Multiple Linear Regression - Estimated Regression Equation |
Werkl[t] = + 613.15504174966 + 6.44234545678934HICP[t] + 0.00395499908705652Consvertr[t] -32.6323833598103Rente[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) | 613.15504174966 | 11.172997 | 54.8783 | 0 | 0 |
HICP | 6.44234545678934 | 2.983358 | 2.1594 | 0.032696 | 0.016348 |
Consvertr | 0.00395499908705652 | 0.441388 | 0.009 | 0.992865 | 0.496432 |
Rente | -32.6323833598103 | 3.806714 | -8.5723 | 0 | 0 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.685303976560405 |
R-squared | 0.469641540289505 |
Adjusted R-squared | 0.457113387697918 |
F-TEST (value) | 37.4868949636597 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 127 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 36.6834954089455 |
Sum Squared Residuals | 170901.212098102 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 493 | 517.226190299049 | -24.2261902990493 |
2 | 481 | 521.977521613884 | -40.9775216138843 |
3 | 462 | 519.341188457204 | -57.3411884572045 |
4 | 457 | 513.480230696386 | -56.4802306963861 |
5 | 442 | 506.296648234798 | -64.2966482347976 |
6 | 439 | 498.422307497514 | -59.4223074975136 |
7 | 488 | 485.47081473514 | 2.52918526486005 |
8 | 521 | 497.078901554622 | 23.9210984453781 |
9 | 501 | 492.118248448542 | 8.88175155145832 |
10 | 485 | 483.674888135891 | 1.32511186410896 |
11 | 464 | 482.043268967901 | -18.0432689679005 |
12 | 460 | 477.537582147235 | -17.5375821472350 |
13 | 467 | 475.596968512024 | -8.59696851202413 |
14 | 460 | 474.288724425231 | -14.2887244252310 |
15 | 448 | 472.352065789107 | -24.3520657891071 |
16 | 443 | 476.845887612511 | -33.8458876125114 |
17 | 436 | 483.681861875037 | -47.681861875037 |
18 | 431 | 485.65217299723 | -54.65217299723 |
19 | 484 | 484.363703905872 | -0.363703905872138 |
20 | 510 | 482.741504106085 | 27.2584958939148 |
21 | 513 | 493.871173181176 | 19.1288268188239 |
22 | 503 | 502.968690531052 | 0.0313094689475637 |
23 | 471 | 514.056293998557 | -43.056293998557 |
24 | 471 | 519.952846751159 | -48.9528467511589 |
25 | 476 | 523.845939018842 | -47.8459390188419 |
26 | 475 | 523.209614471337 | -48.209614471337 |
27 | 470 | 523.213569470424 | -53.2135694704241 |
28 | 461 | 517.40754856114 | -56.4075485611396 |
29 | 455 | 516.123034468869 | -61.1230344688688 |
30 | 456 | 512.253672195708 | -56.2536721957081 |
31 | 517 | 514.182420833658 | 2.81757916634214 |
32 | 525 | 515.462979926842 | 9.53702007315839 |
33 | 523 | 514.818745381163 | 8.18125461883732 |
34 | 519 | 515.462979926842 | 3.53702007315838 |
35 | 509 | 514.170555836397 | -5.17055583639669 |
36 | 512 | 528.49615827533 | -16.4961582753304 |
37 | 519 | 531.111207066545 | -12.1112070665455 |
38 | 517 | 533.672325252913 | -16.672325252913 |
39 | 510 | 540.823261475119 | -30.8232614751187 |
40 | 509 | 541.194096545361 | -32.1940965453608 |
41 | 501 | 537.336599269461 | -36.3365992694613 |
42 | 507 | 554.251004888372 | -47.2510048883719 |
43 | 569 | 556.858143681413 | 12.1418563185871 |
44 | 580 | 558.154522770945 | 21.8454772290551 |
45 | 578 | 558.822487311146 | 19.1775126888539 |
