Multiple Linear Regression - Estimated Regression Equation

y[t] = + 12.9137999388331 + 0.323663672507733x[t] + 0.934728575797638M1[t] -0.516961686524345M2[t] -1.87410454366720M3[t] -0.636699995630935M4[t] + 0.91160974204709M5[t] + 1.22044286151192M6[t] -0.898179717499406M7[t] -1.10405174269112M8[t] -1.92307692307692M9[t] -0.71720489788521M10[t] -1.87328251192189M11[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)	12.9137999388331	1.212086	10.6542	0	0
x	0.323663672507733	0.506173	0.6394	0.523523	0.261762
M1	0.934728575797638	1.192474	0.7839	0.434368	0.217184
M2	-0.516961686524345	1.191166	-0.434	0.664919	0.332459
M3	-1.87410454366720	1.191166	-1.5733	0.117762	0.058881
M4	-0.636699995630935	1.192474	-0.5339	0.594184	0.297092
M5	0.91160974204709	1.191166	0.7653	0.445298	0.222649
M6	1.22044286151192	1.192474	1.0235	0.307752	0.153876
M7	-0.898179717499406	1.213381	-0.7402	0.460326	0.230163
M8	-1.10405174269112	1.215254	-0.9085	0.365084	0.182542
M9	-1.92307692307692	1.212756	-1.5857	0.114926	0.057463
M10	-0.71720489788521	1.213381	-0.5911	0.555363	0.277681
M11	-1.87328251192189	1.215254	-1.5415	0.125323	0.062661

Multiple Linear Regression - Regression Statistics
Multiple R	0.342663940796646
R-squared	0.117418576322287
Adjusted R-squared	0.0463381932073034
F-TEST (value)	1.65191254150029
F-TEST (DF numerator)	12
F-TEST (DF denominator)	149
p-value	0.083263726308721
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.09193395483857
Sum Squared Residuals	1424.44828158147

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12	14.4958558596462	-2.49585585964622
2	11	13.0441655973242	-2.04416559732419
3	14	11.6870227401813	2.31297725981866
4	12	12.6007636157099	-0.600763615709873
5	21	14.4727370258956	6.52726297410438
6	12	14.7815701453605	-2.78157014536045
7	22	12.6629475663491	9.33705243365087
8	11	12.4570755411574	-1.4570755411574
9	10	11.6380503607716	-1.63805036077161
10	13	12.8439223859633	0.156077614036677
11	10	11.3641810994189	-1.36418109941890
12	8	13.5611272838485	-5.56112728384854
13	15	14.1721921871384	0.827807812861563
14	14	13.0441655973242	0.955834402675809
15	10	11.6870227401813	-1.68702274018133
16	14	12.6007636157099	1.39923638429013
17	14	14.1490733533879	-0.14907335338789
18	11	14.7815701453605	-3.78157014536046
19	10	12.3392838938414	-2.33928389384139
20	13	12.4570755411574	0.542924458842584
21	7	11.3143866882639	-4.31438668826388
22	14	12.8439223859633	1.15607761403668
23	12	11.6878447719266	0.312155228073354
24	14	13.5611272838485	0.438872716151467
25	11	14.1721921871384	-3.17219218713844
26	9	13.0441655973242	-4.04416559732419
27	11	11.3633590676736	-0.3633590676736
28	15	12.9244272882176	2.0755727117824
29	14	14.4727370258956	-0.472737025895624
30	13	14.4579064728527	-1.45790647285272
31	9	12.6629475663491	-3.66294756634912
32	15	12.1334118686497	2.86658813135032
33	10	11.6380503607716	-1.63805036077161
34	11	12.8439223859633	-1.84392238596332
35	13	11.3641810994189	1.63581890058109
36	8	13.2374636113408	-5.2374636113408
37	20	14.1721921871384	5.82780781286156
38	12	12.7205019248165	-0.720501924816458
39	10	11.6870227401813	-1.68702274018133
40	10	12.6007636157099	-2.60076361570987
41	9	14.1490733533879	-5.14907335338789
42	14	14.7815701453605	-0.781570145360455
43	8	12.3392838938414	-4.33928389384139
44	14	12.1334118686497	1.86658813135032
45	11	11.6380503607716	-0.63805036077161
46	13	12.8439223859633	0.156077614036678
47	9	11.6878447719266	-2.68784477192664
48	11	13.5611272838485	-2.56112728384853
49	15	14.4958558596462	0.504144140353831
50	11	12.7205019248165	-1.72050192481646
51	10	11.6870227401813	-1.68702274018133
52	14	12.6007636157099	1.39923638429013
53	18	14.1490733533879	3.85092664661211
54	14	14.7815701453605	-0.781570145360455
55	11	12.3392838938414	-1.33928389384139
56	12	12.4570755411574	-0.457075541157416
57	13	11.6380503607716	1.36194963922839
58	9	12.8439223859633	-3.84392238596332
59	10	11.3641810994189	-1.36418109941891
60	15	13.5611272838485	1.43887271615147
