Multiple Linear Regression - Estimated Regression Equation

Y(t)[t] = + 0.103460639622265 -0.119452797409169`X(t)`[t] + 1.52190634840442`Y(t-1)`[t] -0.619397555123749`Y(t-2)`[t] + 0.254793166385373`Y(t-3)`[t] -0.190018800639385`Y(t-4)`[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)	0.103460639622265	0.035236	2.9363	0.00406	0.00203
`X(t)`	-0.119452797409169	0.039381	-3.0333	0.00303	0.001515
`Y(t-1)`	1.52190634840442	0.094088	16.1753	0	0
`Y(t-2)`	-0.619397555123749	0.17246	-3.5915	0.000496	0.000248
`Y(t-3)`	0.254793166385373	0.171865	1.4825	0.141114	0.070557
`Y(t-4)`	-0.190018800639385	0.091765	-2.0707	0.04077	0.020385

Multiple Linear Regression - Regression Statistics
Multiple R	0.994995919607588
R-squared	0.99001688003575
Adjusted R-squared	0.989554698555923
F-TEST (value)	2142.05225273751
F-TEST (DF numerator)	5
F-TEST (DF denominator)	108
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.107112126367783
Sum Squared Residuals	1.23908482242302

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3.75	3.60581182393364	0.144188176066364
2	4.11	3.88521664832076	0.224783351679238
3	4.25	4.2897155557083	-0.0397155557082959
4	4.25	4.31434705248335	-0.0643470524833468
5	4.5	4.27375242251131	0.226247577488695
6	4.7	4.62149328467618	0.0785067153238155
7	4.75	4.74442253348662	0.00557746651338359
8	4.75	4.76033663147843	-0.0103366314784305
9	4.75	4.73282068683947	0.0171793131605282
10	4.75	4.70755658503086	0.0424434149691367
11	4.75	4.69805564499889	0.0519443550011059
12	4.75	4.69805564499889	0.0519443550011059
13	4.58	4.69805564499889	-0.118055644998894
14	4.5	4.43933156577014	0.0606684342298568
15	4.5	4.42287664226883	0.0771233577311728
16	4.49	4.42911360839321	0.0608863916067867
17	4.03	4.42581428770703	-0.395814287707035
18	3.75	3.74713284704339	0.00286715295660920
19	3.39	3.60337401318322	-0.213374013183224
20	3.25	3.11361437466141	0.136385625338595
21	3.25	3.13959716743555	0.110402832564452
22	3.25	3.18779254943317	0.0622074505668336
23	3.25	3.22052827436939	0.0294717256306073
24	3.25	3.24713090645891	0.00286909354109334
25	3.25	3.24713090645891	0.00286909354109334
26	3.25	3.24713090645891	0.00286909354109334
27	3.25	3.24713090645891	0.00286909354109334
28	3.25	3.24713090645891	0.00286909354109334
29	3.25	3.24713090645891	0.00286909354109334
30	3.25	3.24713090645891	0.00286909354109334
31	3.25	3.24713090645891	0.00286909354109334
32	2.85	3.24713090645891	-0.397130906458907
33	2.75	2.63836836709714	0.111631632902860
34	2.75	2.73393675430620	0.0160632456938030
35	2.55	2.69395924326442	-0.143959243264422
36	2.5	2.44010617720076	0.0598938227992451
37	2.5	2.50689225086922	-0.00689225086922279
38	2.1	2.48690349534834	-0.386903495348335
39	2	1.90340505779518	0.0965949422048237
40	2	2.00847438503620	-0.00847438503620295
41	2	1.96849687399443	0.0315031260055718
42	2	2.01902507761164	-0.0190250776116448
43	2	2.03802695767558	-0.0380269576755834
44	2	2.03802695767558	-0.0380269576755834
45	2	2.03802695767558	-0.0380269576755834
