Multiple Linear Regression - Estimated Regression Equation |
Totaal[t] = -84.8598455362288 + 0.00110852737564472t + 0.0431272408509219jaartal[t] + 0.995878671716741jongerdan25jaar[t] + 1.0002341118164vanaf25jaar[t] -0.0766601847092071`Belgi\303\253`[t] -0.461901000716776Eurogebied[t] + 0.385382469325768`EU-27\r`[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) | -84.8598455362288 | 336.990516 | -0.2518 | 0.80156 | 0.40078 |
t | 0.00110852737564472 | 0.014254 | 0.0778 | 0.938126 | 0.469063 |
jaartal | 0.0431272408509219 | 0.168533 | 0.2559 | 0.798414 | 0.399207 |
jongerdan25jaar | 0.995878671716741 | 0.00393 | 253.4034 | 0 | 0 |
vanaf25jaar | 1.0002341118164 | 0.003058 | 327.1342 | 0 | 0 |
`Belgi\303\253` | -0.0766601847092071 | 0.113462 | -0.6756 | 0.500404 | 0.250202 |
Eurogebied | -0.461901000716776 | 0.372345 | -1.2405 | 0.216903 | 0.108452 |
`EU-27\r` | 0.385382469325768 | 0.350866 | 1.0984 | 0.273967 | 0.136983 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.999941101403851 |
R-squared | 0.999882206276746 |
Adjusted R-squared | 0.999876187619353 |
F-TEST (value) | 166130.440903983 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 137 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.504181488531057 |
Sum Squared Residuals | 34.8252593527027 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 501 | 501.842685590958 | -0.842685590957632 |
2 | 485 | 484.883354453119 | 0.116645546880518 |
3 | 464 | 463.935122491918 | 0.0648775080820763 |
4 | 460 | 459.968034204037 | 0.0319657959633536 |
5 | 467 | 467.075430891992 | -0.0754308919914907 |
6 | 460 | 460.095632975422 | -0.0956329754222533 |
7 | 448 | 448.161899461571 | -0.161899461571095 |
8 | 443 | 443.159571713222 | -0.159571713221877 |
9 | 436 | 436.180818658381 | -0.180818658381022 |
10 | 431 | 431.197133525345 | -0.197133525344919 |
11 | 484 | 484.090963372842 | -0.0909633728420994 |
12 | 510 | 509.062420460866 | 0.937579539133901 |
13 | 513 | 513.037111939995 | -0.037111939994909 |
14 | 503 | 502.986202677578 | 0.0137973224224533 |
15 | 471 | 471.068357438314 | -0.0683574383140691 |
16 | 471 | 471.028676167446 | -0.0286761674460842 |
17 | 476 | 476.116962016455 | -0.116962016455051 |
18 | 475 | 474.123016787358 | 0.876983212642239 |
19 | 470 | 470.136255187767 | -0.136255187766788 |
20 | 461 | 461.152692634525 | -0.152692634525302 |
21 | 455 | 455.120317572958 | -0.120317572958242 |
22 | 456 | 455.121426100334 | 0.878573899666104 |
23 | 517 | 516.944203506359 | 0.055796493641379 |
24 | 525 | 525.899509198986 | -0.899509198985624 |
25 | 523 | 522.850414712469 | 0.149585287530861 |
26 | 519 | 518.885430313376 | 0.114569686623559 |
27 | 509 | 508.869540564942 | 0.130459435057583 |
28 | 512 | 511.880062307967 | 0.119937692033441 |
29 | 519 | 518.907308408927 | 0.0926915910733805 |
30 | 517 | 516.871514354526 | 0.128485645474508 |
31 | 510 | 509.892761299685 | 0.107238700315362 |
32 | 509 | 509.903625568988 | -0.903625568987984 |
33 | 501 | 499.936191637269 | 1.06380836273149 |
34 | 507 | 506.879682526988 | 0.120317473011711 |
35 | 569 | 569.721322494811 | -0.721322494810697 |
36 | 580 | 579.736118719625 | 0.26388128037526 |
37 | 578 | 577.687258344925 | 0.312741655075352 |
38 | 565 | 565.775302031572 | -0.775302031571767 |
39 | 547 | 547.761894828706 | -0.761894828706227 |
40 | 555 | 554.799869807358 | 0.200130192642039 |
41 | 562 | 561.827115908318 | 0.172884091681981 |
42 | 561 | 560.841056644176 | 0.158943355823764 |
