Multiple Linear Regression - Estimated Regression Equation |
Werkl[t] = + 595.887010189059 + 4.88997446557134HICP[t] + 0.545185974417897Consvertr[t] -29.9079834813727Rente[t] -0.27597337857964M1[t] -6.15285583451864M2[t] -15.916572621096M3[t] -22.7610629200788M4[t] -33.4316347249648M5[t] -32.0713375490233M6[t] + 23.8141590604126M7[t] + 35.1335939091082M8[t] + 25.8334153518013M9[t] + 11.4828238869186M10[t] -6.82507475222631M11[t] + 0.261359976004442t + 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) | 595.887010189059 | 14.906564 | 39.9748 | 0 | 0 |
HICP | 4.88997446557134 | 2.508727 | 1.9492 | 0.053708 | 0.026854 |
Consvertr | 0.545185974417897 | 0.401827 | 1.3568 | 0.177513 | 0.088756 |
Rente | -29.9079834813727 | 3.313528 | -9.026 | 0 | 0 |
M1 | -0.27597337857964 | 12.979051 | -0.0213 | 0.983073 | 0.491536 |
M2 | -6.15285583451864 | 12.978039 | -0.4741 | 0.636329 | 0.318165 |
M3 | -15.916572621096 | 12.959416 | -1.2282 | 0.221885 | 0.110942 |
M4 | -22.7610629200788 | 12.971826 | -1.7547 | 0.081982 | 0.040991 |
M5 | -33.4316347249648 | 12.948771 | -2.5818 | 0.011084 | 0.005542 |
M6 | -32.0713375490233 | 12.991442 | -2.4687 | 0.015033 | 0.007516 |
M7 | 23.8141590604126 | 12.953742 | 1.8384 | 0.068584 | 0.034292 |
M8 | 35.1335939091082 | 12.99564 | 2.7035 | 0.007903 | 0.003951 |
M9 | 25.8334153518013 | 12.979353 | 1.9903 | 0.048925 | 0.024462 |
M10 | 11.4828238869186 | 12.940197 | 0.8874 | 0.376728 | 0.188364 |
M11 | -6.82507475222631 | 12.935689 | -0.5276 | 0.598782 | 0.299391 |
t | 0.261359976004442 | 0.093594 | 2.7925 | 0.006127 | 0.003064 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.829564855855492 |
R-squared | 0.688177850070543 |
Adjusted R-squared | 0.647505395731918 |
F-TEST (value) | 16.9199980984922 |
F-TEST (DF numerator) | 15 |
F-TEST (DF denominator) | 115 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 29.5591799724786 |
Sum Squared Residuals | 100480.688874219 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 493 | 512.522112451798 | -19.522112451798 |
2 | 481 | 510.51823942764 | -29.5182394276395 |
3 | 462 | 499.276966995111 | -37.2769669951114 |
4 | 457 | 486.983538117209 | -29.9835381172087 |
5 | 442 | 470.430593673773 | -28.4305936737726 |
6 | 439 | 465.309733400603 | -26.309733400603 |
7 | 488 | 509.822133544573 | -21.8221335445726 |
8 | 521 | 531.840440330555 | -10.8404403305547 |
9 | 501 | 514.498497265187 | -13.4984972651874 |
10 | 485 | 495.141420638035 | -10.1414206380348 |
11 | 464 | 475.599482800826 | -11.5994828008257 |
12 | 460 | 479.808121377574 | -19.8081213775744 |
13 | 467 | 477.236143686492 | -10.236143686492 |
14 | 460 | 467.916696441354 | -7.9166964413537 |
15 | 448 | 456.402161316692 | -8.40216131669155 |
16 | 443 | 451.061269221942 | -8.06126922194152 |
17 | 436 | 446.714409478007 | -10.7144094780075 |
18 | 431 | 450.784893836324 | -19.7848938363241 |
19 | 484 | 505.95375552865 | -21.9537555286502 |
20 | 510 | 514.185893950821 | -4.18589395082096 |
21 | 513 | 513.790019193935 | -0.790019193935498 |
