Multiple Linear Regression - Estimated Regression Equation

VDAB-vacatures[t] = + 19.0922638297872 + 2.25662092198582M1[t] + 4.46672037395229M2[t] + 6.38072891682785M3[t] + 6.78373745970341M4[t] + 7.92101872985171M5[t] + 8.71093636363636M6[t] + 7.50621763378466M7[t] + 7.5510443584784M8[t] + 5.67778017408124M9[t] + 3.8207887169568M10[t] + 2.45206998710509M11[t] + 0.134991457124436t + 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)	19.0922638297872	2.053491	9.2975	0	0
M1	2.25662092198582	2.555017	0.8832	0.378918	0.189459
M2	4.46672037395229	2.554694	1.7484	0.082989	0.041495
M3	6.38072891682785	2.554442	2.4979	0.013871	0.006935
M4	6.78373745970341	2.554262	2.6558	0.009004	0.004502
M5	7.92101872985171	2.554154	3.1012	0.002411	0.001206
M6	8.71093636363636	2.554119	3.4105	0.000888	0.000444
M7	7.50621763378466	2.554154	2.9388	0.003964	0.001982
M8	7.5510443584784	2.554262	2.9563	0.003762	0.001881
M9	5.67778017408124	2.554442	2.2227	0.028141	0.01407
M10	3.8207887169568	2.554694	1.4956	0.137429	0.068714
M11	2.45206998710509	2.555017	0.9597	0.339165	0.169582
t	0.134991457124436	0.01355	9.9627	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.716794881754803
R-squared	0.513794902509882
Adjusted R-squared	0.464350316324447
F-TEST (value)	10.3913277903259
F-TEST (DF numerator)	12
F-TEST (DF denominator)	118
p-value	9.84767822842514e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.84558181029365
Sum Squared Residuals	4032.15755069865

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	27.951	21.4838762088975	6.46712379110254
2	29.781	23.8289671179884	5.95203288201161
3	32.914	25.8779671179884	7.03603288201161
4	33.488	26.4159671179884	7.0720328820116
5	35.652	27.6882398452611	7.96376015473888
6	36.488	28.6131489361702	7.87485106382979
7	35.387	27.5434216634429	7.84357833655706
8	35.676	27.7232398452611	7.95276015473888
9	34.844	25.9849671179884	8.8590328820116
10	32.447	24.2629671179884	8.1840328820116
11	31.068	23.0292398452611	8.03876015473888
12	29.01	20.7121613152805	8.29783868471954
13	29.812	23.1037736943907	6.70822630560929
14	30.951	25.4488646034816	5.50213539651837
15	32.974	27.4978646034816	5.47613539651837
16	32.936	28.0358646034816	4.90013539651838
17	34.012	29.3081373307544	4.70386266924565
18	32.946	30.2330464216634	2.71295357833655
19	31.948	29.1633191489362	2.78468085106383
20	30.599	29.3431373307544	1.25586266924565
21	27.691	27.6048646034816	0.0861353965183724
22	25.073	25.8828646034816	-0.809864603481627
23	23.406	24.6491373307544	-1.24313733075436
24	22.248	22.3320588007737	-0.0840588007736956
25	22.896	24.7236711798839	-1.82767117988395
26	25.317	27.0687620889749	-1.75176208897486
27	26.558	29.1177620889749	-2.55976208897485
28	26.471	29.6557620889749	-3.18476208897486
29	27.543	30.9280348162476	-3.38503481624758
30	26.198	31.8529439071567	-5.65494390715667
31	24.725	30.7832166344294	-6.0582166344294
32	25.005	30.9630348162476	-5.95803481624759
33	23.462	29.2247620889749	-5.76276208897485
34	20.78	27.5027620889749	-6.72276208897486
35	19.815	26.2690348162476	-6.45403481624758
36	19.761	23.9519562862669	-4.19095628626692
37	21.454	26.3435686653772	-4.88956866537718
38	23.899	28.6886595744681	-4.78965957446808
39	24.939	30.7376595744681	-5.79865957446809
40	23.58	31.2756595744681	-7.69565957446808
41	24.562	32.5479323017408	-7.98593230174081
42	24.696	33.4728413926499	-8.7768413926499