43 | 555 | 555.886814730109 | -0.886814730109324 |
44 | 544 | 543.903372383237 | 0.0966276167627559 |
45 | 537 | 536.936640786967 | 0.0633592130330377 |
46 | 543 | 542.868920968028 | 0.131079031971837 |
47 | 594 | 593.690153840469 | 0.309846159530917 |
48 | 611 | 610.633045252414 | 0.366954747586178 |
49 | 613 | 612.638977443522 | 0.36102255647809 |
50 | 611 | 610.714881083873 | 0.285118916126623 |
51 | 594 | 593.724706048237 | 0.275293951762989 |
52 | 595 | 595.743704559644 | -0.743704559644064 |
53 | 591 | 590.854737069359 | 0.14526293064139 |
54 | 589 | 589.861011786746 | -0.861011786745899 |
55 | 584 | 583.87482682525 | 0.125173174749477 |
56 | 573 | 572.895137323144 | 0.104862676855925 |
57 | 567 | 566.916604214788 | 0.0833957852121922 |
58 | 569 | 568.921491544168 | 0.0785084558324827 |
59 | 621 | 620.731773777005 | 0.26822622299532 |
60 | 629 | 628.707563531253 | 0.29243646874664 |
61 | 628 | 627.708437946813 | 0.291562053187388 |
62 | 612 | 611.795559351526 | 0.204440648474038 |
63 | 595 | 595.805604262374 | -0.805604262374154 |
64 | 597 | 596.836375955204 | 0.163624044796427 |
65 | 593 | 592.91014919153 | 0.0898508084696743 |
66 | 590 | 589.926918116795 | 0.0730818832048224 |
67 | 580 | 579.959470019744 | 0.0405299802560979 |
68 | 574 | 574.010764278121 | -0.010764278120887 |
69 | 573 | 572.986166767046 | 0.0138332329534836 |
70 | 573 | 573.005903744403 | -0.00590374440345748 |
71 | 620 | 619.901625334042 | 0.0983746659582861 |
72 | 626 | 625.89333792866 | 0.10666207134036 |
73 | 620 | 619.905049078376 | 0.0949509216243334 |
74 | 588 | 586.971415370444 | 1.02858462955585 |
75 | 566 | 565.976979143839 | 0.023020856160887 |
76 | 557 | 558.068210829063 | -1.06821082906286 |
77 | 561 | 561.077907098845 | -0.0779070988455016 |
78 | 549 | 549.109990778161 | -0.109990778161412 |
79 | 532 | 532.140903898395 | -0.14090389839535 |
80 | 526 | 526.15365990984 | -0.153659909839761 |
81 | 511 | 511.189410859138 | -0.18941085913797 |
82 | 499 | 499.196212770338 | -0.196212770338188 |
83 | 555 | 555.090744953285 | -0.090744953284569 |
84 | 565 | 564.083159883352 | 0.91684011664831 |
85 | 542 | 542.120568462975 | -0.120568462974566 |
86 | 527 | 527.103493990127 | -0.103493990126747 |
87 | 510 | 510.178345659121 | -0.178345659121301 |
88 | 514 | 514.14620782693 | -0.146207826929605 |
89 | 517 | 517.198811949076 | -0.19881194907629 |
90 | 508 | 507.237985008768 | 0.762014991232466 |
91 | 493 | 493.269614629782 | -0.26961462978248 |
92 | 490 | 490.232541601837 | -0.232541601836574 |
93 | 469 | 469.260280888826 | -0.260280888825686 |
94 | 478 | 477.234878118824 | 0.765121881176488 |
95 | 528 | 529.10652066082 | -1.10652066081993 |
96 | 534 | 533.075826003453 | 0.924173996547484 |
97 | 518 | 518.125027420814 | -0.125027420813761 |
98 | 506 | 506.11199419245 | -0.111994192450032 |
99 | 502 | 502.11428432668 | -0.114284326680503 |
100 | 516 | 516.040799714466 | -0.0407997144656011 |
101 | 528 | 528.071718576392 | -0.0717185763921175 |
102 | 533 | 533.035710066491 | -0.0357100664906003 |
103 | 536 | 535.972716544594 | 0.0272834554057086 |
104 | 537 | 537.01696703615 | -0.0169670361503836 |
105 | 524 | 523.041989665755 | 0.95801033424538 |
106 | 536 | 536.051940261667 | -0.0519402616673513 |
107 | 587 | 586.873862178736 | 0.126137821263758 |
108 | 597 | 595.881817300323 | 1.11818269967682 |
109 | 581 | 580.880473177513 | 0.119526822486912 |
110 | 564 | 564.887221675322 | -0.887221675321847 |
