Multiple Linear Regression - Estimated Regression Equation |
totaal[t] = + 1.25102743123547 + 0.993824229382807`<25J`[t] + 1.00177511231163`>25J`[t] -0.119519418446503belgie[t] -0.0904039875483088eurogebied[t] + 0.0521462742998931eu[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) | 1.25102743123547 | 0.652478 | 1.9173 | 0.057245 | 0.028623 |
`<25J` | 0.993824229382807 | 0.003169 | 313.6274 | 0 | 0 |
`>25J` | 1.00177511231163 | 0.002749 | 364.4373 | 0 | 0 |
belgie | -0.119519418446503 | 0.107818 | -1.1085 | 0.269548 | 0.134774 |
eurogebied | -0.0904039875483088 | 0.20354 | -0.4442 | 0.657619 | 0.32881 |
eu | 0.0521462742998931 | 0.20794 | 0.2508 | 0.802358 | 0.401179 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.999940423292632 |
R-squared | 0.999880850134648 |
Adjusted R-squared | 0.999876564168269 |
F-TEST (value) | 233291.809031408 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 139 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.50341422455435 |
Sum Squared Residuals | 35.2261975262285 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 501 | 501.961174087868 | -0.961174087867868 |
2 | 485 | 485.002379837339 | -0.00237983733893331 |
3 | 464 | 464.064514132856 | -0.0645141328564004 |
4 | 460 | 460.104994928495 | -0.104994928494615 |
5 | 467 | 467.15036499712 | -0.150364997120161 |
6 | 460 | 460.17374380157 | -0.173743801569872 |
7 | 448 | 448.201237267229 | -0.201237267229252 |
8 | 443 | 443.192310470768 | -0.192310470768267 |
9 | 436 | 436.219639099231 | -0.219639099230981 |
10 | 431 | 431.238617245375 | -0.238617245375124 |
11 | 484 | 484.110124710787 | -0.110124710787306 |
12 | 510 | 509.024552136218 | 0.975447863781942 |
13 | 513 | 512.987845877002 | 0.0121541229981904 |
14 | 503 | 502.964901709338 | 0.0350982906620005 |
15 | 471 | 471.008672103039 | -0.008672103038878 |
16 | 471 | 471.011532411226 | -0.0115324112258603 |
17 | 476 | 476.025447312623 | -0.0254473126230187 |
18 | 475 | 474.041923965461 | 0.958076034538619 |
19 | 470 | 470.058676165001 | -0.058676165001329 |
20 | 461 | 461.082629856432 | -0.0826298564317625 |
21 | 455 | 455.090741256607 | -0.0907412566066105 |
22 | 456 | 455.090741256607 | 0.909258743393389 |
23 | 517 | 516.862984130689 | 0.137015869310556 |
24 | 525 | 525.791500429277 | -0.791500429277056 |
25 | 523 | 522.773133634671 | 0.226866365328494 |
26 | 519 | 518.829640248856 | 0.170359751144423 |
27 | 509 | 508.862454731499 | 0.137545268500796 |
28 | 512 | 511.883681834292 | 0.116318165708262 |
29 | 519 | 518.876328848388 | 0.123671151612173 |
30 | 517 | 516.88358981488 | 0.116410185119621 |
31 | 510 | 509.910918443343 | 0.0890815566569192 |
32 | 509 | 509.930770033214 | -0.930770033213723 |
33 | 501 | 499.972676149515 | 1.02732385048499 |
34 | 507 | 506.952208888155 | 0.0477911118448778 |
35 | 569 | 569.746005646635 | -0.74600564663489 |
36 | 580 | 579.709190105075 | 0.290809894924565 |
37 | 578 | 577.692598422782 | 0.307401577218483 |
38 | 565 | 565.759846303085 | -0.759846303085019 |
39 | 547 | 547.786410770164 | -0.786410770164427 |
40 | 555 | 554.80005012486 | 0.199949875139999 |
41 | 562 | 561.792697138956 | 0.207302861043908 |
42 | 561 | 560.814774675431 | 0.185225324569069 |
43 | 555 | 555.885459178064 | -0.885459178063843 |
44 | 544 | 543.954456267846 | 0.0455437321541697 |
45 | 537 | 537.001687721082 | -0.00168772108200801 |
46 | 543 | 542.96349234665 | 0.0365076533499898 |
47 | 594 | 593.712032638798 | 0.287967361201908 |
