Multiple Linear Regression - Estimated Regression Equation

y[t] = + 13.0264830148500 + 0.802532763952293x[t] -1.28760592963214M1[t] -0.344929698485872M2[t] + 0.940784587228415M3[t] -0.859034501060711M4[t] -0.344929698485872M5[t] -1.50189164391785M6[t] + 0.523271751073256M7[t] -0.414994959391952M8[t] + 1.00000000000000M9[t] -0.83096405876556M10[t] -0.261148805545798M11[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)	13.0264830148500	0.882569	14.7597	0	0
x	0.802532763952293	0.368565	2.1775	0.031021	0.01551
M1	-1.28760592963214	0.868289	-1.4829	0.140207	0.070103
M2	-0.344929698485872	0.867336	-0.3977	0.691429	0.345714
M3	0.940784587228415	0.867336	1.0847	0.279814	0.139907
M4	-0.859034501060711	0.868289	-0.9893	0.3241	0.16205
M5	-0.344929698485872	0.867336	-0.3977	0.691429	0.345714
M6	-1.50189164391785	0.868289	-1.7297	0.085752	0.042876
M7	0.523271751073256	0.883512	0.5923	0.554572	0.277286
M8	-0.414994959391952	0.884876	-0.469	0.639765	0.319882
M9	1.00000000000000	0.883057	1.1324	0.259273	0.129636
M10	-0.83096405876556	0.883512	-0.9405	0.348471	0.174236
M11	-0.261148805545798	0.884876	-0.2951	0.768309	0.384155

Multiple Linear Regression - Regression Statistics
Multiple R	0.376259829312185
R-squared	0.141571459154035
Adjusted R-squared	0.072436274656373
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	2.25136253158707
Sum Squared Residuals	755.226354046484

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.3439426131223	0.656057386877672
2	18	14.2866188442687	3.71338115573135
3	11	15.5723331299830	-4.57233312998296
4	12	12.9699812777415	-0.96998127774155
5	16	14.2866188442687	1.71338115573133
6	18	13.1296568988367	4.87034310116332
7	14	15.1548202938278	-1.15482029382780
8	14	14.2165535833626	-0.216553583362596
9	15	15.6315485427546	-0.631548542754551
10	15	13.800584483989	1.19941551601101
11	17	13.5678669732565	3.43213302674354
12	19	14.6315485427545	4.36845145724546
13	10	12.5414098491701	-2.54140984917012
14	16	14.2866188442687	1.71338115573132
15	18	15.5723331299830	2.42766687001704
16	14	12.9699812777416	1.03001872225845
17	14	13.4840860803164	0.515913919683613
18	17	13.1296568988367	3.87034310116330
19	14	14.3522875298755	-0.352287529875514
20	16	14.2165535833626	1.78344641663741
21	18	14.8290157788023	3.17098422119774
22	11	13.800584483989	-2.80058448398899
23	14	14.3703997372087	-0.370399737208750
24	12	14.6315485427545	-2.63154854275455
25	17	12.5414098491701	4.45859015082988
26	9	14.2866188442687	-5.28661884426868
27	16	14.7698003660307	1.23019963396933
28	14	13.7725140416938	0.227485958306159
29	15	14.2866188442687	0.713381155731324
30	11	12.3271241348844	-1.32712413488441
31	16	15.1548202938278	0.845179706172196
32	13	13.4140208194103	-0.414020819410305
33	17	15.6315485427545	1.36845145724545
34	15	13.800584483989	1.19941551601101
35	14	13.5678669732565	0.432133026743539
36	16	13.8290157788023	2.17098422119774
37	9	12.5414098491701	-3.54140984917012
38	15	13.4840860803164	1.51591391968361
39	17	15.5723331299830	1.42766687001704
40	13	12.9699812777416	0.0300187222584483
41	15	13.4840860803164	1.51591391968361
42	16	13.1296568988367	2.87034310116330
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	0.62960026279125
48	15	14.6315485427545	0.368451457245453
49	17	13.3439426131224	3.65605738687759
50	13	13.4840860803164	-0.484086080316386
51	16	15.5723331299830	0.427666870017036
52	14	12.9699812777416	1.03001872225845
53	11	13.4840860803164	-2.48408608031639
54	12	13.1296568988367	-1.12965689883670
55	12	14.3522875298755	-2.35228752987551
56	15	14.2165535833626	0.783446416637405
57	16	15.6315485427546	0.368451457245450
58	15	13.800584483989	1.19941551601101
59	12	13.5678669732565	-1.56786697325646