61	20	14.1721921871384	5.82780781286156
62	12	12.7205019248165	-0.720501924816458
63	12	11.6870227401813	0.312977259818668
64	14	12.9244272882176	1.07557271178240
65	13	14.4727370258956	-1.47273702589562
66	11	14.4579064728527	-3.45790647285272
67	17	12.6629475663491	4.33705243365087
68	12	12.1334118686497	-0.133411868649683
69	13	11.6380503607716	1.36194963922839
70	14	12.5202587134556	1.47974128654441
71	13	11.3641810994189	1.63581890058109
72	15	13.5611272838485	1.43887271615147
73	13	14.4958558596462	-1.49585585964617
74	10	12.7205019248165	-2.72050192481646
75	11	11.3633590676736	-0.3633590676736
76	19	12.9244272882176	6.0755727117824
77	13	14.4727370258956	-1.47273702589562
78	17	14.7815701453605	2.21842985463954
79	13	12.3392838938414	0.660716106158607
80	9	12.1334118686497	-3.13341186864968
81	11	11.3143866882639	-0.314386688263877
82	10	12.5202587134556	-2.52025871345559
83	9	11.6878447719266	-2.68784477192664
84	12	13.2374636113408	-1.2374636113408
85	12	14.4958558596462	-2.49585585964617
86	13	13.0441655973242	-0.0441655973241913
87	13	11.3633590676736	1.63664093232640
88	12	12.9244272882176	-0.924427288217599
89	15	14.4727370258956	0.527262974104376
90	22	14.7815701453605	7.21842985463954
91	13	12.6629475663491	0.337052433650874
92	15	12.4570755411574	2.54292445884258
93	13	11.6380503607716	1.36194963922839
94	15	12.8439223859633	2.15607761403668
95	10	11.6878447719266	-1.68784477192665
96	11	13.5611272838485	-2.56112728384853
97	16	14.4958558596462	1.50414414035383
98	11	13.0441655973242	-2.04416559732419
99	11	11.3633590676736	-0.3633590676736
100	10	12.6007636157099	-2.60076361570987
101	10	14.4727370258956	-4.47273702589563
102	16	14.4579064728527	1.54209352714728
103	12	12.6629475663491	-0.662947566349126
104	11	12.1334118686497	-1.13341186864968
105	16	11.6380503607716	4.36194963922839
106	19	12.5202587134556	6.47974128654441
107	11	11.6878447719266	-0.687844771926646
108	16	13.2374636113408	2.7625363886592
109	15	14.1721921871384	0.827807812861564
110	24	13.0441655973242	10.9558344026758
111	14	11.6870227401813	2.31297725981867
112	15	12.9244272882176	2.0755727117824
113	11	14.4727370258956	-3.47273702589562
114	15	14.4579064728527	0.542093527147277
115	12	12.6629475663491	-0.662947566349126
116	10	12.1334118686497	-2.13341186864968
117	14	11.6380503607716	2.36194963922839
118	13	12.8439223859633	0.156077614036678
119	9	11.6878447719266	-2.68784477192664
120	15	13.5611272838485	1.43887271615147
121	15	14.4958558596462	0.504144140353831
122	14	13.0441655973242	0.955834402675809
123	11	11.6870227401813	-0.687022740181332
124	8	12.9244272882176	-4.9244272882176
125	11	14.4727370258956	-3.47273702589562
126	11	14.7815701453605	-3.78157014536046
127	8	12.3392838938414	-4.33928389384139
128	10	12.4570755411574	-2.45707554115742
129	11	11.6380503607716	-0.63805036077161
130	13	12.8439223859633	0.156077614036678
131	11	11.3641810994189	-0.364181099418912
132	20	13.2374636113408	6.7625363886592
133	10	14.4958558596462	-4.49585585964617
134	15	12.7205019248165	2.27949807518354
135	12	11.3633590676736	0.636640932326403
136	14	12.9244272882176	1.07557271178240
137	23	14.1490733533879	8.85092664661211
138	14	14.4579064728527	-0.457906472852723
139	16	12.6629475663491	3.33705243365087
140	11	12.4570755411574	-1.45707554115742
141	12	11.3143866882639	0.685613311736124
142	10	12.8439223859633	-2.84392238596332
143	14	11.3641810994189	2.63581890058109
144	12	13.5611272838485	-1.56112728384853
145	12	14.1721921871384	-2.17219218713844
146	11	13.0441655973242	-2.04416559732419
147	12	11.6870227401813	0.312977259818668
148	13	12.6007636157099	0.399236384290135
149	11	14.1490733533879	-3.14907335338789
150	19	14.4579064728527	4.54209352714728
151	12	12.6629475663491	-0.662947566349126
152	17	12.4570755411574	4.54292445884258
153	9	11.3143866882639	-2.31438668826387
154	12	12.8439223859633	-0.843922385963322
155	19	11.6878447719266	7.31215522807335
156	18	13.5611272838485	4.43887271615147