48 | 611 | 610.634795776202 | 0.36520422379756 |
49 | 613 | 612.646296883755 | 0.353703116245475 |
50 | 611 | 610.774013079811 | 0.225986920188908 |
51 | 594 | 593.838208484736 | 0.161791515263921 |
52 | 595 | 595.873562241075 | -0.873562241074632 |
53 | 591 | 590.913481492915 | 0.0865185070845685 |
54 | 589 | 589.923607087546 | -0.923607087545618 |
55 | 584 | 583.940758886475 | 0.0592411135246963 |
56 | 573 | 572.960987065691 | 0.039012934308515 |
57 | 567 | 566.981964635946 | 0.0180353640539828 |
58 | 569 | 568.989515919485 | 0.0104840805149006 |
59 | 621 | 620.778423404978 | 0.22157659502241 |
60 | 629 | 628.732843011365 | 0.267156988635107 |
61 | 628 | 627.731067899053 | 0.26893210094674 |
62 | 612 | 611.79934150063 | 0.200658499369957 |
63 | 595 | 595.857185847347 | -0.857185847346866 |
64 | 597 | 596.902541145627 | 0.0974588543725546 |
65 | 593 | 592.942970706363 | 0.0570292936371271 |
66 | 590 | 589.95737290661 | 0.0426270933895265 |
67 | 580 | 579.991152852392 | 0.00884714760804069 |
68 | 574 | 574.001443284219 | -0.00144328421882253 |
69 | 573 | 573.018306193264 | -0.0183061932636766 |
70 | 573 | 573.038084965349 | -0.0380849653489946 |
71 | 620 | 619.894816645287 | 0.105183354712594 |
72 | 626 | 625.881665905274 | 0.118334094726439 |
73 | 620 | 619.882791885657 | 0.117208114342562 |
74 | 588 | 586.947302194631 | 1.05269780536917 |
75 | 566 | 565.992269920874 | 0.00773007912632591 |
76 | 557 | 558.058543314807 | -1.05854331480672 |
77 | 561 | 561.054528912708 | -0.0545289127076374 |
78 | 549 | 549.084758633866 | -0.0847586338658535 |
79 | 532 | 532.106112793466 | -0.10611279346592 |
80 | 526 | 526.111188597863 | -0.111188597862802 |
81 | 511 | 511.152170035535 | -0.152170035534762 |
82 | 499 | 499.201315535446 | -0.201315535446108 |
83 | 555 | 555.078148337793 | -0.0781483377931809 |
84 | 565 | 564.070322934714 | 0.929677065285787 |
85 | 542 | 542.094753474601 | -0.0947534746007814 |
86 | 527 | 527.110566225166 | -0.110566225166448 |
87 | 510 | 510.149035719138 | -0.149035719138325 |
88 | 514 | 514.158872423884 | -0.15887242388368 |
89 | 517 | 517.176149702663 | -0.17614970266322 |
90 | 508 | 507.217931766276 | 0.782068233723647 |
91 | 493 | 493.252737433331 | -0.252737433331119 |
92 | 490 | 490.254273463499 | -0.254273463499046 |
93 | 469 | 469.284728279989 | -0.284728279989383 |
94 | 478 | 477.259298816526 | 0.740701183473541 |
95 | 528 | 529.097125168106 | -1.09712516810605 |
96 | 534 | 533.056644372468 | 0.94335562753221 |
97 | 518 | 518.05908496401 | -0.0590849640098026 |
98 | 506 | 506.100476451466 | -0.100476451465801 |
99 | 502 | 502.117527991285 | -0.11752799128489 |
100 | 516 | 516.097833914541 | -0.0978339145409005 |
101 | 528 | 528.061114984344 | -0.061114984344326 |
102 | 533 | 533.034609348239 | -0.0346093482386506 |
103 | 536 | 536.019241684853 | -0.0192416848531983 |
104 | 537 | 537.042308478043 | -0.0423084780434488 |
105 | 524 | 523.077238197786 | 0.922761802213626 |
106 | 536 | 536.057948040383 | -0.0579480403827707 |
107 | 587 | 586.8890839925 | 0.11091600750011 |
108 | 597 | 595.850617391317 | 1.14938260868304 |
109 | 581 | 580.836066701175 | 0.163933298824692 |
110 | 564 | 564.898036159496 | -0.898036159496104 |
111 | 558 | 556.924803244161 | 1.07519675583866 |
112 | 575 | 574.911910276385 | 0.0880897236152704 |
113 | 580 | 580.909086321425 | -0.909086321425183 |
114 | 575 | 574.910336354497 | 0.0896636455027791 |
