Multiple Linear Regression - Estimated Regression Equation

(1-B)lnYt[t] = + 0.00298687237561425 + 0.279841978072988`(1-B)lnY_[t-1]`[t] + 0.0924602034106877`(1-B)lnY_[t-2]`[t] -0.0999401043206112`(1-B)lnY_[t-3]`[t] -0.133172004343059`(1-B)lnY_[t-4]`[t] -0.131646989364628`(1-B)lnY_[t-5]`[t] + 0.630660827401185`(1-B)lnX_[t-1]`[t] -0.338975843529546`(1-B)lnX_[t-2]`[t] + 0.510544531512295`(1-B)lnX_[t-3]`[t] -0.405092174192946`(1-B)lnX_[t-4]`[t] + 0.148230264174965`(1-B)lnX_[t-5]`[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)	0.00298687237561425	0.005339	0.5594	0.577382	0.288691
`(1-B)lnY_[t-1]`	0.279841978072988	0.111326	2.5137	0.013855	0.006928
`(1-B)lnY_[t-2]`	0.0924602034106877	0.127783	0.7236	0.47134	0.23567
`(1-B)lnY_[t-3]`	-0.0999401043206112	0.125216	-0.7981	0.427039	0.21352
`(1-B)lnY_[t-4]`	-0.133172004343059	0.121284	-1.098	0.275335	0.137667
`(1-B)lnY_[t-5]`	-0.131646989364628	0.125205	-1.0515	0.296066	0.148033
`(1-B)lnX_[t-1]`	0.630660827401185	0.274683	2.296	0.024169	0.012085
`(1-B)lnX_[t-2]`	-0.338975843529546	0.270783	-1.2518	0.214104	0.107052
`(1-B)lnX_[t-3]`	0.510544531512295	0.264283	1.9318	0.056755	0.028377
`(1-B)lnX_[t-4]`	-0.405092174192946	0.268436	-1.5091	0.13503	0.067515
`(1-B)lnX_[t-5]`	0.148230264174965	0.243634	0.6084	0.544554	0.272277

Multiple Linear Regression - Regression Statistics
Multiple R	0.540465013479973
R-squared	0.292102430795908
Adjusted R-squared	0.207828910652563
F-TEST (value)	3.46612352609762
F-TEST (DF numerator)	10
F-TEST (DF denominator)	84
p-value	0.000752185537719718
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0487324103769968
Sum Squared Residuals	0.19948721697677