46 | 565 | 556.850233683239 | 8.14976631676124 |
47 | 547 | 559.462766857738 | -12.462766857738 |
48 | 555 | 558.818532312059 | -3.81853231205907 |
49 | 562 | 556.897693672283 | 5.10230632771657 |
50 | 561 | 555.6171345791 | 5.38286542090032 |
51 | 555 | 554.320755489568 | 0.679244510432302 |
52 | 544 | 558.826442310233 | -14.8264423102332 |
53 | 537 | 563.328174131812 | -26.3281741318116 |
54 | 543 | 560.774965943618 | -17.7749659436182 |
55 | 594 | 561.403380492949 | 32.5966195070511 |
56 | 611 | 560.767055945444 | 50.2329440545559 |
57 | 613 | 559.478586854086 | 53.5214131459138 |
58 | 611 | 565.260877768848 | 45.7391222311516 |
59 | 594 | 562.679984587046 | 31.3200154129544 |
60 | 595 | 560.107001403417 | 34.8929985965831 |
61 | 591 | 560.751235949096 | 30.2487640509041 |
62 | 589 | 562.695804583394 | 26.3041954166062 |
63 | 584 | 565.920932310876 | 18.0790676891244 |
64 | 573 | 563.332129130899 | 9.66787086910134 |
65 | 567 | 562.664164590697 | 4.33583540930261 |
66 | 569 | 565.241102773413 | 3.75889722658688 |
67 | 621 | 565.241102773413 | 55.7588972265869 |
68 | 629 | 566.533526863858 | 62.466473136142 |
69 | 628 | 567.161941413189 | 60.8380585868112 |
70 | 612 | 562.03179504228 | 49.9682049577204 |
71 | 595 | 562.672074588872 | 32.3279254111285 |
72 | 597 | 559.056266808054 | 37.9437331919458 |
73 | 593 | 557.76679147001 | 35.2332085299900 |
74 | 590 | 557.762836470923 | 32.237163529077 |
75 | 580 | 547.359087527626 | 32.6409124723738 |
76 | 574 | 548.308361541438 | 25.6916384585616 |
77 | 573 | 549.588920634622 | 23.4110793653778 |
78 | 573 | 543.10350332356 | 29.8964966764398 |
79 | 620 | 538.869706608302 | 81.1302933916979 |
80 | 626 | 532.351643057857 | 93.6483569421427 |
81 | 620 | 527.490438039955 | 92.5095619600451 |
82 | 588 | 520.670283773777 | 67.3297162262225 |
83 | 566 | 519.988441742942 | 46.0115582570576 |
84 | 557 | 516.028547626464 | 40.9714523735356 |
85 | 561 | 509.889732267779 | 51.1102677322211 |
86 | 549 | 510.541876811632 | 38.4581231883681 |
87 | 532 | 505.639109309486 | 26.3608906905137 |
88 | 526 | 502.387735970766 | 23.6122640292336 |
89 | 511 | 499.166563242372 | 11.8334367576283 |
90 | 499 | 494.267750739313 | 4.73224926068685 |
91 | 555 | 490.996602405158 | 64.003397594842 |
92 | 565 | 490.348412860392 | 74.651587139608 |
93 | 542 | 491.63688195175 | 50.3631180482501 |
94 | 527 | 496.794713316268 | 30.2052866837316 |
95 | 510 | 501.276670142412 | 8.72332985758845 |
96 | 514 | 502.580959230118 | 11.4190407698824 |
97 | 517 | 505.149987414659 | 11.8500125853407 |
98 | 508 | 505.806086957599 | 2.19391304240064 |
99 | 493 | 510.959963323031 | -17.9599633230308 |
100 | 490 | 509.011439689646 | -19.0114396896458 |
101 | 469 | 515.445875148261 | -46.445875148261 |
102 | 478 | 519.94760696984 | -41.9476069698395 |
103 | 528 | 514.710102512578 | 13.2898974874216 |
104 | 534 | 509.212572947171 | 24.7874270528288 |
105 | 518 | 509.864717491024 | 8.13528250897581 |
106 | 506 | 514.460503019322 | -8.46050301932209 |
107 | 502 | 522.08078614092 | -20.0807861409195 |
108 | 516 | 540.711445266337 | -24.7114452663366 |
