667557024 | 0.629485666221488 |
| 41 | 0.318163418021143 | 0.636326836042285 | 0.681836581978857 |
| 42 | 0.280863380681593 | 0.561726761363185 | 0.719136619318407 |
| 43 | 0.274524921755102 | 0.549049843510203 | 0.725475078244898 |
| 44 | 0.267834489891606 | 0.535668979783213 | 0.732165510108394 |
| 45 | 0.237885225481387 | 0.475770450962773 | 0.762114774518613 |
| 46 | 0.229745884157173 | 0.459491768314346 | 0.770254115842827 |
| 47 | 0.251173235514476 | 0.502346471028953 | 0.748826764485524 |
| 48 | 0.250854209179385 | 0.501708418358769 | 0.749145790820615 |
| 49 | 0.208616347865302 | 0.417232695730604 | 0.791383652134698 |
| 50 | 0.212484221469893 | 0.424968442939787 | 0.787515778530107 |
| 51 | 0.238402714132839 | 0.476805428265677 | 0.761597285867161 |
| 52 | 0.196669643316529 | 0.393339286633058 | 0.803330356683471 |
| 53 | 0.203549416565612 | 0.407098833131224 | 0.796450583434388 |
| 54 | 0.179937276492628 | 0.359874552985257 | 0.820062723507372 |
| 55 | 0.149197021327318 | 0.298394042654635 | 0.850802978672682 |
| 56 | 0.151632331256674 | 0.303264662513347 | 0.848367668743326 |
| 57 | 0.127809807977873 | 0.255619615955747 | 0.872190192022127 |
| 58 | 0.110558747206927 | 0.221117494413854 | 0.889441252793073 |
| 59 | 0.134360876861917 | 0.268721753723833 | 0.865639123138083 |
| 60 | 0.192275946584294 | 0.384551893168589 | 0.807724053415706 |
| 61 | 0.201115532070412 | 0.402231064140825 | 0.798884467929588 |
| 62 | 0.330407322854191 | 0.660814645708382 | 0.669592677145809 |
| 63 | 0.364364544062077 | 0.728729088124155 | 0.635635455937923 |
| 64 | 0.439099571680268 | 0.878199143360536 | 0.560900428319732 |
| 65 | 0.529705095930943 | 0.940589808138114 | 0.470294904069057 |
| 66 | 0.678684462366506 | 0.642631075266988 | 0.321315537633494 |
| 67 | 0.727230046165453 | 0.545539907669094 | 0.272769953834547 |
| 68 | 0.710862256277352 | 0.578275487445297 | 0.289137743722648 |
| 69 | 0.709151289436885 | 0.58169742112623 | 0.290848710563115 |
| 70 | 0.687672089155393 | 0.624655821689214 | 0.312327910844607 |
| 71 | 0.659478005868322 | 0.681043988263357 | 0.340521994131678 |
| 72 | 0.628577114585647 | 0.742845770828707 | 0.371422885414353 |
| 73 | 0.581696031867412 | 0.836607936265176 | 0.418303968132588 |
| 74 | 0.531311927018301 | 0.937376145963398 | 0.468688072981699 |
| 75 | 0.480710325317521 | 0.961420650635042 | 0.519289674682479 |
| 76 | 0.463212918373693 | 0.926425836747387 | 0.536787081626307 |
| 77 | 0.445446557700905 | 0.89089311540181 | 0.554553442299095 |
| 78 | 0.414186759073793 | 0.828373518147587 | 0.585813240926207 |
| 79 | 0.374735853883382 | 0.749471707766763 | 0.625264146116618 |
| 80 | 0.46075915076549 | 0.92151830153098 | 0.53924084923451 |
| 81 | 0.581737151216341 | 0.836525697567317 | 0.418262848783659 |
| 82 | 0.644152405992217 | 0.711695188015566 | 0.355847594007783 |
| 83 | 0.611708432287915 | 0.77658313542417 | 0.388291567712085 |
| 84 | 0.77744156087068 | 0.445116878258641 | 0.222558439129321 |
| 85 | 0.916639283479316 | 0.166721433041369 | 0.0833607165206845 |
| 86 | 0.995618470371817 | 0.00876305925636527 | 0.00438152962818263 |
| 87 | 0.99507306806586 | 0.0098538638682794 | 0.0049269319341397 |
| 88 | 0.993192940407165 | 0.0136141191856695 | 0.00680705959283473 |
| 89 | 0.990316098267428 | 0.019367803465144 | 0.00968390173257202 |
| 90 | 0.989698661492204 | 0.0206026770155925 | 0.0103013385077963 |
| 91 | 0.987008884972325 | 0.0259822300553507 | 0.0129911150276754 |
| 92 | 0.981477428061323 | 0.0370451438773546 | 0.0185225719386773 |
| 93 | 0.9721779443476 | 0.0556441113047996 | 0.0278220556523998 |
| 94 | 0.96013224748218 | 0.0797355050356393 | 0.0398677525178196 |
| 95 | 0.959590826248709 | 0.0808183475025826 | 0.0404091737512913 |
| 96 | 0.957320016645879 | 0.085359966708242 | 0.042679983354121 |
| 97 | 0.949632764336396 | 0.100734471327209 | 0.0503672356636043 |
| 98 | 0.951134583938277 | 0.0977308321234454 | 0.0488654160617227 |
| 99 | 0.964437551289873 | 0.0711248974202543 | 0.0355624487101272 |
| 100 | 0.98213574393786 | 0.0357285121242792 | 0.0178642560621396 |
| 101 | 0.975629467511093 | 0.0487410649778131 | 0.0243705324889066 |
| 102 | 0.961643471247792 | 0.0767130575044162 | 0.0383565287522081 |
| 103 | 0.96557693360804 | 0.068846132783921 | 0.0344230663919605 |
| 104 | 0.98059433571448 | 0.0388113285710384 | 0.0194056642855192 |
| 105 | 0.990115036629306 | 0.0197699267413887 | 0.00988496337069437 |
| 106 | 0.990371477673414 | 0.0192570446531728 | 0.00962852232658638 |
| 107 | 0.983236257611605 | 0.0335274847767891 | 0.0167637423883946 |
| 108 | 0.97159630226495 | 0.0568073954701001 | 0.02840369773505 |
| 109 | 0.955848177307217 | 0.088303645385565 | 0.0441518226927825 |
| 110 | 0.917674184286031 | 0.164651631427938 | 0.082325815713969 |
| 111 | 0.978175269716317 | 0.0436494605673662 | 0.0218247302836831 |
| 112 | 0.948959952976141 | 0.102080094047717 | 0.0510400470238586 |
| 113 | 0.90667521277965 | 0.186649574440699 | 0.0933247872203497 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 2 | 0.0202020202020202 | NOK |
| 5% type I error level | 14 | 0.141414141414141 | NOK |
| 10% type I error level | 24 | 0.242424242424242 | NOK |