115 | 563 | 563.930564533713 | -0.930564533713409 |
116 | 552 | 550.94615297248 | 1.05384702751967 |
117 | 537 | 536.976957580619 | 0.0230424193807341 |
118 | 545 | 544.97908248458 | 0.0209175154204943 |
119 | 601 | 600.867815993868 | 0.132184006131612 |
120 | 604 | 604.839163087387 | -0.839163087386618 |
121 | 586 | 586.843015656408 | -0.843015656408399 |
122 | 564 | 563.91750149316 | 0.0824985068397358 |
123 | 549 | 547.976610643294 | 1.02338935670594 |
124 | 551 | 551.041644454549 | -0.0416444545493731 |
125 | 556 | 556.082250730037 | -0.082250730037493 |
126 | 548 | 548.132797645704 | -0.132797645703873 |
127 | 540 | 540.157137593341 | -0.157137593340795 |
128 | 531 | 531.161013172407 | -0.16101317240676 |
129 | 521 | 520.194406861982 | 0.805593138018239 |
130 | 519 | 518.181816238604 | 0.81818376139633 |
131 | 572 | 572.027317926411 | -0.0273179264105021 |
132 | 581 | 581.9855870977 | -0.985587097700198 |
133 | 563 | 562.971886841241 | 0.0281131587591395 |
134 | 548 | 548.02385475762 | -0.023854757619615 |
135 | 539 | 539.051758273063 | -0.0517582730630412 |
136 | 541 | 541.074121806634 | -0.0741218066337642 |
137 | 562 | 561.066043866897 | 0.933956133102586 |
138 | 559 | 559.066618753878 | -0.0666187538781284 |
139 | 546 | 546.07546987823 | -0.075469878230393 |
140 | 536 | 537.061264659787 | -1.0612646597867 |
141 | 528 | 527.059539355216 | 0.940460644783808 |
142 | 530 | 531.04691226728 | -1.04691226728023 |
143 | 582 | 581.925629464282 | 0.0743705357178721 |
144 | 599 | 598.877562347709 | 0.122437652291408 |
145 | 584 | 583.849846147208 | 0.150153852791857 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.131809267586539 | 0.263618535173077 | 0.868190732413461 |
10 | 0.0517715939787271 | 0.103543187957454 | 0.948228406021273 |
11 | 0.0196250232884528 | 0.0392500465769055 | 0.980374976711547 |
12 | 0.168193093797368 | 0.336386187594735 | 0.831806906202632 |
13 | 0.150559480513693 | 0.301118961027385 | 0.849440519486307 |
14 | 0.103051209683124 | 0.206102419366248 | 0.896948790316876 |
15 | 0.0644973415341103 | 0.128994683068221 | 0.93550265846589 |
16 | 0.0651547827484545 | 0.130309565496909 | 0.934845217251545 |
17 | 0.0463351965736506 | 0.0926703931473012 | 0.953664803426349 |
18 | 0.172829357632618 | 0.345658715265236 | 0.827170642367382 |
19 | 0.156392897279396 | 0.312785794558792 | 0.843607102720604 |
20 | 0.11927077748344 | 0.23854155496688 | 0.88072922251656 |
21 | 0.0818282021800989 | 0.163656404360198 | 0.918171797819901 |
22 | 0.191051034722077 | 0.382102069444155 | 0.808948965277922 |
23 | 0.146610634685978 | 0.293221269371956 | 0.853389365314022 |
24 | 0.220511193757389 | 0.441022387514777 | 0.779488806242612 |
25 | 0.226747326406187 | 0.453494652812374 | 0.773252673593813 |
26 | 0.180830745743507 | 0.361661491487013 | 0.819169254256493 |
27 | 0.139620243502847 | 0.279240487005693 | 0.860379756497153 |
28 | 0.104859710306785 | 0.209719420613571 | 0.895140289693215 |
29 | 0.0803949840030442 | 0.160789968006088 | 0.919605015996956 |
30 | 0.0584459825771731 | 0.116891965154346 | 0.941554017422827 |
31 | 0.0417381868907777 | 0.0834763737815554 | 0.958261813109222 |
32 | 0.119228700113204 | 0.238457400226409 | 0.880771299886796 |
33 | 0.257458930364892 | 0.514917860729784 | 0.742541069635108 |
34 | 0.210428598650926 | 0.420857197301851 | 0.789571401349074 |
35 | 0.244673586390011 | 0.489347172780023 | 0.755326413609989 |
36 | 0.224043917584217 | 0.448087835168433 | 0.775956082415783 |