157	15	14.4958558596462	0.504144140353831
158	14	13.0441655973242	0.955834402675809
159	11	11.6870227401813	-0.687022740181332
160	9	12.9244272882176	-3.9244272882176
161	18	14.4727370258956	3.52726297410438
162	16	14.7815701453605	1.21842985463954

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.337780831063268	0.675561662126535	0.662219168936732
17	0.62871856748692	0.74256286502616	0.37128143251308
18	0.501671424645815	0.99665715070837	0.498328575354185
19	0.752944753543612	0.494110492912775	0.247055246456388
20	0.672512519562935	0.654974960874131	0.327487480437065
21	0.603387153859492	0.793225692281015	0.396612846140508
22	0.507317869080162	0.985364261839677	0.492682130919838
23	0.439215174965781	0.878430349931563	0.560784825034219
24	0.515451878497094	0.969096243005812	0.484548121502906
25	0.436090667770313	0.872181335540626	0.563909332229687
26	0.435920502878543	0.871841005757086	0.564079497121457
27	0.401071275502698	0.802142551005397	0.598928724497302
28	0.339331006960693	0.678662013921385	0.660668993039307
29	0.395189622998765	0.790379245997529	0.604810377001235
30	0.407251498438798	0.814502996877597	0.592748501561202
31	0.626573265129218	0.746853469741564	0.373426734870782
32	0.64292360858431	0.71415278283138	0.35707639141569
33	0.584473513993787	0.831052972012425	0.415526486006213
34	0.544496424205012	0.911007151589976	0.455503575794988
35	0.506074297447569	0.987851405104863	0.493925702552431
36	0.49326477539186	0.98652955078372	0.50673522460814
37	0.698793966125103	0.602412067749794	0.301206033874897
38	0.652654435734238	0.694691128531525	0.347345564265762
39	0.610922794894886	0.778154410210229	0.389077205105114
40	0.600828646299587	0.798342707400826	0.399171353700413
41	0.716586435175849	0.566827129648302	0.283413564824151
42	0.674486142063232	0.651027715873535	0.325513857936768
43	0.710558424199965	0.578883151600071	0.289441575800035
44	0.677048432075357	0.645903135849287	0.322951567924643
45	0.63336346907416	0.73327306185168	0.36663653092584
46	0.578901861736057	0.842196276527886	0.421098138263943
47	0.576113968813167	0.847772062373665	0.423886031186833
48	0.542456327709479	0.915087344581042	0.457543672290521
49	0.488628772445794	0.977257544891588	0.511371227554206
50	0.444423572995858	0.888847145991715	0.555576427004142
51	0.404163395562237	0.808326791124474	0.595836604437763
52	0.362973954767578	0.725947909535156	0.637026045232422
53	0.390604287065507	0.781208574131015	0.609395712934493
54	0.349241291218775	0.69848258243755	0.650758708781225
55	0.3058962993593	0.6117925987186	0.6941037006407
56	0.269859473362723	0.539718946725446	0.730140526637277
57	0.255202718282265	0.51040543656453	0.744797281717735
58	0.27283509128384	0.54567018256768	0.72716490871616
59	0.235339798158879	0.470679596317758	0.764660201841121
60	0.243889276406892	0.487778552813784	0.756110723593108
61	0.355962970263177	0.711925940526354	0.644037029736823
62	0.317377692494738	0.634755384989477	0.682622307505262
63	0.274969806040954	0.549939612081908	0.725030193959046
64	0.236667811214553	0.473335622429105	0.763332188785448
65	0.217845020614632	0.435690041229264	0.782154979385368
66	0.214505168711306	0.429010337422612	0.785494831288694
67	0.247545835642865	0.495091671285729	0.752454164357135
68	0.209980974259345	0.419961948518689	0.790019025740655
69	0.189068272236464	0.378136544472927	0.810931727763536
70	0.175781322997055	0.35156264599411	0.824218677002945
71	0.158807938792301	0.317615877584602	0.841192061207699
72	0.151280769263382	0.302561538526764	0.848719230736618
73	0.139343871174369	0.278687742348738	0.860656128825631
74	0.132252763773357	0.264505527546713	0.867747236226643
75	0.108722955403645	0.217445910807289	0.891277044596355
76	0.180619337073986	0.361238674147973	0.819380662926014
77	0.160666066246838	0.321332132493676	0.839333933753162
78	0.159869274349017	0.319738548698033	0.840130725650983
79	0.133419300521172	0.266838601042344	0.866580699478828
