Multiple Linear Regression - Estimated Regression Equation

y[t] = + 13.02648301485 + 0.802532763952289x[t] -1.28760592963214M1[t] -0.344929698485876M2[t] + 0.94078458722841M3[t] -0.859034501060713M4[t] -0.344929698485876M5[t] -1.50189164391786M6[t] + 0.523271751073253M7[t] -0.414994959391956M8[t] + 1M9[t] -0.830964058765561M10[t] -0.261148805545802M11[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)	13.02648301485	0.882569	14.7597	0	0
x	0.802532763952289	0.368565	2.1775	0.031021	0.01551
M1	-1.28760592963214	0.868289	-1.4829	0.140207	0.070103
M2	-0.344929698485876	0.867336	-0.3977	0.691429	0.345714
M3	0.94078458722841	0.867336	1.0847	0.279814	0.139907
M4	-0.859034501060713	0.868289	-0.9893	0.3241	0.16205
M5	-0.344929698485876	0.867336	-0.3977	0.691429	0.345714
M6	-1.50189164391786	0.868289	-1.7297	0.085752	0.042876
M7	0.523271751073253	0.883512	0.5923	0.554572	0.277286
M8	-0.414994959391956	0.884876	-0.469	0.639765	0.319882
M9	1	0.883057	1.1324	0.259273	0.129636
M10	-0.830964058765561	0.883512	-0.9405	0.348471	0.174236
M11	-0.261148805545802	0.884876	-0.2951	0.768309	0.384155

Multiple Linear Regression - Regression Statistics
Multiple R	0.376259829312185
R-squared	0.141571459154035
Adjusted R-squared	0.0724362746563729
F-TEST (value)	2.0477483380235
F-TEST (DF numerator)	12
F-TEST (DF denominator)	149
p-value	0.0238212360708822
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.25136253158706
Sum Squared Residuals	755.226354046483

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.3439426131224	0.656057386877555
2	18	14.2866188442687	3.71338115573133
3	11	15.572333129983	-4.57233312998296
4	12	12.9699812777415	-0.969981277741548
5	16	14.2866188442687	1.71338115573133
6	18	13.1296568988367	4.8703431011633
7	14	15.1548202938278	-1.1548202938278
8	14	14.2165535833626	-0.216553583362596
9	15	15.6315485427546	-0.63154854275455
10	15	13.800584483989	1.19941551601101
11	17	13.5678669732565	3.43213302674354
12	19	14.6315485427546	4.36845145724545
13	10	12.5414098491701	-2.54140984917012
14	16	14.2866188442687	1.71338115573132
15	18	15.572333129983	2.42766687001704
16	14	12.9699812777415	1.03001872225845
17	14	13.4840860803164	0.515913919683614
18	17	13.1296568988367	3.8703431011633
19	14	14.3522875298755	-0.352287529875515
20	16	14.2165535833626	1.7834464166374
21	18	14.8290157788023	3.17098422119774
22	11	13.800584483989	-2.80058448398899
23	14	14.3703997372087	-0.370399737208749
24	12	14.6315485427546	-2.63154854275455
25	17	12.5414098491701	4.45859015082988
26	9	14.2866188442687	-5.28661884426867
27	16	14.7698003660307	1.23019963396933
28	14	13.7725140416938	0.227485958306162
29	15	14.2866188442687	0.713381155731325
30	11	12.3271241348844	-1.32712413488441
31	16	15.1548202938278	0.845179706172196
32	13	13.4140208194103	-0.414020819410306
33	17	15.6315485427546	1.36845145724545
34	15	13.800584483989	1.19941551601101
35	14	13.5678669732565	0.43213302674354
36	16	13.8290157788023	2.17098422119774
37	9	12.5414098491701	-3.54140984917012
38	15	13.4840860803164	1.51591391968361
39	17	15.572333129983	1.42766687001704
40	13	12.9699812777415	0.0300187222584513
41	15	13.4840860803164	1.51591391968361
42	16	13.1296568988367	2.8703431011633
43	16	14.3522875298755	1.64771247012449
44	12	13.4140208194103	-1.41402081941031
45	12	15.6315485427545	-3.63154854275455
46	11	13.800584483989	-2.80058448398899
47	15	14.3703997372087	0.629600262791251
48	15	14.6315485427546	0.368451457245449
49	17	13.3439426131224	3.65605738687759
50	13	13.4840860803164	-0.484086080316386
51	16	15.572333129983	0.427666870017039
52	14	12.9699812777415	1.03001872225845
53	11	13.4840860803164	-2.48408608031639
54	12	13.1296568988367	-1.1296568988367
55	12	14.3522875298755	-2.35228752987551
56	15	14.2165535833626	0.783446416637405
57	16	15.6315485427546	0.368451457245449
58	15	13.800584483989	1.19941551601101
59	12	13.5678669732565	-1.56786697325646
60	12	14.6315485427546	-2.63154854275455
61	8	12.5414098491701	-4.54140984917012