109 | 528 | 551.224061666015 | -23.2240616660148 |
110 | 533 | 560.03581141985 | -27.0358114198499 |
111 | 536 | 562.755772668359 | -26.7557726683593 |
112 | 537 | 574.829251388146 | -37.8292513881459 |
113 | 524 | 576.222129813455 | -52.222129813455 |
114 | 536 | 574.009122949494 | -38.0091229494935 |
115 | 587 | 569.503436128828 | 17.496563871172 |
116 | 597 | 575.96951158014 | 21.0304884198603 |
117 | 581 | 574.036807943103 | 6.96319205689711 |
118 | 564 | 574.677087489695 | -10.6770874896948 |
119 | 558 | 580.483108398979 | -22.4831083989793 |
120 | 575 | 582.396037040581 | -7.3960370405808 |
121 | 580 | 585.617209768975 | -5.61720976897548 |
122 | 575 | 585.617209768975 | -10.6172097689755 |
123 | 563 | 592.711699769618 | -29.7116997696179 |
124 | 552 | 594.019943856411 | -42.019943856411 |
125 | 537 | 596.577107043691 | -59.5771070436914 |
126 | 545 | 597.881396131398 | -52.8813961313976 |
127 | 601 | 595.956602492535 | 5.04339750746513 |
128 | 604 | 595.968467489796 | 8.03153251020396 |
129 | 586 | 599.189640218191 | -13.1896402181907 |
130 | 564 | 600.486019307723 | -36.4860193077227 |
131 | 549 | 599.849694760218 | -50.8496947602179 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.118275484198380 | 0.236550968396761 | 0.88172451580162 |
8 | 0.597097347126111 | 0.805805305747778 | 0.402902652873889 |
9 | 0.471279387379182 | 0.942558774758363 | 0.528720612620818 |
10 | 0.342424623947969 | 0.684849247895939 | 0.65757537605203 |
11 | 0.27990742775506 | 0.55981485551012 | 0.72009257224494 |
12 | 0.214733830720633 | 0.429467661441266 | 0.785266169279367 |
13 | 0.15410405331017 | 0.30820810662034 | 0.84589594668983 |
14 | 0.131795489992784 | 0.263590979985567 | 0.868204510007216 |
15 | 0.108363412661748 | 0.216726825323495 | 0.891636587338252 |
16 | 0.0836220865753302 | 0.167244173150660 | 0.91637791342467 |
17 | 0.0675431076307039 | 0.135086215261408 | 0.932456892369296 |
18 | 0.0601866763624734 | 0.120373352724947 | 0.939813323637527 |
19 | 0.0707657169556825 | 0.141531433911365 | 0.929234283044318 |
20 | 0.153421645212578 | 0.306843290425157 | 0.846578354787422 |
21 | 0.178736678023073 | 0.357473356046146 | 0.821263321976927 |
22 | 0.135394012234573 | 0.270788024469146 | 0.864605987765427 |
23 | 0.122626861028723 | 0.245253722057446 | 0.877373138971277 |
24 | 0.104365355638079 | 0.208730711276157 | 0.895634644361921 |
25 | 0.0885709939996823 | 0.177141987999365 | 0.911429006000318 |
26 | 0.0779696110122236 | 0.155939222024447 | 0.922030388987776 |
27 | 0.075114844743592 | 0.150229689487184 | 0.924885155256408 |
28 | 0.0821881500799184 | 0.164376300159837 | 0.917811849920082 |
29 | 0.106257046175364 | 0.212514092350727 | 0.893742953824637 |
30 | 0.134404860103754 | 0.268809720207508 | 0.865595139896246 |
31 | 0.180836217895183 | 0.361672435790365 | 0.819163782104817 |
32 | 0.236275348219085 | 0.47255069643817 | 0.763724651780915 |
33 | 0.26804236061761 | 0.53608472123522 | 0.73195763938239 |
34 | 0.278043668532601 | 0.556087337065203 | 0.721956331467399 |
35 | 0.2609272437729 | 0.5218544875458 | 0.7390727562271 |