80	0.133633642628767	0.267267285257535	0.866366357371233
81	0.113071117459237	0.226142234918474	0.886928882540763
82	0.105701182184106	0.211402364368211	0.894298817815894
83	0.102956524518073	0.205913049036145	0.897043475481927
84	0.093538745127504	0.187077490255008	0.906461254872496
85	0.0904650156483978	0.180930031296796	0.909534984351602
86	0.0757091102280865	0.151418220456173	0.924290889771914
87	0.0653086823089265	0.130617364617853	0.934691317691073
88	0.0555025489973315	0.111005097994663	0.944497451002668
89	0.0436330002530659	0.0872660005061317	0.956366999746934
90	0.130303434625050	0.260606869250101	0.86969656537495
91	0.107427291397107	0.214854582794213	0.892572708602893
92	0.101480580545939	0.202961161091878	0.898519419454061
93	0.0853912150184802	0.170782430036960	0.91460878498152
94	0.0755270412448336	0.151054082489667	0.924472958755166
95	0.0652115013261324	0.130423002652265	0.934788498673868
96	0.068089645214674	0.136179290429348	0.931910354785326
97	0.0586370017494233	0.117274003498847	0.941362998250577
98	0.058457359281055	0.11691471856211	0.941542640718945
99	0.0464228148208487	0.0928456296416974	0.953577185179151
100	0.0430237722189214	0.0860475444378427	0.956976227781079
101	0.0565345540050087	0.113069108010017	0.943465445994991
102	0.0468682982208290	0.0937365964416581	0.953131701779171
103	0.0364538707599023	0.0729077415198047	0.963546129240098
104	0.0286516086787033	0.0573032173574066	0.971348391321297
105	0.0380125622788413	0.0760251245576826	0.961987437721159
106	0.08179538238886	0.16359076477772	0.91820461761114
107	0.0676503915196008	0.135300783039202	0.9323496084804
108	0.0642001252248345	0.128400250449669	0.935799874775165
109	0.0517673382719902	0.103534676543980	0.94823266172801
110	0.352429390357195	0.70485878071439	0.647570609642805
111	0.328714954261349	0.657429908522699	0.671285045738651
112	0.328084144451477	0.656168288902954	0.671915855548523
113	0.352576844393672	0.705153688787344	0.647423155606328
114	0.304255974334159	0.608511948668317	0.695744025665841
115	0.258914421790944	0.517828843581889	0.741085578209056
116	0.242136398700441	0.484272797400881	0.75786360129956
117	0.237649890819895	0.47529978163979	0.762350109180105
118	0.199827520034223	0.399655040068446	0.800172479965777
119	0.225315825556131	0.450631651112262	0.77468417444387
120	0.194834720864086	0.389669441728171	0.805165279135914
121	0.172945297275848	0.345890594551695	0.827054702724152
122	0.139599721892354	0.279199443784708	0.860400278107646
123	0.109859561514941	0.219719123029881	0.89014043848506
124	0.125522865758427	0.251045731516855	0.874477134241573
125	0.172505656588698	0.345011313177396	0.827494343411302
126	0.216355271733591	0.432710543467183	0.783644728266409
127	0.274977310018662	0.549954620037324	0.725022689981338
128	0.27435851067944	0.54871702135888	0.72564148932056
129	0.223419497947999	0.446838995895998	0.776580502052001
130	0.185576964848226	0.371153929696451	0.814423035151774
131	0.224563687144847	0.449127374289694	0.775436312855153
132	0.287238779291542	0.574477558583083	0.712761220708458
133	0.290100153562408	0.580200307124816	0.709899846437592
134	0.263814863007056	0.527629726014112	0.736185136992944
135	0.211169720250086	0.422339440500172	0.788830279749914
136	0.175554912968105	0.351109825936209	0.824445087031895
137	0.52550700193366	0.94898599613268	0.47449299806634
138	0.474475385802294	0.948950771604588	0.525524614197706
139	0.459848412813028	0.919696825626056	0.540151587186972
140	0.533088769546092	0.933822460907817	0.466911230453909
141	0.475037316836013	0.950074633672026	0.524962683163987
142	0.392621215211266	0.785242430422533	0.607378784788734
143	0.360157140849169	0.720314281698339	0.639842859150831
144	0.445009733676195	0.89001946735239	0.554990266323805
145	0.352703310900012	0.705406621800025	0.647296689099988
146	0.266671988712201	0.533343977424401	0.7333280112878

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	0	0	OK
10% type I error level	7	0.0534351145038168	OK