Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 0.685919050525686 + 0.845278920723775X[t] + 0.788576291718117`Y-1`[t] -0.607030562122719`Y-2`[t] -0.244013538273027`Y-3`[t] + 0.345411574379241`Y-4`[t] + 0.0826560113300043M1[t] -0.0160550741627145M2[t] + 0.0737205235477154M3[t] + 0.0404901747252967M4[t] + 0.0548013033823734M5[t] + 0.0782958665809638M6[t] -0.00171463003041461M7[t] + 0.0275101232145196M8[t] + 0.0666278757530691M9[t] -0.0270275012858383M10[t] + 0.0108858432721366M11[t] -0.0108698053993793t + 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)	0.685919050525686	0.112217	6.1124	0	0
X	0.845278920723775	0.124268	6.802	0	0
`Y-1`	0.788576291718117	0.162467	4.8538	2.1e-05	1e-05
`Y-2`	-0.607030562122719	0.220893	-2.7481	0.009119	0.004559
`Y-3`	-0.244013538273027	0.232627	-1.0489	0.300828	0.150414
`Y-4`	0.345411574379241	0.128304	2.6921	0.0105	0.00525
M1	0.0826560113300043	0.066421	1.2444	0.220961	0.11048
M2	-0.0160550741627145	0.066433	-0.2417	0.810334	0.405167
M3	0.0737205235477154	0.065686	1.1223	0.268768	0.134384
M4	0.0404901747252967	0.068564	0.5905	0.558319	0.27916
M5	0.0548013033823734	0.070923	0.7727	0.444484	0.222242
M6	0.0782958665809638	0.065971	1.1868	0.242665	0.121332
M7	-0.00171463003041461	0.067359	-0.0255	0.979825	0.489913
M8	0.0275101232145196	0.067721	0.4062	0.686855	0.343428
M9	0.0666278757530691	0.071731	0.9289	0.358824	0.179412
M10	-0.0270275012858383	0.069232	-0.3904	0.698429	0.349214
M11	0.0108858432721366	0.069151	0.1574	0.875747	0.437874
t	-0.0108698053993793	0.001735	-6.2634	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.99746800308064
R-squared	0.99494241716968
Adjusted R-squared	0.992679814324536
F-TEST (value)	439.733565837805
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.095774680561324
Sum Squared Residuals	0.348565998591699

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2.08	2.1440968620871	-0.0640968620871015
2	2.06	2.10805944765967	-0.0480594476596719
3	2.06	2.15583510731601	-0.0958351073160126
4	2.08	2.10273869521331	-0.0227386952133087
5	2.07	2.13719416230221	-0.0671941623022063
6	2.06	2.12288431445420	-0.0628843144541967
7	2.07	2.02530828438202	0.0446917156179751
8	2.06	2.06696766763630	-0.00696766763630282
9	2.09	2.08024556587600	0.00975443412399725
10	2.07	1.99955372668396	0.070446273316036
11	2.09	1.99850907427104	0.0914909257289616
12	2.28	2.2052107709653	0.0747892290346999
13	2.33	2.42992847907675	-0.0999284790767505
14	2.35	2.23265209371420	0.117347906285803
15	2.52	2.46884327315013	0.0511567268498732
16	2.63	2.60008799949636	0.0299120005036413
17	2.58	2.59946782723569	-0.0194678272356881
18	2.7	2.68263606877761	0.0173639312223915
19	2.81	2.7486149283136	0.0613850716864012
20	2.97	3.04238528106973	-0.0723852810697316
21	3.04	3.08347986973858	-0.0434798697385766
22	3.28	3.16295776767734	0.117042232322657
23	3.33	3.33572058455773	-0.00572058455772807
24	3.5	3.45721104996518	0.0427889500348235
25	3.56	3.59831925840277	-0.0383192584027656
26	3.57	3.50355585039026	0.0664441496097411
27	3.69	3.74103357928462	-0.0510335792846186
28	3.82	3.82957142979586	-0.00957142979585707
29	3.79	3.88096856260221	-0.0909685626022074
30	3.96	3.97651427990589	-0.0165142799058946
31	4.06	4.04763049330091	0.0123695066990860
32	4.05	4.09387178557491	-0.04387178557491
33	4.03	4.00168626484684	0.0283137351531647
34	3.94	3.92177847601258	0.0182215239874179
35	4.02	3.92697205297966	0.0930279470203444
36	3.88	4.0243614132583	-0.144361413258301
37	4.02	3.95223748033556	0.0677625196644388
38	4.03	3.98743342422521	0.0425665757747948
39	4.09	4.05103552206482	0.0389644779351797
40	3.99	3.96566012395356	0.0243398760464363
41	4.01	3.89973946934245	0.110260530657550
42	4.01	3.97765211263571	0.0323478873642938
43	4.19	4.1310769778535	0.0589230221465051
44	4.3	4.25195423000493	0.0480457699950725
45	4.27	4.26458829953858	0.0054117004614147
46	3.82	4.02571002962611	-0.205710029626111
47	3.15	3.32879828819158	-0.178798288191578
48	2.49	2.46321676581122	0.026783234188778
49	1.81	1.67541792009782	0.134582079902179
50	1.26	1.43829918401067	-0.178299184010667
51	1.06	1.00325251818442	0.0567474818155784
52	0.84	0.861941751540912	-0.0219417515409118
53	0.78	0.712629978517448	0.067370021482552
54	0.7	0.670313224226594	0.0296867757734061
55	0.36	0.537369316149968	-0.177369316149968
56	0.35	0.274821035714128	0.075178964285872

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.0197401558315580	0.0394803116631159	0.980259844168442
22	0.0156949090654281	0.0313898181308562	0.984305090934572
23	0.00380451728471922	0.00760903456943843	0.99619548271528
24	0.00101238722447987	0.00202477444895974	0.99898761277552
25	0.000280083704313999	0.000560167408627998	0.999719916295686
26	0.000162992130887081	0.000325984261774162	0.999837007869113
27	0.000104324205607190	0.000208648411214380	0.999895675794393
28	2.98189529391630e-05	5.96379058783261e-05	0.99997018104706
29	2.54620718564248e-05	5.09241437128496e-05	0.999974537928144
30	8.13562944900058e-06	1.62712588980012e-05	0.999991864370551
31	3.45168331209004e-06	6.90336662418008e-06	0.999996548316688
32	8.55482100914298e-07	1.71096420182860e-06	0.999999144517899
33	1.10014839048648e-06	2.20029678097297e-06	0.99999889985161
34	4.81055231117813e-06	9.62110462235626e-06	0.99999518944769
35	0.000124737582380854	0.000249475164761708	0.99987526241762

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	13	0.866666666666667	NOK
5% type I error level	15	1	NOK
10% type I error level	15	1	NOK