22 | 503 | 502.623163335663 | 0.376836664337296 |
23 | 471 | 492.673757381588 | -21.6737573815877 |
24 | 471 | 510.377164434504 | -39.3771644345038 |
25 | 476 | 517.112837532197 | -41.1128375321967 |
26 | 475 | 512.098689554541 | -37.0986895545408 |
27 | 470 | 503.141518718386 | -33.1415187183858 |
28 | 461 | 491.067039427558 | -30.0670394275575 |
29 | 455 | 480.22501867998 | -25.2250186799795 |
30 | 456 | 478.367505178165 | -22.3675051781648 |
31 | 517 | 535.436168128859 | -18.4361681288586 |
32 | 525 | 546.904585897837 | -21.9045858978372 |
33 | 523 | 537.376769869977 | -14.3767698699775 |
34 | 519 | 523.776535827656 | -4.77653582765644 |
35 | 509 | 504.206816296984 | 4.79318370301623 |
36 | 512 | 522.053695413206 | -10.0536954132063 |
37 | 519 | 523.995696937793 | -4.99569693779335 |
38 | 517 | 518.155420346416 | -1.15542034641573 |
39 | 510 | 512.397727806585 | -2.39772780658507 |
40 | 509 | 510.148303585486 | -1.14830358548635 |
41 | 501 | 497.895479026098 | 3.10452097390233 |
42 | 507 | 513.869128275518 | -6.86912827551764 |
43 | 569 | 570.882227839284 | -1.88222783928447 |
44 | 580 | 584.531389505935 | -4.53138950593459 |
45 | 578 | 579.252684217697 | -1.25268421769658 |
46 | 565 | 558.244600644968 | 6.75539935503199 |
47 | 547 | 547.060725537817 | -0.0607255378171244 |
48 | 555 | 553.658162819491 | 1.34183718050926 |
49 | 562 | 553.812115000498 | 8.18788499950217 |
50 | 561 | 548.308969576285 | 12.6910304237152 |
51 | 555 | 536.738245923762 | 18.2617540762381 |
52 | 544 | 533.032911752266 | 10.9670882477344 |
53 | 537 | 524.956310100448 | 12.043689899552 |
54 | 543 | 527.893093312673 | 15.1069066873272 |
55 | 594 | 582.348203446999 | 11.6517965530012 |
56 | 611 | 594.530372773978 | 16.4696272260225 |
57 | 613 | 584.513559299561 | 28.4864407004393 |
58 | 611 | 572.644560932025 | 38.3554390679749 |
59 | 594 | 552.096846508238 | 41.9031534917618 |
60 | 595 | 557.772477424658 | 37.2275225753417 |
61 | 591 | 558.24686146864 | 32.7531385313598 |
62 | 589 | 555.733889251631 | 33.2661107483692 |
63 | 584 | 549.221705648261 | 34.7782943517385 |
64 | 573 | 539.047027615801 | 33.9529723841991 |
65 | 567 | 524.877702493855 | 42.1222975061453 |
66 | 569 | 528.455349432029 | 40.5446505679708 |
67 | 621 | 584.60220601747 | 36.3977939825304 |
68 | 629 | 597.706181709702 | 31.2938182902982 |
69 | 628 | 586.975616677285 | 41.0243833227151 |
70 | 612 | 572.245521462457 | 39.754478537543 |
71 | 595 | 554.142794271456 | 40.8572057285443 |
72 | 597 | 559.574283599055 | 37.4257164009445 |
73 | 593 | 560.544094754897 | 32.4559052451031 |
74 | 590 | 554.383386300544 | 35.6166136994555 |
75 | 580 | 534.3298901911 | 45.6701098088994 |
76 | 574 | 528.7525364547 | 45.2474635453 |
77 | 573 | 518.230947570097 | 54.7690524299032 |
78 | 573 | 516.379238592651 | 56.6207614073492 |
79 | 620 | 568.747219548583 | 51.252780451417 |
80 | 626 | 574.455579900079 | 51.5444200999211 |
81 | 620 | 561.367212688852 | 58.6327873111483 |
82 | 588 | 543.396373012697 | 44.6036269873025 |
