Multiple Linear Regression - Estimated Regression Equation |
tot_indus[t] = + 209.298982723361 + 0.200657477896676prijsindex[t] -0.0431033994434085`y(t-1)`[t] -0.6525411392476`y(t-2)`[t] -0.0302790380657440`y(t-3)`[t] -0.535338506090538`y(t-4)`[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) | 209.298982723361 | 26.091732 | 8.0217 | 0 | 0 |
prijsindex | 0.200657477896676 | 0.027945 | 7.1805 | 0 | 0 |
`y(t-1)` | -0.0431033994434085 | 0.110024 | -0.3918 | 0.696555 | 0.348278 |
`y(t-2)` | -0.6525411392476 | 0.112174 | -5.8172 | 0 | 0 |
`y(t-3)` | -0.0302790380657440 | 0.110954 | -0.2729 | 0.785825 | 0.392912 |
`y(t-4)` | -0.535338506090538 | 0.117064 | -4.5731 | 2.3e-05 | 1.2e-05 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.75865628105714 |
R-squared | 0.57555935278745 |
Adjusted R-squared | 0.54187358713566 |
F-TEST (value) | 17.0861294570833 |
F-TEST (DF numerator) | 5 |
F-TEST (DF denominator) | 63 |
p-value | 1.20284671112358e-10 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 5.35827567184311 |
Sum Squared Residuals | 1808.80044505434 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 101.7 | 98.0732065677168 | 3.62679343228316 |
2 | 104.2 | 100.580754262622 | 3.61924573737824 |
3 | 92.7 | 96.7786533030993 | -4.07865330309934 |
4 | 91.9 | 96.8140608472913 | -4.91406084729132 |
5 | 106.5 | 104.966270168677 | 1.53372983132296 |
6 | 112.3 | 103.9290533641 | 8.37094663589992 |
7 | 102.8 | 100.814147011759 | 1.98585298824085 |
8 | 96.5 | 97.5254162868964 | -1.02541628689636 |
9 | 101 | 96.787112080336 | 4.2128879196641 |
10 | 98.9 | 98.549013163459 | 0.350986836541081 |
11 | 105.1 | 101.220357896826 | 3.87964210317380 |
12 | 103 | 105.298975408506 | -2.29897540850587 |
13 | 99 | 99.339417898957 | -0.339417898956908 |
14 | 104.3 | 101.798582968143 | 2.50141703185665 |
15 | 94.6 | 100.964918245840 | -6.36491824583976 |
16 | 90.4 | 99.3705376753783 | -8.97053767537831 |
17 | 108.9 | 108.183148090991 | 0.716851909009263 |
18 | 111.4 | 108.806831188255 | 2.59316881174482 |
19 | 100.8 | 102.408529281683 | -1.60852928168276 |
20 | 102.5 | 103.464107179349 | -0.964107179348907 |
21 | 98.2 | 101.873370098285 | -3.67337009828478 |
22 | 98.7 | 101.095819689242 | -2.39581968924177 |
23 | 113.3 | 109.964820887295 | 3.33517911270495 |
24 | 104.6 | 107.848115881123 | -3.24811588112258 |
25 | 99.3 | 100.079872229887 | -0.779872229886675 |
26 | 111.8 | 105.376013688534 | 6.42398631146593 |
27 | 97.3 | 101.425410100603 | -4.12541010060257 |
28 | 97.7 | 98.7517005522524 | -1.05170055225244 |
29 | 115.6 | 110.815637800341 | 4.78436219965932 |
30 | 111.9 | 104.132357654116 | 7.7676423458838 |
31 | 107 | 101.104083230829 | 5.89591676917102 |
32 | 107.1 | 102.752838693818 | 4.34716130618157 |
33 | 100.6 | 98.582356635925 | 2.01764336407494 |
34 | 99.2 | 101.488235315550 | -2.28823531555028 |
35 | 108.4 | 109.132595176346 | -0.732595176345546 |
36 | 103 | 109.351434941858 | -6.35143494185842 |
37 | 99.8 | 105.638106172010 | -5.83810617200971 |
38 | 115 | 109.269022265746 | 5.73097773425413 |
39 | 90.8 | 106.120966519427 | -15.3209665194275 |
40 | 95.9 | 101.396977695894 | -5.49697769589443 |
41 | 114.4 | 118.682999968578 | -4.28299996857774 |
42 | 108.2 | 107.273629184065 | 0.926370815935249 |
43 | 112.6 | 108.791337380320 | 3.80866261967963 |
44 | 109.1 | 110.641256759365 | -1.54125675936521 |
45 | 105 | 100.211480097027 | 4.78851990297287 |
46 | 105 | 106.821124886288 | -1.82112488628781 |
47 | 118.5 | 107.487819737111 | 11.0121802628893 |
48 | 103.7 | 111.712957362565 | -8.0129573625646 |
49 | 112.5 | 109.348304771596 | 3.15169522840418 |
50 | 116.6 | 116.130998933345 | 0.469001066654665 |
51 | 96.6 | 105.319153193628 | -8.71915319362799 |
52 | 101.9 | 111.162356866742 | -9.2623568667424 |
53 | 116.5 | 118.587767786867 | -2.08776778686737 |
54 | 119.3 | 113.974167636177 | 5.32583236382262 |
55 | 115.4 | 114.792405713625 | 0.607594286375487 |
56 | 108.5 | 110.656655655108 | -2.15665565510752 |
57 | 111.5 | 105.698584797775 | 5.80141520222492 |
58 | 108.8 | 109.473513055453 | -0.673513055453239 |
59 | 121.8 | 111.714865905895 | 10.0851340941052 |