36 | 0.240855861356294 | 0.481711722712587 | 0.759144138643706 |
37 | 0.222678474397216 | 0.445356948794432 | 0.777321525602784 |
38 | 0.194745217105764 | 0.389490434211528 | 0.805254782894236 |
39 | 0.161802084321626 | 0.323604168643252 | 0.838197915678374 |
40 | 0.144071017680131 | 0.288142035360261 | 0.85592898231987 |
41 | 0.139719180338267 | 0.279438360676533 | 0.860280819661733 |
42 | 0.138224454007067 | 0.276448908014134 | 0.861775545992933 |
43 | 0.207975889761094 | 0.415951779522188 | 0.792024110238906 |
44 | 0.306314534772259 | 0.612629069544519 | 0.69368546522774 |
45 | 0.373937925323961 | 0.747875850647922 | 0.626062074676039 |
46 | 0.358915483364669 | 0.717830966729337 | 0.641084516635331 |
47 | 0.327065580855237 | 0.654131161710474 | 0.672934419144763 |
48 | 0.299229256130481 | 0.598458512260962 | 0.700770743869519 |
49 | 0.287717103479384 | 0.575434206958768 | 0.712282896520616 |
50 | 0.278239832794941 | 0.556479665589882 | 0.721760167205059 |
51 | 0.258317486876486 | 0.516634973752972 | 0.741682513123514 |
52 | 0.236680733949975 | 0.473361467899951 | 0.763319266050025 |
53 | 0.222433840827079 | 0.444867681654158 | 0.777566159172921 |
54 | 0.220161529528795 | 0.440323059057591 | 0.779838470471205 |
55 | 0.256761703060909 | 0.513523406121817 | 0.743238296939091 |
56 | 0.354752917978875 | 0.70950583595775 | 0.645247082021125 |
57 | 0.454075815418488 | 0.908151630836976 | 0.545924184581512 |
58 | 0.502354407530619 | 0.995291184938763 | 0.497645592469382 |
59 | 0.491258706101855 | 0.98251741220371 | 0.508741293898145 |
60 | 0.489161045093197 | 0.978322090186395 | 0.510838954906803 |
61 | 0.469556595890204 | 0.939113191780408 | 0.530443404109796 |
62 | 0.43345201107991 | 0.86690402215982 | 0.56654798892009 |
63 | 0.384925628906787 | 0.769851257813575 | 0.615074371093213 |
64 | 0.336858861701909 | 0.673717723403818 | 0.663141138298091 |
65 | 0.292976009038686 | 0.585952018077372 | 0.707023990961314 |
66 | 0.254237721993077 | 0.508475443986153 | 0.745762278006923 |
67 | 0.342406818106331 | 0.684813636212661 | 0.657593181893669 |
68 | 0.47902398275019 | 0.95804796550038 | 0.52097601724981 |
69 | 0.664385193944269 | 0.671229612111462 | 0.335614806055731 |
70 | 0.728502340912842 | 0.542995318174316 | 0.271497659087158 |
71 | 0.732667031144359 | 0.534665937711282 | 0.267332968855641 |
72 | 0.73719226999978 | 0.525615460000439 | 0.262807730000219 |
73 | 0.719993613908104 | 0.560012772183792 | 0.280006386091896 |
74 | 0.700174926811227 | 0.599650146377547 | 0.299825073188773 |
75 | 0.687385248362369 | 0.625229503275263 | 0.312614751637631 |
76 | 0.655215596040658 | 0.689568807918684 | 0.344784403959342 |
77 | 0.626018858649538 | 0.747962282700925 | 0.373981141350462 |
78 | 0.596281892759566 | 0.807436214480868 | 0.403718107240434 |
79 | 0.819873751942891 | 0.360252496114217 | 0.180126248057109 |
80 | 0.973541588210925 | 0.0529168235781498 | 0.0264584117890749 |
81 | 0.998532220404986 | 0.00293555919002742 | 0.00146777959501371 |
82 | 0.99954691671317 | 0.000906166573660823 | 0.000453083286830412 |