83 | 566 | 523.879002036301 | 42.1209979636993 |
84 | 557 | 522.360642753935 | 34.6393572460647 |
85 | 561 | 520.916463203106 | 40.0835367968941 |
86 | 549 | 516.880310118564 | 32.1196898814358 |
87 | 532 | 501.80138383695 | 30.1986161630503 |
88 | 526 | 493.863013089088 | 32.1369869109123 |
89 | 511 | 481.00881402742 | 29.9911859725796 |
90 | 499 | 477.599087682743 | 21.4009123172574 |
91 | 555 | 529.66477397121 | 25.3352260287901 |
92 | 565 | 540.211385374935 | 24.7886146250651 |
93 | 542 | 532.150561686747 | 9.84943831325333 |
94 | 527 | 522.518495744743 | 4.48150425525658 |
95 | 510 | 504.078637386578 | 5.92136261342241 |
96 | 514 | 514.323810905594 | -0.323810905594187 |
97 | 517 | 515.174815340412 | 1.82518465958827 |
98 | 508 | 511.683848230288 | -3.683848230288 |
99 | 493 | 506.093470992172 | -13.0934709921722 |
100 | 490 | 495.862604431851 | -5.86260443185086 |
101 | 469 | 489.252995119705 | -20.2529951197047 |
102 | 478 | 493.207262448715 | -15.2072624487149 |
103 | 528 | 543.36930750523 | -15.3693075052295 |
104 | 534 | 551.501928202284 | -17.5019282022836 |
105 | 518 | 544.042479016374 | -26.042479016374 |
106 | 506 | 530.543012981037 | -24.543012981037 |
107 | 502 | 518.395976215648 | -16.3959762156479 |
108 | 516 | 541.440214720359 | -25.440214720359 |
109 | 528 | 554.377059242335 | -26.3770592423345 |
110 | 533 | 554.87427285084 | -21.8742728508397 |
111 | 536 | 549.183663618691 | -13.1836636186908 |
112 | 537 | 554.647696909586 | -17.6476969095858 |
113 | 524 | 548.052822350846 | -24.0528223508456 |
114 | 536 | 548.999404418076 | -12.999404418076 |
115 | 587 | 602.268464852034 | -15.2684648520343 |
116 | 597 | 622.010349988813 | -25.0103499888131 |
117 | 581 | 611.504539067839 | -30.5045390678392 |
118 | 564 | 597.3591190511 | -33.3591190511002 |
119 | 558 | 584.80392935581 | -26.8039293558097 |
120 | 575 | 590.631426551622 | -15.6314265516224 |
121 | 580 | 593.061800381833 | -13.0618003818328 |
122 | 575 | 587.446277901898 | -12.4462779018983 |
123 | 563 | 584.41326495229 | -21.4132649522897 |
124 | 552 | 581.534059394515 | -29.5340593945151 |
125 | 537 | 570.354907479772 | -33.3549074797724 |
126 | 545 | 575.135303422504 | -30.1353034225043 |
127 | 601 | 630.905539617109 | -29.905539617109 |
128 | 604 | 644.121892365063 | -40.1218923650628 |
129 | 586 | 637.528061016546 | -51.528061016546 |
130 | 564 | 625.507196369618 | -61.5071963696178 |
131 | 549 | 608.062032208756 | -59.062032208756 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
19 | 0.00053028704633239 | 0.00106057409266478 | 0.999469712953668 |
20 | 0.000305766629476034 | 0.000611533258952068 | 0.999694233370524 |
21 | 0.000113385798053101 | 0.000226771596106201 | 0.999886614201947 |
22 | 1.80145305515799e-05 | 3.60290611031598e-05 | 0.999981985469448 |
23 | 1.04861377555783e-05 | 2.09722755111566e-05 | 0.999989513862244 |
24 | 2.09223779202034e-06 | 4.18447558404067e-06 | 0.999997907762208 |
25 | 4.25883013823577e-07 | 8.51766027647153e-07 | 0.999999574116986 |
26 | 8.25146851985324e-08 | 1.65029370397065e-07 | 0.999999917485315 |