60	12	14.6315485427545	-2.63154854275455
61	8	12.5414098491701	-4.54140984917012
62	13	13.4840860803164	-0.484086080316386
63	11	15.5723331299830	-4.57233312998296
64	14	13.7725140416938	0.227485958306159
65	15	14.2866188442687	0.713381155731324
66	10	12.3271241348844	-2.32712413488441
67	11	15.1548202938278	-4.15482029382781
68	12	13.4140208194103	-1.41402081941031
69	15	15.6315485427546	-0.63154854275455
70	15	12.9980517200367	2.0019482799633
71	14	13.5678669732565	0.432133026743539
72	16	14.6315485427545	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	-0.129656898836697
79	15	14.3522875298755	0.647712470124486
80	13	13.4140208194103	-0.414020819410305
81	15	14.8290157788023	0.170984221197739
82	16	12.9980517200367	3.0019482799633
83	15	14.3703997372087	0.62960026279125
84	16	13.8290157788023	2.17098422119774
85	15	13.3439426131224	1.65605738687759
86	14	14.2866188442687	-0.286618844268675
87	15	14.7698003660307	0.230199633969326
88	14	13.7725140416938	0.227485958306159
89	13	14.2866188442687	-1.28661884426868
90	7	13.1296568988367	-6.1296568988367
91	17	15.1548202938278	1.84517970617220
92	13	14.2165535833626	-1.21655358336259
93	15	15.6315485427546	-0.63154854275455
94	14	13.800584483989	0.19941551601101
95	13	14.3703997372087	-1.37039973720875
96	16	14.6315485427545	1.36845145724545
97	12	13.3439426131224	-1.34394261312241
98	14	14.2866188442687	-0.286618844268675
99	17	14.7698003660307	2.23019963396933
100	15	12.9699812777416	2.03001872225845
101	17	14.2866188442687	2.71338115573133
102	12	12.3271241348844	-0.327124134884407
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	-4.28661884426868
111	15	15.5723331299830	-0.572333129982964
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	-0.370399737208750
120	14	14.6315485427545	-0.631548542754547
121	12	13.3439426131224	-1.34394261312241
122	14	14.2866188442687	-0.286618844268675
123	15	15.5723331299830	-0.572333129982964
124	15	13.7725140416938	1.22748595830616
125	15	14.2866188442687	0.713381155731324
126	13	13.1296568988367	-0.129656898836697
127	17	14.3522875298755	2.64771247012448
128	17	14.2165535833626	2.78344641663741
129	19	15.6315485427546	3.36845145724545
130	15	13.800584483989	1.19941551601101
131	13	13.5678669732565	-0.567866973256461
132	9	13.8290157788023	-4.82901577880226
133	15	13.3439426131224	1.65605738687759
134	15	13.4840860803164	1.51591391968361
135	15	14.7698003660307	0.230199633969326
136	16	13.7725140416938	2.22748595830616
137	11	13.4840860803164	-2.48408608031639
138	14	12.3271241348844	1.67287586511559
139	11	15.1548202938278	-4.15482029382781
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	14.6315485427545	-0.631548542754547
145	15	12.5414098491701	2.45859015082988
146	16	14.2866188442687	1.71338115573132
147	16	15.5723331299830	0.427666870017036
148	11	12.9699812777416	-1.96998127774155
149	12	13.4840860803164	-1.48408608031639
150	9	12.3271241348844	-3.32712413488441
151	16	15.1548202938278	0.845179706172196
152	13	14.2165535833626	-1.21655358336259
153	16	14.8290157788023	1.17098422119774
154	12	13.800584483989	-1.80058448398899
155	9	14.3703997372088	-5.37039973720875
156	13	14.6315485427545	-1.63154854275455
157	13	13.3439426131224	-0.343942613122411
158	14	14.2866188442687	-0.286618844268675
159	19	15.5723331299830	3.42766687001704
160	13	13.7725140416938	-0.772514041693841
161	12	14.2866188442687	-2.28661884426867
162	13	13.1296568988367	-0.129656898836697

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.882203877441682	0.235592245116636	0.117796122558318
17	0.805134592909796	0.389730814180408	0.194865407090204
18	0.724817162947947	0.550365674104107	0.275182837052053
