Multiple Linear Regression - Estimated Regression Equation

Y1[t] = -0.996170178492618 -0.0268429787707296X1[t] + 0.0790401730395211X2[t] + 0.323763854841615X3[t] + 0.474394463844188`X4 `[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)	-0.996170178492618	1.607037	-0.6199	0.536284	0.268142
X1	-0.0268429787707296	0.077845	-0.3448	0.730712	0.365356
X2	0.0790401730395211	0.025026	3.1584	0.001921	0.000961
X3	0.323763854841615	0.058811	5.5052	0	0
`X4 `	0.474394463844188	0.093995	5.047	1e-06	1e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.6876699174452
R-squared	0.472889915359088
Adjusted R-squared	0.458739309060003
F-TEST (value)	33.4183500949828
F-TEST (DF numerator)	4
F-TEST (DF denominator)	149
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.16086383895017
Sum Squared Residuals	695.730547041885

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	12.6206944053634	0.37930559463656
2	12	11.3089438973572	0.691056102642809
3	15	13.5037220022956	1.49627799770435
4	12	10.1692706710153	1.83072932898474
5	10	10.3783388215812	-0.378338821581222
6	12	10.3795482113631	1.62045178863692
7	15	16.0353952994652	-1.03539529946516
8	9	9.88188044071155	-0.881880440711552
9	12	12.3568843330811	-0.35688433308115
10	11	8.44767764013913	2.55232235986087
11	11	13.8768314727444	-2.87683147274445
12	11	10.4114496253699	0.588550374630133
13	15	13.1083461544808	1.89165384551922
14	7	11.3392031224843	-4.33920312248425
15	11	10.3021502272033	0.697849772796714
16	11	10.6636230442484	0.336376955751568
17	10	10.8603364481089	-0.860336448108933
18	14	14.4198388460064	-0.419838846006353
19	10	8.69389008521389	1.30610991478611
20	6	9.3954106036527	-3.3954106036527
21	11	10.880785653978	0.119214346022004
22	15	13.5963263118225	1.40367368817751
23	11	11.7613729143363	-0.761372914336336
24	12	9.17141550121048	2.82858449878953
25	14	12.9698124757031	1.03018752429694
26	15	15.0688553189623	-0.0688553189622511
27	9	13.9722873609329	-4.9722873609329
28	13	13.3575636038242	-0.357563603824196
29	13	12.3568843330811	0.64311566691885
30	16	11.2330346764701	4.76696532352993
31	13	8.25543052609663	4.74456947390337
32	12	12.7519317726717	-0.751931772671696
33	14	13.5157973755103	0.484202624489701
34	11	11.4148270491674	-0.414827049167445
35	9	10.8318512804585	-1.83185128045848
36	16	14.5078175193950	1.49218248060499
37	12	12.6711175421556	-0.671117542155571
38	10	8.386821319012	1.61317868098800
39	13	12.8309719457112	0.169028054288782
40	16	15.2715296966266	0.728470303373445
41	14	12.4564996598735	1.54350034012652
42	15	8.91759989345218	6.08240010654782
43	5	9.83535892604263	-4.83535892604263
44	8	10.2487436431526	-2.24874364315263
45	11	10.4408373315881	0.559162668411931
46	16	13.0352885122552	2.96471148774475
47	17	13.7633451582507	3.23665484174933
48	9	7.94941772406955	1.05058227593045
49	9	11.1305677710161	-2.13056777101615
50	13	13.9800439492235	-0.980043949223485
51	10	9.83805707909716	0.161942920902841
52	6	12.6831654376469	-6.68316543764692
53	12	12.7130134206863	-0.713013420686302
54	8	10.6796000395864	-2.67960003958636
55	14	12.4818538753715	1.51814612462846
56	12	12.3045337132053	-0.304533713205298
57	11	10.7605676957095	0.239432304290455
58	16	15.2476642444012	0.752335755598839
59	8	11.9865989635706	-3.98659896357061
60	15	14.3674882261305	0.632511773869499
61	7	10.0456364663905	-3.04563646639046
62	16	14.4286239207484	1.57137607925157
63	14	14.6599153346601	-0.659915334660067
64	16	13.5948375485498	2.40516245145018
65	9	10.5046711792605	-1.50467117926053
66	14	12.5086968541423	1.49130314585773
67	11	12.8652646615584	-1.86526466155842
68	13	9.22227735781366	3.77772264218634
69	15	12.5340510696403	2.46594893035967
70	5	5.01075348269169	-0.0107534826916893
71	15	12.7787747514424	2.22122524855757
72	13	12.7189743944901	0.281025605509896
73	11	12.3609178238013	-1.36091782380129