43	23.785	32.4031141199226	-8.61811411992263
44	23.812	32.5829323017408	-8.77093230174082
45	21.917	30.8446595744681	-8.92765957446809
46	19.713	29.1226595744681	-9.4096595744681
47	19.282	27.8889323017408	-8.60693230174082
48	18.788	25.5718537717602	-6.78385377176016
49	21.453	27.9634661508704	-6.51046615087041
50	24.482	30.3085570599613	-5.82655705996132
51	27.474	32.3575570599613	-4.88355705996131
52	27.264	32.8955570599613	-5.63155705996132
53	27.349	34.167829787234	-6.81882978723405
54	30.632	35.0927388781431	-4.46073887814313
55	29.429	34.0230116054159	-4.59401160541586
56	30.084	34.202829787234	-4.11882978723404
57	26.29	32.4645570599613	-6.17455705996132
58	24.379	30.7425570599613	-6.36355705996132
59	23.335	29.508829787234	-6.17382978723404
60	21.346	27.1917512572534	-5.84575125725338
61	21.106	29.5833636363636	-8.47736363636364
62	24.514	31.9284545454545	-7.41445454545455
63	28.353	33.9774545454545	-5.62445454545454
64	30.805	34.5154545454545	-3.71045454545454
65	31.348	35.7877272727273	-4.43972727272727
66	34.556	36.7126363636364	-2.15663636363637
67	33.855	35.6429090909091	-1.7879090909091
68	34.787	35.8227272727273	-1.03572727272727
69	32.529	34.0844545454545	-1.55545454545454
70	29.998	32.3624545454545	-2.36445454545455
71	29.257	31.1287272727273	-1.87172727272727
72	28.155	28.8116487427466	-0.656648742746615
73	30.466	31.2032611218569	-0.73726112185687
74	35.704	33.5483520309478	2.15564796905222
75	39.327	35.5973520309478	3.72964796905222
76	39.351	36.1353520309478	3.21564796905222
77	42.234	37.4076247582205	4.8263752417795
78	43.63	38.3325338491296	5.29746615087041
79	43.722	37.2628065764023	6.45919342359768
80	43.121	37.4426247582205	5.6783752417795
81	37.985	35.7043520309478	2.28064796905222
82	37.135	33.9823520309478	3.15264796905222
83	34.646	32.7486247582205	1.8973752417795
84	33.026	30.4315462282398	2.59445377176016
85	35.087	32.8231586073501	2.2638413926499
86	38.846	35.168249516441	3.67775048355899
87	42.013	37.217249516441	4.79575048355899
88	43.908	37.755249516441	6.152750483559
89	42.868	39.0275222437137	3.84047775628627
90	44.423	39.9524313346228	4.47056866537718
91	44.167	38.8827040618956	5.28429593810445
92	43.636	39.0625222437137	4.57347775628627
93	44.382	37.324249516441	7.057750483559
94	42.142	35.602249516441	6.539750483559
95	43.452	34.3685222437137	9.08347775628627
96	36.912	32.0514437137331	4.86055628626692
97	42.413	34.4430560928433	7.96994390715667
98	45.344	36.7881470019342	8.55585299806577
99	44.873	38.8371470019342	6.03585299806576
100	47.51	39.3751470019342	8.13485299806577
101	49.554	40.647419729207	8.90658027079304
102	47.369	41.5723288201161	5.79667117988395
103	45.998	40.5026015473888	5.49539845261121
104	48.14	40.682419729207	7.45758027079304
105	48.441	38.9441470019342	9.49685299806577
106	44.928	37.2221470019342	7.70585299806576
107	40.454	35.988419729207	4.46558027079303
108	38.661	33.6713411992263	4.9896588007737
109	37.246	36.0629535783366	1.18304642166344
110	36.843	38.4080444874275	-1.56504448742746
111	36.424	40.4570444874275	-4.03304448742746
112	37.594	40.9950444874275	-3.40104448742746
113	38.144	42.2673172147002	-4.12331721470019
114	38.737	43.1922263056093	-4.45522630560928
115	34.56	42.122499032882	-7.56249903288201
116	36.08	42.3023172147002	-6.2223172147002
117	33.508	40.5640444874275	-7.05604448742747
118	35.462	38.8420444874275	-3.38004448742746