83 | 0.999609021874119 | 0.000781956251762229 | 0.000390978125881114 |
84 | 0.999684511428546 | 0.000630977142907498 | 0.000315488571453749 |
85 | 0.99978202468282 | 0.000435950634361655 | 0.000217975317180827 |
86 | 0.999745402923141 | 0.000509194153717759 | 0.000254597076858879 |
87 | 0.999629908759439 | 0.0007401824811225 | 0.00037009124056125 |
88 | 0.999483345057866 | 0.00103330988426715 | 0.000516654942133576 |
89 | 0.999503187800064 | 0.000993624399871088 | 0.000496812199935544 |
90 | 0.999735920399324 | 0.000528159201351106 | 0.000264079600675553 |
91 | 0.99980764084675 | 0.000384718306500412 | 0.000192359153250206 |
92 | 0.99992903098374 | 0.000141938032519331 | 7.09690162596655e-05 |
93 | 0.999922627489489 | 0.000154745021022214 | 7.73725105111071e-05 |
94 | 0.999869825096486 | 0.000260349807028452 | 0.000130174903514226 |
95 | 0.999758609977528 | 0.000482780044944881 | 0.000241390022472441 |
96 | 0.999560915248856 | 0.00087816950228874 | 0.00043908475114437 |
97 | 0.9992351104767 | 0.00152977904660097 | 0.000764889523300483 |
98 | 0.998704980405034 | 0.00259003918993267 | 0.00129501959496634 |
99 | 0.998544179564226 | 0.00291164087154889 | 0.00145582043577444 |
100 | 0.998622882274636 | 0.00275423545072878 | 0.00137711772536439 |
101 | 0.999702973214997 | 0.000594053570005291 | 0.000297026785002646 |
102 | 0.999894333090402 | 0.000211333819195543 | 0.000105666909597772 |
103 | 0.999825051120518 | 0.000349897758963706 | 0.000174948879481853 |
104 | 0.999746370896074 | 0.000507258207851318 | 0.000253629103925659 |
105 | 0.999489652085739 | 0.00102069582852207 | 0.000510347914261033 |
106 | 0.999008974371821 | 0.00198205125635770 | 0.000991025628178851 |
107 | 0.998315401689853 | 0.00336919662029354 | 0.00168459831014677 |
108 | 0.997051697847067 | 0.00589660430586576 | 0.00294830215293288 |
109 | 0.995039715521574 | 0.00992056895685127 | 0.00496028447842563 |
110 | 0.992041801532923 | 0.0159163969341532 | 0.0079581984670766 |
111 | 0.988025677131217 | 0.0239486457375668 | 0.0119743228687834 |
112 | 0.990229272391572 | 0.0195414552168566 | 0.00977072760842829 |
113 | 0.984461283889383 | 0.0310774322212337 | 0.0155387161106168 |
114 | 0.989705733659934 | 0.0205885326801311 | 0.0102942663400655 |
115 | 0.981452618902727 | 0.0370947621945459 | 0.0185473810972730 |
116 | 0.97363223184517 | 0.0527355363096585 | 0.0263677681548292 |
117 | 0.95306822497136 | 0.0938635500572801 | 0.0469317750286401 |
118 | 0.928320123283877 | 0.143359753432246 | 0.071679876716123 |
119 | 0.942358067657372 | 0.115283864685256 | 0.0576419323426282 |
120 | 0.909456507547592 | 0.181086984904815 | 0.0905434924524075 |
121 | 0.842120302452757 | 0.315759395094485 | 0.157879697547243 |
122 | 0.761567663885348 | 0.476864672229305 | 0.238432336114652 |
123 | 0.632635674315066 | 0.734728651369868 | 0.367364325684934 |
124 | 0.741706165452315 | 0.516587669095369 | 0.258293834547685 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 29 | 0.245762711864407 | NOK |
5% type I error level | 35 | 0.296610169491525 | NOK |
10% type I error level | 38 | 0.322033898305085 | NOK |