111 | 558 | 556.943462177226 | 1.05653782277409 |
112 | 575 | 574.924989519306 | 0.0750104806939537 |
113 | 580 | 580.989247174503 | -0.98924717450338 |
114 | 575 | 574.994351332809 | 0.00564866719130946 |
115 | 563 | 564.014661830702 | -1.01466183070225 |
116 | 552 | 550.992669444991 | 1.007330555009 |
117 | 537 | 537.020988487635 | -0.0209884876346796 |
118 | 545 | 545.022910882481 | -0.0229108824812848 |
119 | 601 | 600.922843367256 | 0.0771566327443079 |
120 | 604 | 604.90642171977 | -0.906421719769919 |
121 | 586 | 586.92404857322 | -0.924048573220318 |
122 | 564 | 563.984059268585 | 0.015940731414714 |
123 | 549 | 548.031597564638 | 0.968402435362333 |
124 | 551 | 551.069472803174 | -0.0694728031742298 |
125 | 556 | 556.141173598935 | -0.141173598934989 |
126 | 548 | 548.219353129192 | -0.219353129191604 |
127 | 540 | 540.205138293973 | -0.20513829397304 |
128 | 531 | 531.213895556929 | -0.213895556928815 |
129 | 521 | 520.277099741855 | 0.722900258145392 |
130 | 519 | 518.231549945526 | 0.768450054474221 |
131 | 572 | 572.100364298116 | -0.100364298115542 |
132 | 581 | 582.065674009819 | -1.06567400981846 |
133 | 563 | 563.067748879842 | -0.0677488798424492 |
134 | 548 | 548.062724196229 | -0.0627241962288378 |
135 | 539 | 539.080206504716 | -0.080206504715741 |
136 | 541 | 541.051970054323 | -0.0519700543227406 |
137 | 562 | 561.07145900524 | 0.928540994760145 |
138 | 559 | 559.068802895943 | -0.0688028959432636 |
139 | 546 | 546.077682738694 | -0.0776827386936581 |
140 | 536 | 536.994059801506 | -0.994059801506085 |
141 | 528 | 526.994931099506 | 1.00506890049364 |
142 | 530 | 530.980613340809 | -0.980613340809183 |
143 | 582 | 581.835274889887 | 0.164725110113281 |
144 | 599 | 598.834302302349 | 0.165697697651263 |
145 | 584 | 583.790064492506 | 0.209935507493581 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.0441230366919825 | 0.0882460733839651 | 0.955876963308018 |
12 | 0.357318528776994 | 0.714637057553988 | 0.642681471223006 |
13 | 0.29686243146562 | 0.59372486293124 | 0.70313756853438 |
14 | 0.193403277944362 | 0.386806555888724 | 0.806596722055638 |
15 | 0.115702003370109 | 0.231404006740217 | 0.884297996629891 |
16 | 0.104758583280093 | 0.209517166560185 | 0.895241416719907 |
17 | 0.0663808915133673 | 0.132761783026735 | 0.933619108486633 |
18 | 0.238926168995315 | 0.47785233799063 | 0.761073831004685 |
19 | 0.242573244058059 | 0.485146488116119 | 0.757426755941941 |
20 | 0.204092508750798 | 0.408185017501596 | 0.795907491249202 |
21 | 0.147249321635143 | 0.294498643270287 | 0.852750678364857 |
22 | 0.222342287097812 | 0.444684574195623 | 0.777657712902188 |
23 | 0.184194415765918 | 0.368388831531837 | 0.815805584234082 |
24 | 0.18213022404044 | 0.36426044808088 | 0.81786977595956 |
25 | 0.2417708528076 | 0.483541705615199 | 0.7582291471924 |
26 | 0.186775528954181 | 0.373551057908362 | 0.813224471045819 |
27 | 0.145207813254428 | 0.290415626508856 | 0.854792186745572 |
28 | 0.120720685523595 | 0.241441371047189 | 0.879279314476405 |
29 | 0.0883050196253093 | 0.176610039250619 | 0.911694980374691 |
30 | 0.0632875751773212 | 0.126575150354642 | 0.936712424822679 |
31 | 0.0452865732702503 | 0.0905731465405007 | 0.95471342672975 |
32 | 0.147901904423976 | 0.295803808847952 | 0.852098095576024 |
33 | 0.263710537389926 | 0.527421074779852 | 0.736289462610074 |
34 | 0.218883013294155 | 0.437766026588309 | 0.781116986705845 |