37 | 0.211831365623696 | 0.423662731247392 | 0.788168634376304 |
38 | 0.278525218441126 | 0.557050436882252 | 0.721474781558874 |
39 | 0.313953410400938 | 0.627906820801875 | 0.686046589599062 |
40 | 0.269631307377623 | 0.539262614755247 | 0.730368692622377 |
41 | 0.225431783039313 | 0.450863566078627 | 0.774568216960687 |
42 | 0.185765962146525 | 0.37153192429305 | 0.814234037853475 |
43 | 0.323813033983096 | 0.647626067966191 | 0.676186966016904 |
44 | 0.28021773120977 | 0.560435462419541 | 0.71978226879023 |
45 | 0.237218064693568 | 0.474436129387137 | 0.762781935306431 |
46 | 0.201988726130763 | 0.403977452261526 | 0.798011273869237 |
47 | 0.197452905026176 | 0.394905810052352 | 0.802547094973824 |
48 | 0.189752493204558 | 0.379504986409117 | 0.810247506795442 |
49 | 0.169663676028912 | 0.339327352057823 | 0.830336323971088 |
50 | 0.140523841548692 | 0.281047683097383 | 0.859476158451308 |
51 | 0.115788803100761 | 0.231577606201523 | 0.884211196899239 |
52 | 0.173430201010171 | 0.346860402020342 | 0.826569798989829 |
53 | 0.142621162309169 | 0.285242324618337 | 0.857378837690831 |
54 | 0.217521486210189 | 0.435042972420378 | 0.782478513789811 |
55 | 0.184253008996192 | 0.368506017992384 | 0.815746991003808 |
56 | 0.153352989662568 | 0.306705979325136 | 0.846647010337432 |
57 | 0.125219758832943 | 0.250439517665887 | 0.874780241167057 |
58 | 0.100973435406005 | 0.201946870812009 | 0.899026564593995 |
59 | 0.0846830241728484 | 0.169366048345697 | 0.915316975827152 |
60 | 0.0694395915738521 | 0.138879183147704 | 0.930560408426148 |
61 | 0.0560015416484293 | 0.112003083296859 | 0.943998458351571 |
62 | 0.0437191498632366 | 0.0874382997264732 | 0.956280850136763 |
63 | 0.0736741799727023 | 0.147348359945405 | 0.926325820027298 |
64 | 0.0581525676524686 | 0.116305135304937 | 0.941847432347531 |
65 | 0.0449945072813587 | 0.0899890145627173 | 0.955005492718641 |
66 | 0.0344195112063121 | 0.0688390224126241 | 0.965580488793688 |
67 | 0.0260685468402735 | 0.0521370936805471 | 0.973931453159727 |
68 | 0.0198152014250241 | 0.0396304028500482 | 0.980184798574976 |
69 | 0.0146470711434716 | 0.0292941422869431 | 0.985352928856528 |
70 | 0.0106520900457482 | 0.0213041800914964 | 0.989347909954252 |
71 | 0.00769260908617645 | 0.0153852181723529 | 0.992307390913824 |
72 | 0.00550981056628659 | 0.0110196211325732 | 0.994490189433713 |
73 | 0.00389220466448595 | 0.00778440932897191 | 0.996107795335514 |
74 | 0.0112235872842354 | 0.0224471745684708 | 0.988776412715765 |
75 | 0.00823657273319034 | 0.0164731454663807 | 0.99176342726681 |
76 | 0.0268406037596976 | 0.0536812075193953 | 0.973159396240302 |
77 | 0.0200414548547662 | 0.0400829097095324 | 0.979958545145234 |
78 | 0.014768086992505 | 0.0295361739850101 | 0.985231913007495 |
79 | 0.010781747770323 | 0.0215634955406459 | 0.989218252229677 |
80 | 0.00779217605478505 | 0.0155843521095701 | 0.992207823945215 |
81 | 0.0056575872407731 | 0.0113151744815462 | 0.994342412759227 |
82 | 0.00420189719855155 | 0.0084037943971031 | 0.995798102801448 |
83 | 0.0029397080641744 | 0.00587941612834879 | 0.997060291935826 |
84 | 0.00950235674868109 | 0.0190047134973622 | 0.990497643251319 |
85 | 0.00677165911986909 | 0.0135433182397382 | 0.993228340880131 |
86 | 0.00475551783386232 | 0.00951103566772465 | 0.995244482166138 |
87 | 0.00338232553993094 | 0.00676465107986188 | 0.996617674460069 |
88 | 0.00233866031969958 | 0.00467732063939916 | 0.9976613396803 |