27 | 6.86884632922866e-08 | 1.37376926584573e-07 | 0.999999931311537 |
28 | 1.54960593929597e-08 | 3.09921187859193e-08 | 0.99999998450394 |
29 | 3.47298940621542e-09 | 6.94597881243085e-09 | 0.99999999652701 |
30 | 8.18350335358698e-10 | 1.6367006707174e-09 | 0.99999999918165 |
31 | 5.74469530078686e-09 | 1.14893906015737e-08 | 0.999999994255305 |
32 | 6.45654608024987e-09 | 1.29130921604997e-08 | 0.999999993543454 |
33 | 2.14491891376328e-09 | 4.28983782752656e-09 | 0.999999997855081 |
34 | 9.06396386003604e-10 | 1.81279277200721e-09 | 0.999999999093604 |
35 | 2.00928819846689e-08 | 4.01857639693379e-08 | 0.999999979907118 |
36 | 9.0537237908035e-07 | 1.8107447581607e-06 | 0.99999909462762 |
37 | 6.14612329942463e-06 | 1.22922465988493e-05 | 0.9999938538767 |
38 | 3.14471343012247e-05 | 6.28942686024494e-05 | 0.9999685528657 |
39 | 0.000102197579351031 | 0.000204395158702062 | 0.999897802420649 |
40 | 0.000214493786849836 | 0.000428987573699672 | 0.99978550621315 |
41 | 0.000365550327857871 | 0.000731100655715741 | 0.999634449672142 |
42 | 0.000609696312114446 | 0.00121939262422889 | 0.999390303687886 |
43 | 0.000984379924613835 | 0.00196875984922767 | 0.999015620075386 |
44 | 0.000898656987565213 | 0.00179731397513043 | 0.999101343012435 |
45 | 0.000899980800404347 | 0.00179996160080869 | 0.999100019199596 |
46 | 0.000710168732260361 | 0.00142033746452072 | 0.99928983126774 |
47 | 0.000828714363276981 | 0.00165742872655396 | 0.999171285636723 |
48 | 0.00180798781975862 | 0.00361597563951724 | 0.998192012180241 |
49 | 0.00303591115294193 | 0.00607182230588385 | 0.996964088847058 |
50 | 0.00540947616151307 | 0.0108189523230261 | 0.994590523838487 |
51 | 0.0109187651447274 | 0.0218375302894548 | 0.989081234855273 |
52 | 0.018691560930755 | 0.0373831218615099 | 0.981308439069245 |
53 | 0.0303004841196284 | 0.0606009682392567 | 0.969699515880372 |
54 | 0.0670249052379763 | 0.134049810475953 | 0.932975094762024 |
55 | 0.14579500744176 | 0.29159001488352 | 0.85420499255824 |
56 | 0.251709811586859 | 0.503419623173719 | 0.74829018841314 |
57 | 0.323114171397763 | 0.646228342795527 | 0.676885828602237 |
58 | 0.318035000098715 | 0.636070000197429 | 0.681964999901285 |
59 | 0.369133498784415 | 0.73826699756883 | 0.630866501215585 |
60 | 0.489495394768331 | 0.978990789536662 | 0.510504605231669 |
61 | 0.547238573746209 | 0.905522852507582 | 0.452761426253791 |
62 | 0.605946332448538 | 0.788107335102924 | 0.394053667551462 |
63 | 0.65800582962493 | 0.683988340750139 | 0.34199417037507 |
64 | 0.72398240900424 | 0.55203518199152 | 0.27601759099576 |
65 | 0.74067188968723 | 0.518656220625539 | 0.259328110312769 |
66 | 0.766906335421041 | 0.466187329157918 | 0.233093664578959 |
67 | 0.7946738700034 | 0.410652259993202 | 0.205326129996601 |
68 | 0.834338094104609 | 0.331323811790783 | 0.165661905895391 |
69 | 0.800939550921098 | 0.398120898157804 | 0.199060449078902 |
70 | 0.778965702941559 | 0.442068594116883 | 0.221034297058441 |