35 | 0.263616846585749 | 0.527233693171498 | 0.736383153414251 |
36 | 0.234654311952681 | 0.469308623905361 | 0.765345688047319 |
37 | 0.213312903143948 | 0.426625806287896 | 0.786687096856052 |
38 | 0.309318618123797 | 0.618637236247594 | 0.690681381876203 |
39 | 0.364566579474553 | 0.729133158949106 | 0.635433420525447 |
40 | 0.313418835716303 | 0.626837671432606 | 0.686581164283697 |
41 | 0.265835175033228 | 0.531670350066456 | 0.734164824966772 |
42 | 0.220875572397894 | 0.441751144795788 | 0.779124427602106 |
43 | 0.361816603200833 | 0.723633206401666 | 0.638183396799167 |
44 | 0.312149547447711 | 0.624299094895421 | 0.687850452552289 |
45 | 0.26492961442961 | 0.529859228859221 | 0.73507038557039 |
46 | 0.223614044002057 | 0.447228088004115 | 0.776385955997943 |
47 | 0.20864920442201 | 0.41729840884402 | 0.79135079557799 |
48 | 0.195993803797886 | 0.391987607595773 | 0.804006196202114 |
49 | 0.173477263651761 | 0.346954527303523 | 0.826522736348239 |
50 | 0.145663397562235 | 0.29132679512447 | 0.854336602437765 |
51 | 0.119401009529955 | 0.23880201905991 | 0.880598990470045 |
52 | 0.168253002060023 | 0.336506004120045 | 0.831746997939977 |
53 | 0.137106724401689 | 0.274213448803377 | 0.862893275598311 |
54 | 0.212359253986216 | 0.424718507972433 | 0.787640746013784 |
55 | 0.180009192209098 | 0.360018384418197 | 0.819990807790902 |
56 | 0.148951291581452 | 0.297902583162903 | 0.851048708418549 |
57 | 0.121049612394756 | 0.242099224789513 | 0.878950387605244 |
58 | 0.0973733493666939 | 0.194746698733388 | 0.902626650633306 |
59 | 0.0772537227161637 | 0.154507445432327 | 0.922746277283836 |
60 | 0.0604042693951205 | 0.120808538790241 | 0.93959573060488 |
61 | 0.0468166912251561 | 0.0936333824503121 | 0.953183308774844 |
62 | 0.0357297953035981 | 0.0714595906071963 | 0.964270204696402 |
63 | 0.0853567860921782 | 0.170713572184356 | 0.914643213907822 |
64 | 0.068070416051634 | 0.136140832103268 | 0.931929583948366 |
65 | 0.0537999153306525 | 0.107599830661305 | 0.946200084669347 |
66 | 0.0419611809133777 | 0.0839223618267553 | 0.958038819086622 |
67 | 0.0324296373194017 | 0.0648592746388033 | 0.967570362680598 |
68 | 0.0251521358846732 | 0.0503042717693464 | 0.974847864115327 |
69 | 0.0187285748581844 | 0.0374571497163689 | 0.981271425141816 |
70 | 0.0138277201929409 | 0.0276554403858818 | 0.986172279807059 |
71 | 0.00994131297566094 | 0.0198826259513219 | 0.990058687024339 |
72 | 0.00705067687319016 | 0.0141013537463803 | 0.99294932312681 |
73 | 0.00493506245444703 | 0.00987012490889406 | 0.995064937545553 |
74 | 0.00940218668967125 | 0.0188043733793425 | 0.990597813310329 |
75 | 0.00734468883688321 | 0.0146893776737664 | 0.992655311163117 |
76 | 0.0309156179850324 | 0.0618312359700648 | 0.969084382014968 |
77 | 0.0236197170858081 | 0.0472394341716161 | 0.976380282914192 |
78 | 0.0177937217083825 | 0.035587443416765 | 0.982206278291618 |
79 | 0.0132957378555297 | 0.0265914757110594 | 0.98670426214447 |
80 | 0.0097026420054275 | 0.019405284010855 | 0.990297357994573 |
81 | 0.00719321052181044 | 0.0143864210436209 | 0.99280678947819 |
82 | 0.00578005565461692 | 0.0115601113092338 | 0.994219944345383 |
83 | 0.00417562458514366 | 0.00835124917028733 | 0.995824375414856 |
84 | 0.00803885446317285 | 0.0160777089263457 | 0.991961145536827 |
85 | 0.00601169799220959 | 0.0120233959844192 | 0.99398830200779 |
86 | 0.00427290069053406 | 0.00854580138106813 | 0.995727099309466 |