119	33.374	37.6083172147002	-4.23431721470019
120	32.11	35.2912386847195	-3.18123868471954
121	35.533	37.6828510638298	-2.14985106382979
122	35.532	40.0279419729207	-4.4959419729207
123	37.903	42.0769419729207	-4.17394197292069
124	36.763	42.6149419729207	-5.8519419729207
125	40.399	43.8872147001934	-3.48821470019342
126	44.164	44.8121237911025	-0.648123791102515
127	44.496	43.7423965183752	0.753603481624759
128	43.11	43.9222147001934	-0.812214700193427
129	43.88	42.1839419729207	1.69605802707931
130	43.93	40.4619419729207	3.4680580270793
131	44.327	39.2282147001934	5.09878529980657

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.00469531525251385	0.0093906305050277	0.995304684747486
17	0.00280325949891358	0.00560651899782716	0.997196740501086
18	0.00442510215152771	0.00885020430305542	0.995574897848472
19	0.00293842977451971	0.00587685954903943	0.99706157022548
20	0.00355527074316024	0.00711054148632047	0.99644472925684
21	0.00745539473496915	0.0149107894699383	0.99254460526503
22	0.00934211823241927	0.0186842364648385	0.99065788176758
23	0.00977927081496118	0.0195585416299224	0.990220729185039
24	0.00715194397352384	0.0143038879470477	0.992848056026476
25	0.00348326627336476	0.00696653254672953	0.996516733726635
26	0.0015883240735687	0.0031766481471374	0.998411675926431
27	0.000742309765745696	0.00148461953149139	0.999257690234254
28	0.00034481678425491	0.00068963356850982	0.999655183215745
29	0.000167916413059483	0.000335832826118966	0.99983208358694
30	0.00010359413862204	0.00020718827724408	0.999896405861378
31	6.69557557392967e-05	0.000133911511478593	0.99993304424426
32	3.23421093144452e-05	6.46842186288904e-05	0.999967657890686
33	1.4080559200877e-05	2.8161118401754e-05	0.9999859194408
34	6.16445084039201e-06	1.2328901680784e-05	0.99999383554916
35	2.40847501663382e-06	4.81695003326764e-06	0.999997591524983
36	9.1703094812339e-07	1.83406189624678e-06	0.999999082969052
37	7.76748682885126e-07	1.55349736577025e-06	0.999999223251317
38	7.37546973762461e-07	1.47509394752492e-06	0.999999262453026
39	3.84767832148696e-07	7.69535664297392e-07	0.999999615232168
40	1.49890267202105e-07	2.9978053440421e-07	0.999999850109733
41	5.69099199198933e-08	1.13819839839787e-07	0.99999994309008
42	2.36774710957823e-08	4.73549421915646e-08	0.999999976322529
43	1.01060159686703e-08	2.02120319373407e-08	0.999999989893984
44	4.62217639580791e-09	9.24435279161583e-09	0.999999995377824
45	2.10113403164327e-09	4.20226806328654e-09	0.999999997898866
46	1.12157557881827e-09	2.24315115763654e-09	0.999999998878424
47	7.422095125092e-10	1.4844190250184e-09	0.99999999925779
48	5.21957580190219e-10	1.04391516038044e-09	0.999999999478042
49	1.83818552444284e-09	3.67637104888568e-09	0.999999998161815
50	8.50716871561119e-09	1.70143374312224e-08	0.999999991492831
51	4.73569876256369e-08	9.47139752512737e-08	0.999999952643012
52	1.56694745934738e-07	3.13389491869475e-07	0.999999843305254
53	2.23862112344181e-07	4.47724224688362e-07	0.999999776137888
54	1.50585961547965e-06	3.01171923095929e-06	0.999998494140385
55	5.4507034690268e-06	1.09014069380536e-05	0.99999454929653
56	1.91872657578322e-05	3.83745315156645e-05	0.999980812734242
57	3.09771607813497e-05	6.19543215626995e-05	0.999969022839219
58	5.96530114247191e-05	0.000119306022849438	0.999940346988575
59	0.000108445743805156	0.000216891487610312	0.999891554256195