60 | 109.6 | 119.388783300849 | -9.78878330084894 |
61 | 112.2 | 110.047808082873 | 2.15219191712671 |
62 | 119.6 | 117.082413070292 | 2.51758692970814 |
63 | 104.1 | 108.998554080123 | -4.89855408012331 |
64 | 105.3 | 109.263616089641 | -3.9636160896411 |
65 | 115 | 117.610005932177 | -2.61000593217657 |
66 | 124.1 | 114.060421359438 | 10.0395786405615 |
67 | 116.8 | 114.335801261777 | 2.46419873822286 |
68 | 107.5 | 106.291353497579 | 1.20864650242091 |
69 | 115.6 | 111.967035514755 | 3.63296448524526 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
9 | 0.507426227272045 | 0.985147545455911 | 0.492573772727955 |
10 | 0.357463833644103 | 0.714927667288206 | 0.642536166355897 |
11 | 0.241708104014202 | 0.483416208028405 | 0.758291895985798 |
12 | 0.347043051433719 | 0.694086102867438 | 0.652956948566281 |
13 | 0.236733725378626 | 0.473467450757252 | 0.763266274621374 |
14 | 0.167362611780725 | 0.334725223561451 | 0.832637388219275 |
15 | 0.244787562666659 | 0.489575125333317 | 0.755212437333342 |
16 | 0.298850970417961 | 0.597701940835921 | 0.701149029582039 |
17 | 0.218682184421183 | 0.437364368842367 | 0.781317815578817 |
18 | 0.156821781202718 | 0.313643562405435 | 0.843178218797282 |
19 | 0.107924299925842 | 0.215848599851684 | 0.892075700074158 |
20 | 0.0750416912885637 | 0.150083382577127 | 0.924958308711436 |
21 | 0.0490128145962606 | 0.0980256291925212 | 0.95098718540374 |
22 | 0.0394272904855781 | 0.0788545809711562 | 0.960572709514422 |
23 | 0.0337843377145679 | 0.0675686754291357 | 0.966215662285432 |
24 | 0.0261260742569473 | 0.0522521485138946 | 0.973873925743053 |
25 | 0.0187390581070881 | 0.0374781162141763 | 0.981260941892912 |
26 | 0.0287120352840848 | 0.0574240705681696 | 0.971287964715915 |
27 | 0.0199006714412746 | 0.0398013428825493 | 0.980099328558725 |
28 | 0.0142087215926446 | 0.0284174431852893 | 0.985791278407355 |
29 | 0.0107353739277771 | 0.0214707478555542 | 0.989264626072223 |
30 | 0.0265928590501273 | 0.0531857181002545 | 0.973407140949873 |
31 | 0.0347894824103153 | 0.0695789648206307 | 0.965210517589685 |
32 | 0.0299507044351416 | 0.0599014088702831 | 0.970049295564858 |
33 | 0.0220842634996639 | 0.0441685269993278 | 0.977915736500336 |
34 | 0.0142877284058930 | 0.0285754568117861 | 0.985712271594107 |
35 | 0.00920689027723683 | 0.0184137805544737 | 0.990793109722763 |
36 | 0.0136231069897485 | 0.027246213979497 | 0.986376893010251 |
37 | 0.0126436543231170 | 0.0252873086462339 | 0.987356345676883 |
38 | 0.0150233237718476 | 0.0300466475436952 | 0.984976676228152 |
39 | 0.178224892294303 | 0.356449784588606 | 0.821775107705697 |
40 | 0.176954902346483 | 0.353909804692967 | 0.823045097653517 |
41 | 0.165151262397159 | 0.330302524794318 | 0.83484873760284 |
42 | 0.136569588234607 | 0.273139176469214 | 0.863430411765393 |
43 | 0.113880348545090 | 0.227760697090180 | 0.88611965145491 |
44 | 0.0835289372949523 | 0.167057874589905 | 0.916471062705048 |
45 | 0.0799067398872224 | 0.159813479774445 | 0.920093260112778 |
46 | 0.056260788505587 | 0.112521577011174 | 0.943739211494413 |
47 | 0.167775105162648 | 0.335550210325296 | 0.832224894837352 |
48 | 0.187490601798392 | 0.374981203596784 | 0.812509398201608 |
49 | 0.157451938478646 | 0.314903876957293 | 0.842548061521354 |
50 | 0.118355969655952 | 0.236711939311904 | 0.881644030344048 |
51 | 0.249512670946705 | 0.49902534189341 | 0.750487329053295 |
52 | 0.384906761729616 | 0.769813523459232 | 0.615093238270384 |
53 | 0.335015917454758 | 0.670031834909515 | 0.664984082545242 |
54 | 0.280130541707999 | 0.560261083415998 | 0.719869458292001 |
55 | 0.199437447594646 | 0.398874895189293 | 0.800562552405354 |
56 | 0.135056038966217 | 0.270112077932433 | 0.864943961033783 |
57 | 0.106938096933296 | 0.213876193866591 | 0.893061903066704 |
58 | 0.0705540858946835 | 0.141108171789367 | 0.929445914105317 |
59 | 0.0836400325316719 | 0.167280065063344 | 0.916359967468328 |
60 | 0.246902375499842 | 0.493804750999685 | 0.753097624500158 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 0 | 0 | OK |
5% type I error level | 10 | 0.192307692307692 | NOK |
10% type I error level | 18 | 0.346153846153846 | NOK |