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	-0.03086	-0.00295004353653766	-0.0279099564634623
2	0.04033	0.00275482761272255	0.0375751723872775
3	-0.02352	-0.00300798064250723	-0.0205120193574928
4	0.00573	-0.00222745061184229	0.0079574506118423
5	0.01805	-0.00196315971509568	0.0200131597150957
6	-0.01887	0.0190922575860881	-0.0379622575860881
7	0.04363	-0.0082158294957098	0.0518458294957098
8	0.02875	0.0307230893782364	-0.00197308937823643
9	-0.00393	0.00933831196456645	-0.0132683119645664
10	0.0528	0.00215728647027257	0.0506427135297274
11	-0.00351	0.0281395364335619	-0.0316495364335619
12	0.05407	-0.00146561208189627	0.0555356120818963
13	-0.01299	0.0330896671455471	-0.0460796671455471
14	0.00747	0.00677608274515331	0.000693917254846692
15	-0.03288	0.0082671282298679	-0.0411471282298679
16	-0.05013	-0.00992726424360557	-0.0402027357563944
17	0.03715	-0.0166292345759382	0.0537792345759382
18	0.00205	-0.00605956827330505	0.00810956827330505
19	0.02912	0.0341193585230271	-0.00499935852302714
20	-0.00832	0.0107708211865912	-0.0190908211865912
21	0.02908	0.0131639586826495	0.0159160413173505
22	-0.00942	0.00580963934823189	-0.0152296393482319
23	0.04381	0.00423015618474289	0.0395798438152571
24	0.00603	0.0115073360573358	-0.00547733605733578
25	0.02253	0.0153291006820232	0.00720089931797678
26	0.05789	0.0132086697793045	0.0446813302206955
27	-0.03783	0.0181211803959200	-0.05595118039592
28	-0.03176	0.00891838517239862	-0.0406783851723986
29	-0.00572	-0.0350393410837487	0.0293193410837487
30	0.0104	-0.00488487506469647	0.0152848750646965
31	0.03662	0.00420091256460438	0.0324190874353956
32	0.03771	0.0214251066999267	0.0162848933000733
33	0.05981	0.0387191686200905	0.0210908313799095
34	-0.03204	0.00774959784482731	-0.0397895978448273
35	0.02837	0.007819294380573	0.020550705619427
36	0.05003	-0.00797781582787613	0.0580078158278761
37	0.0498	0.0334480674746007	0.0163519325253993
38	-0.02299	0.0280668608970190	-0.051056860897019
39	0.0403	0.00577216462242457	0.0345278353775754
40	0.03176	0.00131532384691163	0.0304446761530884
41	-0.00135	0.0378674526300908	-0.0392174526300908
42	-0.02473	0.0165019872321261	-0.0412319872321261
43	-0.00171	-0.0258077410241390	0.0240977410241390
44	-0.01575	0.0272979939802998	-0.0430479939802998
45	-0.02624	-0.0432276321462390	0.0169876321462390
46	0.06724	0.0351059973241281	0.0321340026758719
47	-0.01362	0.0223413850163344	-0.0359613850163344
48	-0.00422	0.00729291941407819	-0.0115129194140782
49	0.00754	0.0128583715559720	-0.00531837155597196
50	0.00087	-0.0182740098245231	0.0191440098245231
51	0.02715	0.0135789225301420	0.0135710774698580
52	0.02976	0.0138313631427299	0.0159286368572701
53	0.07946	0.0426312125028364	0.0368287874971636
54	0.01909	0.0213437958321560	-0.00225379583215603
55	-0.02483	0.00812445947874088	-0.0329544594787409
56	-0.0187	-0.0223275762168767	0.00362757621687672
57	0.09682	-0.050201147480897	0.147021147480897
58	0.03823	0.0300939387662498	0.00813606123375024
59	0.09571	0.0159073372893001	0.0798026627106999
60	-0.04663	0.0230716219180722	-0.0697016219180722
61	-0.01359	-0.0205675144092911	0.00697751440929106
62	0.05114	-0.0138472905263623	0.0649872905263623
63	-0.04275	0.00307669910642426	-0.0458266991064243
64	0.05739	0.0238619566770628	0.0335280433229371
65	0.01186	0.00199122313078438	0.00986877686921562
66	0.01066	0.00620372069919461	0.00445627930080539
67	-0.07387	-0.00658866365134271	-0.0672813363486573
68	-0.04131	-0.0185943162843078	-0.0227156837156922
69	-0.17889	-0.0444555147755726	-0.134434485224427
70	-0.12781	-0.0504551548188985	-0.0773548451811015
71	-0.26933	-0.106873303847466	-0.162456696152534
72	-0.05095	-0.0535345205366059	0.00258452053660586
73	-0.01074	-0.0500623980737165	0.0393223980737165
74	0.08172	0.0692202291196775	0.0124997708803225
75	0.1187	0.0649833379734368	0.0537166620265632
76	0.08475	0.0979769068198936	-0.0132269068198936
77	0.04663	0.0536657870585285	-0.0070357870585285
78	-0.04415	0.0104575537102259	-0.0546075537102259
79	0.0097	-0.0148879229791154	0.0245879229791154
80	-0.03341	-0.0356082277933871	0.00219822779338712
81	0.04031	0.0230096112960700	0.0173003887039300
82	0.01938	-0.0155524189000331	0.0349324189000331
83	0.05928	0.055094487585293	0.00418551241470694
84	0.02343	0.00107218938441441	0.0223578106155856
85	-0.04536	0.0388445707983923	-0.0842045707983923
86	0.03355	-0.0194330070999772	0.0529830070999772
87	0.05659	-0.0170702513654430	0.073660251365443
88	-0.06579	0.0430963815628115	-0.108886381562811
89	-0.04267	-0.00336374700380879	-0.0393062529961912
90	-0.02422	-0.0374038344966273	0.0131838344966273
91	0.07584	-0.00109736086760083	0.0769373608676008
92	-0.00903	0.0155580915439419	-0.0245880915439419
93	0.06617	0.0468139426117253	0.0193560573882747
94	0.04485	0.0400981452594403	0.0047518547405597
95	-0.00665	0.0167148457951973	-0.0233648457951973