71 | 0.760608062433502 | 0.478783875132995 | 0.239391937566498 |
72 | 0.77575932455893 | 0.448481350882138 | 0.224240675441069 |
73 | 0.902949039804002 | 0.194101920391997 | 0.0970509601959983 |
74 | 0.964853334374726 | 0.0702933312505486 | 0.0351466656252743 |
75 | 0.971492600540145 | 0.0570147989197093 | 0.0285073994598546 |
76 | 0.979265809743957 | 0.0414683805120856 | 0.0207341902560428 |
77 | 0.971150041299922 | 0.057699917400157 | 0.0288499587000785 |
78 | 0.962128271201896 | 0.0757434575962079 | 0.0378717287981039 |
79 | 0.959634986552482 | 0.0807300268950362 | 0.0403650134475181 |
80 | 0.947560988625747 | 0.104878022748506 | 0.0524390113742532 |
81 | 0.957805767136187 | 0.0843884657276261 | 0.0421942328638131 |
82 | 0.967585025063212 | 0.064829949873576 | 0.032414974936788 |
83 | 0.969322369830563 | 0.0613552603388737 | 0.0306776301694369 |
84 | 0.96536383404436 | 0.0692723319112779 | 0.0346361659556389 |
85 | 0.965505036678056 | 0.068989926643887 | 0.0344949633219435 |
86 | 0.963190785308693 | 0.0736184293826135 | 0.0368092146913067 |
87 | 0.964193892184672 | 0.0716122156306569 | 0.0358061078153285 |
88 | 0.96948932715009 | 0.0610213456998219 | 0.030510672849911 |
89 | 0.979017676824547 | 0.0419646463509059 | 0.020982323175453 |
90 | 0.97514753258166 | 0.0497049348366807 | 0.0248524674183404 |
91 | 0.969854167256808 | 0.0602916654863846 | 0.0301458327431923 |
92 | 0.976416285616554 | 0.0471674287668912 | 0.0235837143834456 |
93 | 0.98584083328949 | 0.028318333421019 | 0.0141591667105095 |
94 | 0.99725616470094 | 0.00548767059811967 | 0.00274383529905983 |
95 | 0.999867965023785 | 0.000264069952430343 | 0.000132034976215171 |
96 | 0.999908630432595 | 0.000182739134809078 | 9.1369567404539e-05 |
97 | 0.999938475738538 | 0.000123048522924766 | 6.1524261462383e-05 |
98 | 0.999916183990593 | 0.000167632018814775 | 8.38160094073876e-05 |
99 | 0.999908561698749 | 0.000182876602502694 | 9.14383012513468e-05 |
100 | 0.99984118391276 | 0.000317632174480638 | 0.000158816087240319 |
101 | 0.99977765760451 | 0.000444684790980873 | 0.000222342395490437 |
102 | 0.999539278256993 | 0.000921443486013308 | 0.000460721743006654 |
103 | 0.999241841776163 | 0.00151631644767294 | 0.000758158223836469 |
104 | 0.998312826227871 | 0.00337434754425784 | 0.00168717377212892 |
105 | 0.997181730115745 | 0.00563653976850964 | 0.00281826988425482 |
106 | 0.998871582265994 | 0.00225683546801289 | 0.00112841773400645 |
107 | 0.999788929011325 | 0.000422141977349618 | 0.000211070988674809 |
108 | 0.999478886698605 | 0.00104222660279041 | 0.000521113301395207 |
109 | 0.998549586400919 | 0.00290082719816247 | 0.00145041359908124 |
110 | 0.994828032427047 | 0.0103439351459055 | 0.00517196757295276 |
111 | 0.9934316351715 | 0.0131367296570007 | 0.00656836482850034 |
112 | 0.97371708310323 | 0.05256583379354 | 0.02628291689677 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 47 | 0.5 | NOK |
5% type I error level | 57 | 0.606382978723404 | NOK |
10% type I error level | 73 | 0.776595744680851 | NOK |