87 | 0.00314721132543037 | 0.00629442265086074 | 0.99685278867457 |
88 | 0.00224161020262855 | 0.00448322040525709 | 0.997758389797371 |
89 | 0.00155174491943617 | 0.00310348983887234 | 0.998448255080564 |
90 | 0.00271812607393628 | 0.00543625214787255 | 0.997281873926064 |
91 | 0.00205896490239115 | 0.00411792980478229 | 0.997941035097609 |
92 | 0.00147640211930862 | 0.00295280423861725 | 0.998523597880691 |
93 | 0.00118701504988064 | 0.00237403009976127 | 0.998812984950119 |
94 | 0.00168690135168503 | 0.00337380270337006 | 0.998313098648315 |
95 | 0.00588061484075004 | 0.0117612296815001 | 0.99411938515925 |
96 | 0.0151041295304916 | 0.0302082590609832 | 0.984895870469508 |
97 | 0.0113876456281921 | 0.0227752912563842 | 0.988612354371808 |
98 | 0.00812149152428892 | 0.0162429830485778 | 0.991878508475711 |
99 | 0.00578418767606726 | 0.0115683753521345 | 0.994215812323933 |
100 | 0.00419472472644888 | 0.00838944945289775 | 0.995805275273551 |
101 | 0.00288046255865231 | 0.00576092511730463 | 0.997119537441348 |
102 | 0.0019347062899753 | 0.00386941257995059 | 0.998065293710025 |
103 | 0.00132862831689331 | 0.00265725663378663 | 0.998671371683107 |
104 | 0.00106047216130455 | 0.00212094432260911 | 0.998939527838695 |
105 | 0.00121454481909697 | 0.00242908963819394 | 0.998785455180903 |
106 | 0.00101362770738702 | 0.00202725541477404 | 0.998986372292613 |
107 | 0.000643694858890779 | 0.00128738971778156 | 0.999356305141109 |
108 | 0.00235345754985925 | 0.00470691509971851 | 0.997646542450141 |
109 | 0.00175029104724436 | 0.00350058209448871 | 0.998249708952756 |
110 | 0.00761843782559501 | 0.01523687565119 | 0.992381562174405 |
111 | 0.0119480600020657 | 0.0238961200041314 | 0.988051939997934 |
112 | 0.00937729161710706 | 0.0187545832342141 | 0.990622708382893 |
113 | 0.0164155658244015 | 0.0328311316488029 | 0.983584434175598 |
114 | 0.011950965703082 | 0.023901931406164 | 0.988049034296918 |
115 | 0.0299097473011411 | 0.0598194946022822 | 0.970090252698859 |
116 | 0.0574369465534188 | 0.114873893106838 | 0.942563053446581 |
117 | 0.0410948858867961 | 0.0821897717735922 | 0.958905114113204 |
118 | 0.0288160627182293 | 0.0576321254364586 | 0.971183937281771 |
119 | 0.0249079025703991 | 0.0498158051407982 | 0.975092097429601 |
120 | 0.0260044944908343 | 0.0520089889816686 | 0.973995505509166 |
121 | 0.0427253266315109 | 0.0854506532630219 | 0.957274673368489 |
122 | 0.0327664504356665 | 0.0655329008713329 | 0.967233549564333 |
123 | 0.0555698400584714 | 0.111139680116943 | 0.944430159941529 |
124 | 0.0528936703183841 | 0.105787340636768 | 0.947106329681616 |
125 | 0.0489782355951149 | 0.0979564711902298 | 0.951021764404885 |
126 | 0.0494801822052018 | 0.0989603644104037 | 0.950519817794798 |
127 | 0.0359346922059046 | 0.0718693844118092 | 0.964065307794095 |
128 | 0.0223799436410383 | 0.0447598872820766 | 0.977620056358962 |
129 | 0.0189573541190179 | 0.0379147082380358 | 0.981042645880982 |
130 | 0.0168841897853216 | 0.0337683795706433 | 0.983115810214678 |
131 | 0.0123757382255768 | 0.0247514764511537 | 0.987624261774423 |
132 | 0.0225683385715193 | 0.0451366771430386 | 0.977431661428481 |
133 | 0.19308319204377 | 0.38616638408754 | 0.80691680795623 |
134 | 0.13017689293642 | 0.26035378587284 | 0.86982310706358 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 21 | 0.169354838709677 | NOK |
5% type I error level | 51 | 0.411290322580645 | NOK |
10% type I error level | 68 | 0.548387096774194 | NOK |