74	11	14.5704694550089	-3.57046945500892
75	12	11.3154910958659	0.684508904134079
76	12	13.2382422634104	-1.23824226341036
77	12	11.4886243417050	0.511375658295036
78	12	12.6130912426799	-0.613091242679853
79	14	11.6013925628969	2.39860743710305
80	6	9.45015252536896	-3.45015252536896
81	7	6.53342271119727	0.466577288802734
82	14	11.8493790654483	2.15062093455169
83	14	13.8796830514060	0.120316948593959
84	10	11.4404606381563	-1.44046063815631
85	13	9.54858594010274	3.45141405989726
86	12	11.0513741723696	0.948625827630432
87	9	9.36229979986405	-0.362299799864049
88	12	12.7831150933767	-0.783115093376685
89	16	13.9646841982494	2.03531580175064
90	10	10.6094983668960	-0.609498366895977
91	14	13.1440232427271	0.855976757272909
92	10	13.5081942128268	-3.50819421282677
93	16	15.0597633930061	0.940236606993947
94	15	13.6112257859754	1.38877421402457
95	12	11.4911690691524	0.508830930847565
96	10	9.22823833161746	0.77176166838254
97	8	8.56878867432662	-0.568788674326625
98	8	9.35171911063518	-1.35171911063518
99	11	13.8066038521703	-2.80660385217032
100	13	12.2026840521152	0.797315947884813
101	16	14.9744553949486	1.02554460505139
102	14	13.5405559036547	0.459444096345263
103	11	10.4703784634133	0.529621536586671
104	4	7.3558828231419	-3.3558828231419
105	14	13.0634943064149	0.936505693585098
106	9	10.9648842622536	-1.96488426225358
107	14	14.0781705127431	-0.0781705127431459
108	8	11.8268764286118	-3.82687642861184
109	8	13.0050292871282	-5.00502928712819
110	11	12.4475611595243	-1.44756115952434
111	12	13.2874619311338	-1.28746193113381
112	11	10.4333875945116	0.566612405488402
113	14	13.5618801703682	0.438119829631772
114	15	13.7915509524103	1.20844904758968
115	16	12.4642562481641	3.53574375183593
116	16	13.8571588575594	2.14284114244061
117	14	13.4725386815906	0.527461318409354
118	14	11.5778124048755	2.42218759512451
119	12	12.1312470417592	-0.131247041759196
120	14	13.7676639431747	0.232336056825257
121	8	10.5304581938565	-2.53045819385646
122	13	13.2607723779701	-0.260772377970143
123	16	13.7350134162073	2.26498658379273
124	12	11.3475769551387	0.652423044861346
125	16	14.6776879444848	1.32231205551522
126	12	13.0488526487426	-1.04885264874258
127	11	11.3541241536474	-0.354124153647380
128	4	5.60295304595373	-1.60295304595373
129	16	14.3093300580579	1.69066994194209
130	15	12.2893273878382	2.71067261216176
131	10	12.2847292294234	-2.28472922942336
132	13	13.4944766507324	-0.494476650732376
133	15	13.0889744697967	1.91102553020329
134	12	11.5029591481632	0.497040851836835
135	14	13.7350134162073	0.264986583792729
136	7	12.8232153574206	-5.82321535742063
137	19	14.2616050743203	4.73839492567975
138	12	13.2009720210178	-1.20097202101782
139	12	13.0594333379714	-1.05943333797145
140	13	13.4917784976778	-0.491778497677845
141	15	14.8864767215599	0.113523278440050
142	8	7.8736403717793	0.126359628220702
143	12	11.774525808736	0.225474191264012
144	10	9.8319426796863	0.168057320313702
145	8	11.1793487189286	-3.17934871892861
146	10	14.7358461125574	-4.73584611255738
147	15	13.7948137731596	1.20518622684041
148	16	13.1605649057598	2.83943509424024
149	13	12.0805386107631	0.919461389236928
150	16	15.1326891666347	0.867310833365288
151	9	11.4759627437854	-2.47596274378538
152	14	12.8966014078705	1.10339859212953
153	14	12.8308185201042	1.16918147989584
154	12	12.8888448195799	-0.888844819579876

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.122295528643141	0.244591057286282	0.877704471356859
9	0.0480362566872007	0.0960725133744013	0.9519637433128
10	0.0397219524321037	0.0794439048642075	0.960278047567896
11	0.0410006855100272	0.0820013710200545	0.958999314489973
12	0.0182749768316880	0.0365499536633759	0.981725023168312
13	0.0518876561373771	0.103775312274754	0.948112343862623
14	0.350265460647852	0.700530921295705	0.649734539352148