60	0.000136714925019997	0.000273429850039994	0.99986328507498
61	0.000203994582957987	0.000407989165915974	0.999796005417042
62	0.000333455899499254	0.000666911798998508	0.9996665441005
63	0.000576197003364854	0.00115239400672971	0.999423802996635
64	0.00146507077635992	0.00293014155271983	0.99853492922364
65	0.00322713916820042	0.00645427833640084	0.9967728608318
66	0.00911874248962296	0.0182374849792459	0.990881257510377
67	0.0213269835876653	0.0426539671753306	0.978673016412335
68	0.045309036904641	0.0906180738092819	0.95469096309536
69	0.0873398587302893	0.174679717460579	0.91266014126971
70	0.169897691084843	0.339795382169687	0.830102308915157
71	0.290958102849959	0.581916205699918	0.709041897150041
72	0.378786662282695	0.757573324565391	0.621213337717305
73	0.49065014270819	0.98130028541638	0.50934985729181
74	0.592059386409939	0.815881227180122	0.407940613590061
75	0.671665177225944	0.656669645548113	0.328334822774056
76	0.729970004247863	0.540059991504275	0.270029995752137
77	0.786803112708075	0.42639377458385	0.213196887291925
78	0.827805121808176	0.344389756383648	0.172194878191824
79	0.861817916501631	0.276364166996737	0.138182083498369
80	0.877948419897603	0.244103160204795	0.122051580102397
81	0.896639135431296	0.206721729137408	0.103360864568704
82	0.920137769402561	0.159724461194878	0.079862230597439
83	0.946700761830403	0.106598476339193	0.0532992381695965
84	0.949616181280732	0.100767637438537	0.0503838187192684
85	0.955085710128038	0.0898285797439238	0.0449142898719619
86	0.951772017893277	0.0964559642134462	0.0482279821067231
87	0.943362085182401	0.113275829635197	0.0566379148175987
88	0.936016459901916	0.127967080196168	0.0639835400980841
89	0.927103854809047	0.145792290381905	0.0728961451909527
90	0.915483736531509	0.169032526936983	0.0845162634684913
91	0.899255468238788	0.201489063522423	0.100744531761212
92	0.882781741842266	0.234436516315468	0.117218258157734
93	0.870108489033867	0.259783021932266	0.129891510966133
94	0.863548913869966	0.272902172260069	0.136451086130034
95	0.851751090344524	0.296497819310952	0.148248909655476
96	0.82025774164353	0.359484516712939	0.179742258356469
97	0.793710875463388	0.412578249073224	0.206289124536612
98	0.788131398027251	0.423737203945498	0.211868601972749
99	0.75973268561837	0.480534628763259	0.240267314381629
100	0.775853103774931	0.448293792450138	0.224146896225069
101	0.806262675642326	0.387474648715349	0.193737324357674
102	0.7768148964333	0.4463702071334	0.2231851035667
103	0.757092776612015	0.485814446775969	0.242907223387985
104	0.795344223752346	0.409311552495308	0.204655776247654
105	0.89667840728065	0.2066431854387	0.10332159271935
106	0.928929528249322	0.142140943501357	0.0710704717506783
107	0.931949506573689	0.136100986852622	0.068050493426311
108	0.970308056523485	0.0593838869530308	0.0296919434765154
109	0.972213498717203	0.0555730025655934	0.0277865012827967
110	0.978070512110099	0.043858975779803	0.0219294878899015
111	0.972841585774507	0.054316828450987	0.0271584142254935
112	0.991373311419847	0.0172533771603058	0.0086266885801529
113	0.99719313015231	0.00561373969537926	0.00280686984768963
114	0.997606491735448	0.00478701652910367	0.00239350826455184
115	0.98754272276539	0.0249145544692185	0.0124572772346093

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	48	0.48	NOK
5% type I error level	57	0.57	NOK
10% type I error level	63	0.63	NOK