62	13	13.4840860803164	-0.484086080316386
63	11	15.572333129983	-4.57233312998296
64	14	13.7725140416938	0.227485958306162
65	15	14.2866188442687	0.713381155731325
66	10	12.3271241348844	-2.32712413488441
67	11	15.1548202938278	-4.1548202938278
68	12	13.4140208194103	-1.41402081941031
69	15	15.6315485427546	-0.63154854275455
70	15	12.9980517200367	2.0019482799633
71	14	13.5678669732565	0.43213302674354
72	16	14.6315485427546	1.36845145724545
73	15	13.3439426131224	1.65605738687759
74	15	13.4840860803164	1.51591391968361
75	13	14.7698003660307	-1.76980036603067
76	12	13.7725140416938	-1.77251404169384
77	17	14.2866188442687	2.71338115573133
78	13	13.1296568988367	-0.129656898836696
79	15	14.3522875298755	0.647712470124486
80	13	13.4140208194103	-0.414020819410306
81	15	14.8290157788023	0.170984221197739
82	16	12.9980517200367	3.0019482799633
83	15	14.3703997372087	0.629600262791251
84	16	13.8290157788023	2.17098422119774
85	15	13.3439426131224	1.65605738687759
86	14	14.2866188442687	-0.286618844268675
87	15	14.7698003660307	0.230199633969329
88	14	13.7725140416938	0.227485958306162
89	13	14.2866188442687	-1.28661884426868
90	7	13.1296568988367	-6.12965689883669
91	17	15.1548202938278	1.8451797061722
92	13	14.2165535833626	-1.2165535833626
93	15	15.6315485427546	-0.63154854275455
94	14	13.800584483989	0.19941551601101
95	13	14.3703997372087	-1.37039973720875
96	16	14.6315485427546	1.36845145724545
97	12	13.3439426131224	-1.34394261312241
98	14	14.2866188442687	-0.286618844268675
99	17	14.7698003660307	2.23019963396933
100	15	12.9699812777415	2.03001872225845
101	17	14.2866188442687	2.71338115573133
102	12	12.3271241348844	-0.327124134884406
103	16	15.1548202938278	0.845179706172196
104	11	13.4140208194103	-2.41402081941031
105	15	15.6315485427546	-0.63154854275455
106	9	12.9980517200367	-3.9980517200367
107	16	14.3703997372087	1.62960026279125
108	15	13.8290157788023	1.17098422119774
109	10	12.5414098491701	-2.54140984917012
110	10	14.2866188442687	-4.28661884426867
111	15	15.572333129983	-0.57233312998296
112	11	13.7725140416938	-2.77251404169384
113	13	14.2866188442687	-1.28661884426868
114	14	12.3271241348844	1.67287586511559
115	18	15.1548202938278	2.8451797061722
116	16	13.4140208194103	2.58597918058969
117	14	15.6315485427546	-1.63154854275455
118	14	13.800584483989	0.19941551601101
119	14	14.3703997372087	-0.370399737208749
120	14	14.6315485427546	-0.631548542754551
121	12	13.3439426131224	-1.34394261312241
122	14	14.2866188442687	-0.286618844268675
123	15	15.572333129983	-0.57233312998296
124	15	13.7725140416938	1.22748595830616
125	15	14.2866188442687	0.713381155731325
126	13	13.1296568988367	-0.129656898836696
127	17	14.3522875298755	2.64771247012449
128	17	14.2165535833626	2.78344641663741
129	19	15.6315485427545	3.36845145724545
130	15	13.800584483989	1.19941551601101
131	13	13.5678669732565	-0.56786697325646
132	9	13.8290157788023	-4.82901577880226
133	15	13.3439426131224	1.65605738687759
134	15	13.4840860803164	1.51591391968361
135	15	14.7698003660307	0.230199633969329
136	16	13.7725140416938	2.22748595830616
137	11	13.4840860803164	-2.48408608031639
138	14	12.3271241348844	1.67287586511559
139	11	15.1548202938278	-4.1548202938278
140	15	14.2165535833626	0.783446416637405
141	13	14.8290157788023	-1.82901577880226
142	15	13.800584483989	1.19941551601101
143	16	13.5678669732565	2.43213302674354
144	14	14.6315485427546	-0.631548542754551
145	15	12.5414098491701	2.45859015082988
146	16	14.2866188442687	1.71338115573132
147	16	15.572333129983	0.427666870017039
148	11	12.9699812777415	-1.96998127774155
149	12	13.4840860803164	-1.48408608031639
150	9	12.3271241348844	-3.32712413488441
151	16	15.1548202938278	0.845179706172196
152	13	14.2165535833626	-1.2165535833626
153	16	14.8290157788023	1.17098422119774
154	12	13.800584483989	-1.80058448398899
155	9	14.3703997372087	-5.37039973720875
156	13	14.6315485427546	-1.63154854275455
157	13	13.3439426131224	-0.343942613122407