19	0.672338442094652	0.655323115810695	0.327661557905348
20	0.60682474213205	0.7863505157359	0.39317525786795
21	0.687265188161831	0.625469623676337	0.312734811838169
22	0.729332827527833	0.541334344944334	0.270667172472167
23	0.725599070003954	0.548801859992092	0.274400929996046
24	0.893657450751135	0.212685098497729	0.106342549248865
25	0.943526663540305	0.11294667291939	0.056473336459695
26	0.994810763458627	0.0103784730827452	0.00518923654137259
27	0.991675447959283	0.0166491040814341	0.00832455204071703
28	0.987871374439767	0.0242572511204653	0.0121286255602327
29	0.98131283666808	0.0373743266638404	0.0186871633319202
30	0.993481809637261	0.013036380725478	0.006518190362739
31	0.99077511073127	0.0184497785374604	0.00922488926873018
32	0.986583188955517	0.0268336220889658	0.0134168110444829
33	0.98072472864637	0.0385505427072597	0.0192752713536298
34	0.975427845549628	0.0491443089007438	0.0245721544503719
35	0.96622920398868	0.0675415920226397	0.0337707960113199
36	0.95829826022815	0.0834034795436984	0.0417017397718492
37	0.973056716355036	0.053886567289928	0.026943283644964
38	0.965831633165075	0.0683367336698505	0.0341683668349253
39	0.95806493755597	0.0838701248880609	0.0419350624440305
40	0.943048396303493	0.113903207393014	0.056951603696507
41	0.928212280528469	0.143575438943061	0.0717877194715305
42	0.92204864108671	0.155902717826581	0.0779513589132906
43	0.909846556367034	0.180306887265932	0.0901534436329658
44	0.89593362426549	0.208132751469019	0.104066375734510
45	0.935768342364545	0.12846331527091	0.064231657635455
46	0.938487306709479	0.123025386581042	0.0615126932905211
47	0.921431195922346	0.157137608155309	0.0785688040776545
48	0.901864562982252	0.196270874035496	0.0981354370177479
49	0.93049978186107	0.139000436277858	0.0695002181389291
50	0.912407379636587	0.175185240726825	0.0875926203634126
51	0.889776355102082	0.220447289795836	0.110223644897918
52	0.867557126460885	0.264885747078231	0.132442873539115
53	0.881192868709276	0.237614262581448	0.118807131290724
54	0.888775077047267	0.222449845905466	0.111224922952733
55	0.888316742061832	0.223366515876336	0.111683257938168
56	0.864567329374435	0.270865341251129	0.135432670625565
57	0.83514537724557	0.329709245508859	0.164854622754429
58	0.81628010119523	0.367439797609539	0.183719898804769
59	0.804582178227603	0.390835643544793	0.195417821772397
60	0.825754210371209	0.348491579257582	0.174245789628791
61	0.90217603940361	0.195647921192778	0.097823960596389
62	0.879837768335077	0.240324463329846	0.120162231664923
63	0.93494299148003	0.130114017039941	0.0650570085199706
64	0.918071622766738	0.163856754466525	0.0819283772332624
65	0.899625281538449	0.200749436923102	0.100374718461551
66	0.907665826829513	0.184668346340975	0.0923341731704874
67	0.94523241648955	0.109535167020901	0.0547675835104507
68	0.93580144514216	0.128397109715679	0.0641985548578396
69	0.920269129677918	0.159461740644163	0.0797308703220816
70	0.917686285651136	0.164627428697728	0.0823137143488639
71	0.898345695692975	0.203308608614051	0.101654304307025
72	0.883861878739305	0.232276242521391	0.116138121260695
73	0.870983650629036	0.258032698741928	0.129016349370964
74	0.855489876919081	0.289020246161838	0.144510123080919
75	0.84592981770068	0.308140364598639	0.154070182299319
76	0.835510038679418	0.328979922641164	0.164489961320582
77	0.848944049363714	0.302111901272571	0.151055950636286
78	0.825879072689692	0.348241854620615	0.174120927310308
79	0.800880804105546	0.398238391788908	0.199119195894454
80	0.767494675319723	0.465010649360554	0.232505324680277
81	0.729022019294454	0.541955961411093	0.270977980705546
82	0.75651858394346	0.486962832113081	0.243481416056541
83	0.722983555249994	0.554032889500011	0.277016444750006