15	0.262635888502977	0.525271777005953	0.737364111497023
16	0.211599397603859	0.423198795207719	0.78840060239614
17	0.159451252941621	0.318902505883242	0.840548747058379
18	0.111887894198079	0.223775788396159	0.88811210580192
19	0.0760020904624192	0.152004180924838	0.92399790953758
20	0.133114101885191	0.266228203770382	0.866885898114809
21	0.106130865003053	0.212261730006106	0.893869134996947
22	0.103622766471158	0.207245532942315	0.896377233528842
23	0.0736758489767836	0.147351697953567	0.926324151023216
24	0.0941172663080095	0.188234532616019	0.90588273369199
25	0.0824674982851736	0.164934996570347	0.917532501714826
26	0.0601833469515753	0.120366693903151	0.939816653048425
27	0.202952211524517	0.405904423049033	0.797047788475483
28	0.158389011064893	0.316778022129786	0.841610988935107
29	0.151701962357905	0.303403924715811	0.848298037642095
30	0.278195983767821	0.556391967535642	0.721804016232179
31	0.398535105750248	0.797070211500495	0.601464894249752
32	0.342933830852711	0.685867661705422	0.657066169147289
33	0.304704332912259	0.609408665824519	0.695295667087741
34	0.286798207921088	0.573596415842175	0.713201792078912
35	0.287432631573007	0.574865263146013	0.712567368426993
36	0.275241456258855	0.55048291251771	0.724758543741145
37	0.254429080914762	0.508858161829525	0.745570919085238
38	0.219460618096459	0.438921236192918	0.780539381903541
39	0.180977130327486	0.361954260654973	0.819022869672514
40	0.153109892553383	0.306219785106767	0.846890107446617
41	0.1326557916651	0.2653115833302	0.8673442083349
42	0.292963712875834	0.585927425751668	0.707036287124166
43	0.5817129369753	0.836574126049399	0.418287063024699
44	0.607652639865722	0.784694720268555	0.392347360134277
45	0.561614015547539	0.876771968904922	0.438385984452461
46	0.59866072181978	0.80267855636044	0.40133927818022
47	0.638378490082785	0.72324301983443	0.361621509917215
48	0.612648012662566	0.774703974674868	0.387351987337434
49	0.588247236376275	0.823505527247451	0.411752763623725
50	0.557381650314967	0.885236699370066	0.442618349685033
51	0.514487082754772	0.971025834490456	0.485512917245228
52	0.910659095783542	0.178681808432916	0.089340904216458
53	0.89381268654461	0.212374626910780	0.106187313455390
54	0.915186564420892	0.169626871158215	0.0848134355791076
55	0.905114543143451	0.189770913713099	0.0948854568565493
56	0.884196155100995	0.231607689798011	0.115803844899005
57	0.861807858614069	0.276384282771863	0.138192141385931
58	0.836192466996715	0.327615066006569	0.163807533003285
59	0.899065337980423	0.201869324039153	0.100934662019577
60	0.877749944340806	0.244500111318388	0.122250055659194
61	0.902236779760657	0.195526440478686	0.0977632202393432
62	0.8892069763304	0.221586047339202	0.110793023669601
63	0.869328653228496	0.261342693543009	0.130671346771504
64	0.877216306091028	0.245567387817944	0.122783693908972
65	0.88033124929142	0.239337501417159	0.119668750708580
66	0.866353436604929	0.267293126790142	0.133646563395071
67	0.861627761946789	0.276744476106422	0.138372238053211
68	0.912061630616419	0.175876738767162	0.0879383693835812
69	0.916856386836403	0.166287226327194	0.083143613163597
70	0.899848763080267	0.200302473839466	0.100151236919733
71	0.900684849228096	0.198630301543808	0.0993151507719041
72	0.878698553476471	0.242602893047057	0.121301446523529
73	0.865023676089467	0.269952647821066	0.134976323910533
74	0.909026652653155	0.18194669469369	0.0909733473468451
75	0.891686659323597	0.216626681352806	0.108313340676403
76	0.877250342467122	0.245499315065756	0.122749657532878
77	0.854780767187685	0.290438465624630	0.145219232812315
78	0.828933413710888	0.342133172578223	0.171066586289112
79	0.839268951348324	0.321462097303352	0.160731048651676
80	0.880387314475978	0.239225371048044	0.119612685524022
81	0.859770295763191	0.280459408473617	0.140229704236809
82	0.859778731714419	0.280442536571162	0.140221268285581