158	14	14.2866188442687	-0.286618844268675
159	19	15.572333129983	3.42766687001704
160	13	13.7725140416938	-0.772514041693838
161	12	14.2866188442687	-2.28661884426867
162	13	13.1296568988367	-0.129656898836696

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.882203877441682	0.235592245116637	0.117796122558318
17	0.805134592909796	0.389730814180409	0.194865407090204
18	0.724817162947947	0.550365674104107	0.275182837052053
19	0.672338442094653	0.655323115810694	0.327661557905347
20	0.606824742132048	0.786350515735903	0.393175257867952
21	0.687265188161829	0.625469623676342	0.312734811838171
22	0.729332827527834	0.541334344944332	0.270667172472166
23	0.725599070003955	0.548801859992089	0.274400929996045
24	0.893657450751136	0.212685098497729	0.106342549248864
25	0.943526663540306	0.112946672919388	0.0564733364596938
26	0.994810763458627	0.0103784730827452	0.00518923654137258
27	0.991675447959283	0.0166491040814341	0.00832455204071705
28	0.987871374439767	0.0242572511204653	0.0121286255602327
29	0.98131283666808	0.0373743266638403	0.0186871633319201
30	0.993481809637261	0.013036380725478	0.00651819036273902
31	0.99077511073127	0.0184497785374604	0.00922488926873022
32	0.986583188955517	0.0268336220889656	0.0134168110444828
33	0.98072472864637	0.0385505427072599	0.0192752713536299
34	0.975427845549628	0.0491443089007435	0.0245721544503718
35	0.96622920398868	0.0675415920226391	0.0337707960113196
36	0.95829826022815	0.0834034795436984	0.0417017397718492
37	0.973056716355037	0.0538865672899268	0.0269432836449634
38	0.965831633165075	0.0683367336698507	0.0341683668349253
39	0.95806493755597	0.0838701248880605	0.0419350624440302
40	0.943048396303493	0.113903207393013	0.0569516036965066
41	0.92821228052847	0.14357543894306	0.0717877194715299
42	0.922048641086709	0.155902717826582	0.077951358913291
43	0.909846556367035	0.18030688726593	0.0901534436329652
44	0.89593362426549	0.20813275146902	0.10406637573451
45	0.935768342364545	0.12846331527091	0.0642316576354552
46	0.938487306709479	0.123025386581043	0.0615126932905215
47	0.921431195922345	0.157137608155309	0.0785688040776545
48	0.901864562982252	0.196270874035497	0.0981354370177485
49	0.930499781861071	0.139000436277858	0.0695002181389289
50	0.912407379636588	0.175185240726825	0.0875926203634123
51	0.889776355102082	0.220447289795836	0.110223644897918
52	0.867557126460885	0.26488574707823	0.132442873539115
53	0.881192868709276	0.237614262581449	0.118807131290724
54	0.888775077047266	0.222449845905469	0.111224922952734
55	0.888316742061832	0.223366515876336	0.111683257938168
56	0.864567329374435	0.27086534125113	0.135432670625565
57	0.83514537724557	0.329709245508861	0.164854622754431
58	0.81628010119523	0.36743979760954	0.18371989880477
59	0.804582178227604	0.390835643544793	0.195417821772396
60	0.825754210371211	0.348491579257579	0.174245789628789
61	0.90217603940361	0.195647921192779	0.0978239605963897
62	0.879837768335076	0.240324463329848	0.120162231664924
63	0.934942991480029	0.130114017039942	0.0650570085199711
64	0.918071622766737	0.163856754466526	0.0819283772332629
65	0.899625281538448	0.200749436923105	0.100374718461552
66	0.90766582682951	0.184668346340978	0.0923341731704892
67	0.94523241648955	0.109535167020901	0.0547675835104505
68	0.93580144514216	0.12839710971568	0.06419855485784
69	0.920269129677919	0.159461740644163	0.0797308703220815
70	0.917686285651136	0.164627428697728	0.0823137143488642
71	0.898345695692974	0.203308608614051	0.101654304307026
72	0.883861878739305	0.232276242521391	0.116138121260695
73	0.870983650629035	0.258032698741929	0.129016349370965
74	0.85548987691908	0.28902024616184	0.14451012308092
75	0.84592981770068	0.30814036459864	0.15407018229932
76	0.835510038679416	0.328979922641168	0.164489961320584
77	0.848944049363714	0.302111901272572	0.151055950636286
78	0.825879072689692	0.348241854620617	0.174120927310308
79	0.800880804105544	0.398238391788913	0.199119195894456