84	0.723149654474598	0.553700691050803	0.276850345525402
85	0.704517637173358	0.590964725653285	0.295482362826642
86	0.66232344504366	0.67535310991268	0.33767655495634
87	0.622612767857022	0.754774464285957	0.377387232142978
88	0.575772481856688	0.848455036286624	0.424227518143312
89	0.543831293196989	0.912337413606021	0.456168706803011
90	0.799430588026306	0.401138823947389	0.200569411973694
91	0.784106269248113	0.431787461503773	0.215893730751887
92	0.760355755819587	0.479288488360826	0.239644244180413
93	0.723517181506599	0.552965636986802	0.276482818493401
94	0.68340258016531	0.633194839669379	0.316597419834689
95	0.651758556888809	0.696482886222383	0.348241443111191
96	0.6387579987946	0.7224840024108	0.3612420012054
97	0.606131612476706	0.787736775046589	0.393868387523294
98	0.557568338153297	0.884863323693405	0.442431661846703
99	0.546141898404707	0.907716203190587	0.453858101595293
100	0.54200521719592	0.91598956560816	0.45799478280408
101	0.589156656655473	0.821686686689055	0.410843343344527
102	0.539696387896134	0.920607224207731	0.460303612103866
103	0.493694296908206	0.987388593816412	0.506305703091794
104	0.522490610315274	0.955018779369451	0.477509389684726
105	0.475920335218087	0.951840670436173	0.524079664781913
106	0.579619426895621	0.840761146208758	0.420380573104379
107	0.574964569938554	0.850070860122892	0.425035430061446
108	0.571143197667222	0.857713604665555	0.428856802332778
109	0.602220825401787	0.795558349196426	0.397779174598213
110	0.735880882708501	0.528238234582997	0.264119117291499
111	0.700350320520394	0.599299358959211	0.299649679479606
112	0.720073975363049	0.559852049273903	0.279926024636952
113	0.680342021869935	0.63931595626013	0.319657978130065
114	0.661316282104168	0.677367435791663	0.338683717895832
115	0.688606967301727	0.622786065396547	0.311393032698274
116	0.673139683410071	0.653720633179858	0.326860316589929
117	0.664685210956554	0.670629578086892	0.335314789043446
118	0.60996749142881	0.78006501714238	0.39003250857119
119	0.557337072994412	0.885325854011177	0.442662927005588
120	0.522974420943695	0.95405115811261	0.477025579056305
121	0.512339007499745	0.97532198500051	0.487660992500255
122	0.463323516785534	0.926647033571069	0.536676483214466
123	0.429961798653905	0.85992359730781	0.570038201346095
124	0.385886986949904	0.771773973899809	0.614113013050096
125	0.379104470935954	0.758208941871908	0.620895529064046
126	0.321651181701052	0.643302363402103	0.678348818298948
127	0.396406058351702	0.792812116703403	0.603593941648298
128	0.412413450309794	0.824826900619588	0.587586549690206
129	0.461402356561667	0.922804713123334	0.538597643438333
130	0.412442243135632	0.824884486271263	0.587557756864368
131	0.352025904986528	0.704051809973057	0.647974095013472
132	0.451030791604215	0.90206158320843	0.548969208395785
133	0.390002289753081	0.780004579506163	0.609997710246919
134	0.323728440441358	0.647456880882716	0.676271559558642
135	0.300180748049238	0.600361496098476	0.699819251950762
136	0.375578172061749	0.751156344123498	0.624421827938251
137	0.326225222110987	0.652450444221973	0.673774777889014
138	0.307727132607384	0.615454265214769	0.692272867392616
139	0.421468594760816	0.842937189521631	0.578531405239184
140	0.359987822576811	0.719975645153622	0.640012177423189
141	0.338552031721902	0.677104063443803	0.661447968278098
142	0.313190689714743	0.626381379429485	0.686809310285257
143	0.765768724149192	0.468462551701617	0.234231275850808
144	0.661914588453642	0.676170823092715	0.338085411546358
145	0.724043356775592	0.551913286448817	0.275956643224408
146	0.643231210942311	0.713537578115377	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