46	2	2.03802695767558	-0.0380269576755834
47	2	2.03802695767558	-0.0380269576755834
48	2	2.03802695767558	-0.0380269576755834
49	2	2.03802695767558	-0.0380269576755834
50	2	2.03802695767558	-0.0380269576755834
51	2	2.03802695767558	-0.0380269576755834
52	2	2.03802695767558	-0.0380269576755834
53	2	2.03802695767558	-0.0380269576755834
54	2	2.03802695767558	-0.0380269576755834
55	2	2.03802695767558	-0.0380269576755834
56	2	2.03802695767558	-0.0380269576755834
57	2	2.03802695767558	-0.0380269576755834
58	2	2.03802695767558	-0.0380269576755834
59	2	2.03802695767558	-0.0380269576755834
60	2	2.03802695767558	-0.0380269576755834
61	2	2.03802695767558	-0.0380269576755834
62	2	2.03802695767558	-0.0380269576755834
63	2	2.03802695767558	-0.0380269576755834
64	2	2.03802695767558	-0.0380269576755834
65	2	2.03802695767558	-0.0380269576755834
66	2	2.03802695767558	-0.0380269576755834
67	2	2.03802695767558	-0.0380269576755834
68	2.21	2.03802695767558	0.171973042324417
69	2.25	2.35762729084051	-0.107627290840511
70	2.25	2.28843005820070	-0.0384300582007008
71	2.45	2.31716072093668	0.132839279063321
72	2.5	2.59182976913871	-0.0918297691387076
73	2.5	2.5364448235086	-0.0364448235086029
74	2.64	2.55643357902949	0.0835664209705096
75	2.75	2.7442363659975	0.00576363400249928
76	2.93	2.81542946657269	0.114570533427308
77	3	3.05690992151583	-0.0569099215158281
78	3.17	3.05337642219474	0.116623577805260
79	3.25	3.29370337444386	-0.0437033744438632
80	3.39	3.29379043547707	0.0962095645229338
81	3.5	3.48731904208454	0.0126809579154582
82	3.5	3.55609333989384	-0.0560933398938371
83	3.65	3.50842914807303	0.141570851926973
84	3.75	3.73813971654657	0.0118602834534337
85	3.75	3.77651865004811	-0.0265186500481137
86	3.9	3.75279786949354	0.147202130506455
87	4	3.97806031829684	0.0219396817031628
88	4	4.01833943980478	-0.0183394398047782
89	4	3.99461865925021	0.0053813407497906
90	4	3.99159515579284	0.00840484420716092
91	4	3.9725932757289	0.0274067242710995
92	4	3.9725932757289	0.0274067242710995
93	4	3.9725932757289	0.0274067242710995
94	4	3.9725932757289	0.0274067242710995
95	4	3.9725932757289	0.0274067242710995
96	4	3.9725932757289	0.0274067242710995
97	4	3.9725932757289	0.0274067242710995
98	4	3.9725932757289	0.0274067242710995
99	4.18	3.9725932757289	0.207406724271099
100	4.25	4.2465364184417	0.00346358155830441
101	4.25	4.24157830290773	0.0084216970922696
102	3.97	4.12463044658926	-0.154630446589265
103	3.42	3.68212880656791	-0.262128806567915
104	2.75	3.00521031433538	-0.255210314335377
105	2.31	2.25485962963457	0.0551403703654259
106	2	1.91328622093661	0.0867137790633864
107	1.66	1.64782909605915	0.0121709039408454
108	1.31	1.33759778290884	-0.0275977829088377
109	1.09	1.02014812041123	0.0698518795887705
110	1	0.874394019682752	0.125605980317248
111	1	0.849118694436089	0.150881305563911
112	1	0.915316558016229	0.0846834419837712
113	1	0.93418930918221	0.0658106908177902
114	1	0.951291001239755	0.0487089987602455