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
14	0.319150213574145	0.63830042714829	0.680849786425855
15	0.198841123903732	0.397682247807463	0.801158876096268
16	0.265563531235032	0.531127062470065	0.734436468764968
17	0.247959853862547	0.495919707725093	0.752040146137454
18	0.216556249706311	0.433112499412623	0.783443750293689
19	0.137457199680465	0.274914399360930	0.862542800319535
20	0.083671977168837	0.167343954337674	0.916328022831163
21	0.0486432878445747	0.0972865756891494	0.951356712155425
22	0.0286706724502357	0.0573413449004713	0.971329327549764
23	0.0198628606666119	0.0397257213332238	0.980137139333388
24	0.0104005996650542	0.0208011993301085	0.989599400334946
25	0.0057328905749026	0.0114657811498052	0.994267109425097
26	0.00852739957853813	0.0170547991570763	0.991472600421462
27	0.00639650750211865	0.0127930150042373	0.993603492497881
28	0.0117414803880480	0.0234829607760960	0.988258519611952
29	0.0072203134737224	0.0144406269474448	0.992779686526278
30	0.00418618889021487	0.00837237778042975	0.995813811109785
31	0.00240345533912383	0.00480691067824767	0.997596544660876
32	0.00147810943946668	0.00295621887893335	0.998521890560533
33	0.00144856631911248	0.00289713263822495	0.998551433680888
34	0.00091101734069738	0.00182203468139476	0.999088982659303
35	0.000480698117336848	0.000961396234673696	0.999519301882663
36	0.000506433131593135	0.00101286626318627	0.999493566868407
37	0.000480552411287615	0.000961104822575231	0.999519447588712
38	0.000278270137910424	0.000556540275820848	0.99972172986209
39	0.000466916902958264	0.000933833805916528	0.999533083097042
40	0.000427775155929249	0.000855550311858498	0.99957222484407
41	0.000281269633480703	0.000562539266961406	0.99971873036652
42	0.000177923074115139	0.000355846148230277	0.999822076925885
43	0.000117041083225965	0.000234082166451931	0.999882958916774
44	7.45114703772047e-05	0.000149022940754409	0.999925488529623
45	4.38980632655861e-05	8.77961265311721e-05	0.999956101936734
46	2.32752551316538e-05	4.65505102633077e-05	0.999976724744868
47	1.61798897740603e-05	3.23597795481207e-05	0.999983820110226
48	7.77160411642169e-06	1.55432082328434e-05	0.999992228395884
49	3.90432474718083e-06	7.80864949436167e-06	0.999996095675253
50	1.80064328833247e-06	3.60128657666495e-06	0.999998199356712
51	8.2506646789337e-07	1.65013293578674e-06	0.999999174933532
52	3.94551722036872e-07	7.89103444073743e-07	0.999999605448278
53	5.95779233752204e-07	1.19155846750441e-06	0.999999404220766
54	4.77011948463465e-07	9.5402389692693e-07	0.999999522988052
55	2.19137546179377e-07	4.38275092358755e-07	0.999999780862454
56	1.02739635473992e-07	2.05479270947983e-07	0.999999897260365
57	1.08192218136744e-05	2.16384436273489e-05	0.999989180778186
58	6.41924253313564e-06	1.28384850662713e-05	0.999993580757467
59	6.2161016779161e-05	0.000124322033558322	0.99993783898322
60	0.000143670714123549	0.000287341428247098	0.999856329285876
61	0.000317743938039025	0.000635487876078049	0.99968225606196
62	0.000439183740623539	0.000878367481247078	0.999560816259377
63	0.000764234717522974	0.00152846943504595	0.999235765282477
64	0.000463844596152753	0.000927689192305507	0.999536155403847
65	0.000499356311365925	0.00099871262273185	0.999500643688634
66	0.000457857366416631	0.000915714732833261	0.999542142633583
67	0.000808645820829055	0.00161729164165811	0.999191354179171
68	0.00118890650434876	0.00237781300869752	0.998811093495651
69	0.0286462011067609	0.0572924022135218	0.971353798893239
70	0.0420076400270183	0.0840152800540366	0.957992359972982
71	0.493676341798356	0.987352683596712	0.506323658201644
72	0.494361703067334	0.988723406134668	0.505638296932666
73	0.495759475264645	0.99151895052929	0.504240524735355
74	0.423838741805159	0.847677483610319	0.576161258194841
75	0.370180719810211	0.740361439620423	0.629819280189789
76	0.294270407674759	0.588540815349518	0.705729592325241
77	0.250378935069395	0.50075787013879	0.749621064930605
78	0.178253383503421	0.356506767006843	0.821746616496579
79	0.134127751546327	0.268255503092653	0.865872248453673
80	0.0758109084855753	0.151621816971151	0.924189091514425
81	0.131076356198907	0.262152712397814	0.868923643801093

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	39	0.573529411764706	NOK
5% type I error level	46	0.676470588235294	NOK
10% type I error level	50	0.735294117647059	NOK