83	0.831603609746586	0.336792780506829	0.168396390253414
84	0.813624985259714	0.372750029480571	0.186375014740286
85	0.878717506008067	0.242564987983866	0.121282493991933
86	0.858707535497189	0.282584929005623	0.141292464502811
87	0.832994859632823	0.334010280734354	0.167005140367177
88	0.805480812887628	0.389038374224744	0.194519187112372
89	0.799626727596245	0.400746544807509	0.200373272403755
90	0.766670029623622	0.466659940752756	0.233329970376378
91	0.736710419889539	0.526579160220922	0.263289580110461
92	0.804316818760653	0.391366362478694	0.195683181239347
93	0.77383781355849	0.45232437288302	0.22616218644151
94	0.748934940960345	0.502130118079311	0.251065059039655
95	0.713159852468703	0.573680295062594	0.286840147531297
96	0.684206401815491	0.631587196369018	0.315793598184509
97	0.644461422331675	0.71107715533665	0.355538577668325
98	0.612525957742574	0.774948084514853	0.387474042257426
99	0.656905999815574	0.686188000368853	0.343094000184426
100	0.620471175795513	0.759057648408973	0.379528824204486
101	0.579453453522351	0.841093092955297	0.420546546477649
102	0.57028877593993	0.85942244812014	0.42971122406007
103	0.559617340682954	0.880765318634093	0.440382659317046
104	0.590525754063268	0.818948491873465	0.409474245936732
105	0.550212161228172	0.899575677543656	0.449787838771828
106	0.573334705732857	0.853330588534285	0.426665294267143
107	0.527453180966574	0.945093638066853	0.472546819033426
108	0.654462849267741	0.691074301464517	0.345537150732259
109	0.785880208043771	0.428239583912457	0.214119791956229
110	0.780924543041382	0.438150913917236	0.219075456958618
111	0.760857225765021	0.478285548469958	0.239142774234979
112	0.720792699861737	0.558414600276527	0.279207300138263
113	0.673597197000813	0.652805605998375	0.326402802999187
114	0.631283310641212	0.737433378717575	0.368716689358788
115	0.652830080565779	0.694339838868442	0.347169919434221
116	0.656938895396043	0.686122209207913	0.343061104603957
117	0.604288961811493	0.791422076377014	0.395711038188507
118	0.621730696997076	0.756538606005848	0.378269303002924
119	0.564958658661469	0.870082682677063	0.435041341338531
120	0.515103770791667	0.969792458416666	0.484896229208333
121	0.559339727688492	0.881320544623016	0.440660272311508
122	0.507994604861184	0.984010790277633	0.492005395138816
123	0.507815987971629	0.984368024056742	0.492184012028371
124	0.502394350368667	0.995211299262667	0.497605649631333
125	0.451342524516146	0.902685049032291	0.548657475483854
126	0.400905716902107	0.801811433804214	0.599094283097893
127	0.381318569120824	0.762637138241648	0.618681430879176
128	0.327962614477013	0.655925228954025	0.672037385522987
129	0.276812664913321	0.553625329826642	0.723187335086679
130	0.325668640441461	0.651337280882923	0.674331359558539
131	0.324866010870884	0.649732021741768	0.675133989129116
132	0.266426151880435	0.532852303760869	0.733573848119565
133	0.241485190543775	0.48297038108755	0.758514809456225
134	0.200894692104940	0.401789384209881	0.79910530789506
135	0.151682338169898	0.303364676339797	0.848317661830101
136	0.304318496616007	0.608636993232013	0.695681503383993
137	0.618123740907624	0.763752518184752	0.381876259092376
138	0.555618026657775	0.88876394668445	0.444381973342225
139	0.622928716664113	0.754142566671774	0.377071283335887
140	0.590192064155411	0.819615871689179	0.409807935844589
141	0.555701325198505	0.88859734960299	0.444298674801495
142	0.512178975484287	0.975642049031426	0.487821024515713
143	0.394752986446904	0.789505972893807	0.605247013553096
144	0.461618124716159	0.923236249432319	0.538381875283841
145	0.388749714177449	0.777499428354898	0.611250285822551
146	0.758901524687866	0.482196950624269	0.241098475312134

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	1	0.00719424460431655	OK
10% type I error level	4	0.0287769784172662	OK