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.596192813611031	0.807614372777937	0.403807186388969
10	0.464381220833799	0.928762441667597	0.535618779166201
11	0.321926475649817	0.643852951299633	0.678073524350183
12	0.209648200070897	0.419296400141794	0.790351799929103
13	0.36451494678391	0.72902989356782	0.63548505321609
14	0.264565225547494	0.529130451094987	0.735434774452506
15	0.204120514176133	0.408241028352265	0.795879485823867
16	0.145165991807863	0.290331983615725	0.854834008192137
17	0.95819901596784	0.0836019680643205	0.0418009840321602
18	0.935931983217985	0.12813603356403	0.064068016782015
19	0.991978973447512	0.0160420531049758	0.00802102655248791
20	0.996158211336097	0.00768357732780503	0.00384178866390252
21	0.994562591849704	0.0108748163005928	0.00543740815029642
22	0.991377023479837	0.0172459530403268	0.0086229765201634
23	0.98772391638902	0.0245521672219584	0.0122760836109792
24	0.98412875203906	0.0317424959218782	0.0158712479609391
25	0.978675302098263	0.0426493958034739	0.0213246979017370
26	0.970987602536733	0.058024794926535	0.0290123974632675
27	0.960567113881305	0.0788657722373898	0.0394328861186949
28	0.946852807000816	0.106294385998367	0.0531471929991837
29	0.929268873723969	0.141462252552063	0.0707311262760313
30	0.907274904140037	0.185450191719925	0.0927250958599626
31	0.880420028165533	0.239159943668934	0.119579971834467
32	0.99857183708365	0.00285632583270026	0.00142816291635013
33	0.99843309026715	0.00313381946569921	0.00156690973284961
34	0.997479692994839	0.00504061401032232	0.00252030700516116
35	0.998089801415298	0.0038203971694034	0.0019101985847017
36	0.997252488891891	0.00549502221621701	0.00274751110810851
37	0.99574943639707	0.00850112720586102	0.00425056360293051
38	0.999991164642495	1.76707150100390e-05	8.83535750501948e-06
39	0.999991767776044	1.64644479127333e-05	8.23222395636666e-06
40	0.999984556785835	3.0886428330954e-05	1.5443214165477e-05
41	0.999978396862047	4.3206275906652e-05	2.1603137953326e-05
42	0.99996197413485	7.60517302979685e-05	3.80258651489842e-05
43	0.999936105402834	0.0001277891943319	6.389459716595e-05
44	0.999894166828347	0.000211666343306229	0.000105833171653114
45	0.999827475445936	0.000345049108128598	0.000172524554064299
46	0.999723476814157	0.000553046371686031	0.000276523185843016
47	0.999564483265553	0.0008710334688942	0.0004355167344471
48	0.999326237297076	0.00134752540584816	0.00067376270292408
49	0.998976399512638	0.00204720097472384	0.00102360048736192
50	0.998473136517497	0.00305372696500498	0.00152686348250249
51	0.997764076903653	0.00447184619269329	0.00223592309634665
52	0.99678600683724	0.0064279863255185	0.00321399316275925
53	0.995465780372792	0.00906843925441578	0.00453421962720789
54	0.9937230093142	0.0125539813715996	0.00627699068579978
55	0.991475156942774	0.0170496861144513	0.00852484305722563
56	0.988645673663683	0.0227086526726335	0.0113543263363168
57	0.9851757691965	0.0296484616069999	0.0148242308035000
58	0.981040310986274	0.0379193780274518	0.0189596890137259
59	0.976268173991232	0.0474636520175363	0.0237318260087682
60	0.970967140870586	0.058065718258827	0.0290328591294135
61	0.96535312426867	0.0692937514626605	0.0346468757313303
62	0.959782887866388	0.080434224267224	0.040217112133612
63	0.954788059954476	0.090423880091048	0.045211940045524
64	0.951104617905578	0.0977907641888445	0.0488953820944222
65	0.94968238482308	0.100635230353841	0.0503176151769204
66	0.951633947319137	0.096732105361726	0.048366052680863
67	0.9580203831753	0.0839592336494	0.0419796168247
68	0.964102331464142	0.071795337071716	0.035897668535858
69	0.985340126498857	0.029319747002286	0.014659873501143
70	0.987689731443744	0.0246205371125127	0.0123102685562563
71	0.985755816374864	0.0284883672502718	0.0142441836251359
72	0.995558591792018	0.0088828164159642	0.0044414082079821
73	0.997245126016366	0.00550974796726816	0.00275487398363408
74	0.995815927402692	0.00836814519461604	0.00418407259730802
75	0.996438206774812	0.00712358645037524	0.00356179322518762
76	0.995322186829989	0.00935562634002227	0.00467781317001113
77	0.997781965214724	0.00443606957055196	0.00221803478527598
78	0.996981265342451	0.00603746931509735	0.00301873465754868
79	0.998479247981446	0.00304150403710772	0.00152075201855386
80	0.997771657784045	0.0044566844319108	0.0022283422159554
81	0.997315630523956	0.00536873895208884	0.00268436947604442
82	0.998292543761142	0.00341491247771547	0.00170745623885773
83	0.998495240049271	0.00300951990145713	0.00150475995072856
84	0.998568961840543	0.00286207631891415	0.00143103815945707
85	0.997981619380393	0.00403676123921382	0.00201838061960691
86	0.999090833751536	0.00181833249692860	0.000909166248464302
87	0.99891322568516	0.00217354862968281	0.00108677431484141
88	0.997999536062183	0.00400092787563344	0.00200046393781672
89	0.99627571511424	0.00744856977151825	0.00372428488575913
90	0.99422003029413	0.0115599394117393	0.00577996970586964
91	0.989934744812815	0.0201305103743696	0.0100652551871848
92	0.983013155563142	0.0339736888737169	0.0169868444368585
93	0.97226366545695	0.0554726690860994	0.0277363345430497
94	0.956280424012992	0.0874391519740157	0.0437195759870078
95	0.933681788161396	0.132636423677208	0.066318211838604
96	0.903681388181757	0.192637223636486	0.0963186118182428
97	0.867388779065267	0.265222441869466	0.132611220934733
98	0.831274455261593	0.337451089476814	0.168725544738407
99	0.940190171919675	0.11961965616065	0.059809828080325
100	0.970072781457326	0.0598544370853483	0.0299272185426741
101	0.940016119684102	0.119967760631797	0.0599838803158983
102	0.913624298899143	0.172751402201713	0.0863757011008567
103	0.912602533152274	0.174794933695453	0.0873974668477265
104	0.93577797909424	0.128444041811521	0.0642220209057607
105	0.982225092677804	0.0355498146443914	0.0177749073221957

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	41	0.422680412371134	NOK
5% type I error level	60	0.618556701030928	NOK
10% type I error level	74	0.762886597938144	NOK