89 | 0.0015957667374166 | 0.0031915334748332 | 0.998404233262583 |
90 | 0.00336900458862333 | 0.00673800917724667 | 0.996630995411377 |
91 | 0.00241526180248263 | 0.00483052360496525 | 0.997584738197517 |
92 | 0.00170247740003334 | 0.00340495480006668 | 0.998297522599967 |
93 | 0.00135393715235028 | 0.00270787430470055 | 0.99864606284765 |
94 | 0.0023042983385706 | 0.0046085966771412 | 0.997695701661429 |
95 | 0.00733032414116753 | 0.0146606482823351 | 0.992669675858832 |
96 | 0.0171138488928927 | 0.0342276977857855 | 0.982886151107107 |
97 | 0.0124160109077794 | 0.0248320218155588 | 0.987583989092221 |
98 | 0.00905777808391577 | 0.0181155561678315 | 0.990942221916084 |
99 | 0.00687689186372904 | 0.0137537837274581 | 0.993123108136271 |
100 | 0.00513539800672652 | 0.010270796013453 | 0.994864601993274 |
101 | 0.00386299011720941 | 0.00772598023441882 | 0.996137009882791 |
102 | 0.00295511593792426 | 0.00591023187584853 | 0.997044884062076 |
103 | 0.00238645949276729 | 0.00477291898553458 | 0.997613540507233 |
104 | 0.00208923721210869 | 0.00417847442421739 | 0.997910762787891 |
105 | 0.00300600388539385 | 0.0060120077707877 | 0.996993996114606 |
106 | 0.00227206422973888 | 0.00454412845947777 | 0.997727935770261 |
107 | 0.00148515769235769 | 0.00297031538471538 | 0.998514842307642 |
108 | 0.00748102777210877 | 0.0149620555442175 | 0.992518972227891 |
109 | 0.00540400334298101 | 0.010808006685962 | 0.994595996657019 |
110 | 0.0144615305674229 | 0.0289230611348459 | 0.985538469432577 |
111 | 0.0303399693813929 | 0.0606799387627858 | 0.969660030618607 |
112 | 0.0219794535801501 | 0.0439589071603003 | 0.97802054641985 |
113 | 0.0312666766796921 | 0.0625333533593842 | 0.968733323320308 |
114 | 0.0231338415541965 | 0.0462676831083929 | 0.976866158445803 |
115 | 0.0488517900326337 | 0.0977035800652673 | 0.951148209967366 |
116 | 0.0920920162464324 | 0.184184032492865 | 0.907907983753568 |
117 | 0.0693053862521694 | 0.138610772504339 | 0.930694613747831 |
118 | 0.0506623572611518 | 0.101324714522304 | 0.949337642738848 |
119 | 0.0460408664897172 | 0.0920817329794343 | 0.953959133510283 |
120 | 0.0456358843840893 | 0.0912717687681787 | 0.954364115615911 |
121 | 0.0699060618214116 | 0.139812123642823 | 0.930093938178588 |
122 | 0.0541691097945052 | 0.10833821958901 | 0.945830890205495 |
123 | 0.0935262782158785 | 0.187052556431757 | 0.906473721784122 |
124 | 0.0698885335961862 | 0.139777067192372 | 0.930111466403814 |
125 | 0.048400204698706 | 0.0968004093974121 | 0.951599795301294 |
126 | 0.0340257946194539 | 0.0680515892389078 | 0.965974205380546 |
127 | 0.0262192185397827 | 0.0524384370795654 | 0.973780781460217 |
128 | 0.0215120643480884 | 0.0430241286961769 | 0.978487935651912 |
129 | 0.024821430610168 | 0.049642861220336 | 0.975178569389832 |
130 | 0.0374278005651843 | 0.0748556011303685 | 0.962572199434816 |
131 | 0.0279722105024822 | 0.0559444210049644 | 0.972027789497518 |
132 | 0.0529528942252633 | 0.105905788450527 | 0.947047105774737 |
133 | 0.0319272317130943 | 0.0638544634261885 | 0.968072768286906 |
134 | 0.0182233595279126 | 0.0364467190558252 | 0.981776640472087 |
135 | 0.0168308849586466 | 0.0336617699172933 | 0.983169115041353 |
136 | 0.292978749146021 | 0.585957498292043 | 0.707021250853979 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 19 | 0.1484375 | NOK |
5% type I error level | 49 | 0.3828125 | NOK |
10% type I error level | 67 | 0.5234375 | NOK |