80	0.767494675319724	0.465010649360552	0.232505324680276
81	0.729022019294455	0.54195596141109	0.270977980705545
82	0.756518583943459	0.486962832113083	0.243481416056541
83	0.722983555249995	0.55403288950001	0.277016444750005
84	0.723149654474596	0.553700691050807	0.276850345525404
85	0.704517637173358	0.590964725653284	0.295482362826642
86	0.66232344504366	0.675353109912679	0.33767655495634
87	0.622612767857022	0.754774464285957	0.377387232142978
88	0.575772481856687	0.848455036286627	0.424227518143313
89	0.543831293196993	0.912337413606014	0.456168706803007
90	0.799430588026306	0.401138823947388	0.200569411973694
91	0.784106269248114	0.431787461503773	0.215893730751886
92	0.760355755819587	0.479288488360827	0.239644244180413
93	0.723517181506599	0.552965636986802	0.276482818493401
94	0.68340258016531	0.633194839669379	0.31659741983469
95	0.651758556888809	0.696482886222382	0.348241443111191
96	0.638757998794601	0.722484002410797	0.361242001205399
97	0.606131612476705	0.78773677504659	0.393868387523295
98	0.557568338153297	0.884863323693407	0.442431661846703
99	0.546141898404705	0.90771620319059	0.453858101595295
100	0.542005217195921	0.915989565608157	0.457994782804079
101	0.589156656655473	0.821686686689053	0.410843343344526
102	0.539696387896134	0.920607224207732	0.460303612103866
103	0.493694296908206	0.987388593816413	0.506305703091794
104	0.522490610315274	0.955018779369452	0.477509389684726
105	0.475920335218087	0.951840670436173	0.524079664781913
106	0.57961942689562	0.84076114620876	0.42038057310438
107	0.574964569938556	0.850070860122889	0.425035430061444
108	0.571143197667222	0.857713604665556	0.428856802332778
109	0.602220825401792	0.795558349196415	0.397779174598208
110	0.735880882708502	0.528238234582997	0.264119117291498
111	0.700350320520395	0.59929935895921	0.299649679479605
112	0.720073975363048	0.559852049273904	0.279926024636952
113	0.680342021869937	0.639315956260127	0.319657978130063
114	0.66131628210417	0.677367435791661	0.338683717895831
115	0.688606967301726	0.622786065396548	0.311393032698274
116	0.673139683410071	0.653720633179858	0.326860316589929
117	0.664685210956554	0.670629578086892	0.335314789043446
118	0.609967491428809	0.780065017142381	0.390032508571191
119	0.557337072994412	0.885325854011175	0.442662927005588
120	0.522974420943696	0.954051158112607	0.477025579056304
121	0.512339007499745	0.97532198500051	0.487660992500255
122	0.463323516785533	0.926647033571067	0.536676483214467
123	0.429961798653906	0.859923597307812	0.570038201346094
124	0.385886986949905	0.771773973899811	0.614113013050095
125	0.379104470935952	0.758208941871903	0.620895529064048
126	0.321651181701053	0.643302363402105	0.678348818298947
127	0.3964060583517	0.7928121167034	0.6035939416483
128	0.412413450309795	0.82482690061959	0.587586549690205
129	0.461402356561669	0.922804713123337	0.538597643438331
130	0.412442243135632	0.824884486271263	0.587557756864368
131	0.352025904986528	0.704051809973056	0.647974095013472
132	0.451030791604216	0.902061583208433	0.548969208395784
133	0.390002289753082	0.780004579506165	0.609997710246918
134	0.32372844044136	0.64745688088272	0.67627155955864
135	0.300180748049237	0.600361496098475	0.699819251950763
136	0.375578172061749	0.751156344123498	0.624421827938251
137	0.326225222110987	0.652450444221974	0.673774777889013
138	0.307727132607384	0.615454265214768	0.692272867392616
139	0.421468594760815	0.84293718952163	0.578531405239185
140	0.359987822576812	0.719975645153625	0.640012177423188
141	0.338552031721901	0.677104063443802	0.661447968278099
142	0.313190689714745	0.62638137942949	0.686809310285255
143	0.765768724149192	0.468462551701617	0.234231275850809
144	0.661914588453643	0.676170823092714	0.338085411546357
145	0.724043356775591	0.551913286448817	0.275956643224409
146	0.643231210942311	0.713537578115378	0.356768789057689

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	9	0.0687022900763359	NOK
10% type I error level	14	0.106870229007634	NOK