Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 6.56129173056506 -0.0297605284888526X[t] + 0.0498385336793684M1[t] + 0.243588533679369M2[t] + 0.0673085997404747M3[t] + 0.132308599740474M4[t] + 0.0723085997404747M5[t] + 0.0628571428571433M6[t] -0.402857142857143M7[t] -0.305714285714286M8[t] -0.202857142857143M9[t] -0.0585714285714285M10[t] -0.0657142857142855M11[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)	6.56129173056506	0.172243	38.0932	0	0
X	-0.0297605284888526	0.093196	-0.3193	0.750349	0.375175
M1	0.0498385336793684	0.224396	0.2221	0.824831	0.412416
M2	0.243588533679369	0.224396	1.0855	0.281119	0.14056
M3	0.0673085997404747	0.224353	0.3	0.764987	0.382494
M4	0.132308599740474	0.224353	0.5897	0.557119	0.278559
M5	0.0723085997404747	0.224353	0.3223	0.748112	0.374056
M6	0.0628571428571433	0.231654	0.2713	0.786864	0.393432
M7	-0.402857142857143	0.231654	-1.739	0.086075	0.043038
M8	-0.305714285714286	0.231654	-1.3197	0.190895	0.095448
M9	-0.202857142857143	0.231654	-0.8757	0.383957	0.191978
M10	-0.0585714285714285	0.231654	-0.2528	0.801074	0.400537
M11	-0.0657142857142855	0.231654	-0.2837	0.777431	0.388715

Multiple Linear Regression - Regression Statistics
Multiple R	0.407134600910004
R-squared	0.165758583258149
Adjusted R-squared	0.0340362542989089
F-TEST (value)	1.25839396074937
F-TEST (DF numerator)	12
F-TEST (DF denominator)	76
p-value	0.260958704740839
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.433384220039064
Sum Squared Residuals	14.2744630455939

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	5.81	6.61113026424442	-0.80113026424442
2	5.76	6.80488026424442	-1.04488026424442
3	5.99	6.62860033030553	-0.638600330305532
4	6.12	6.69360033030553	-0.573600330305533
5	6.03	6.63360033030553	-0.603600330305533
6	6.25	6.6241488734222	-0.374148873422202
7	5.8	6.15843458770792	-0.358434587707916
8	5.67	6.25557744485077	-0.585577444850773
9	5.89	6.35843458770792	-0.468434587707915
10	5.91	6.50272030199363	-0.592720301993629
11	5.86	6.49557744485077	-0.635577444850772
12	6.07	6.56129173056506	-0.491291730565058
13	6.27	6.61113026424443	-0.341130264244427
14	6.68	6.80488026424443	-0.124880264244427
15	6.77	6.62860033030553	0.141399669694467
16	6.71	6.69360033030553	0.0163996696944679
17	6.62	6.63360033030553	-0.0136003303055325
18	6.5	6.6241488734222	-0.124148873422201
19	5.89	6.15843458770791	-0.268434587707915
20	6.05	6.25557744485077	-0.205577444850773
21	6.43	6.35843458770792	0.0715654122920845
22	6.47	6.50272030199363	-0.0327203019936298
23	6.62	6.49557744485077	0.124422555149227
24	6.77	6.56129173056506	0.208708269434942
25	6.7	6.61113026424443	0.0888697357555737
26	6.95	6.80488026424443	0.145119735755574
27	6.73	6.62860033030553	0.101399669694468
28	7.07	6.69360033030553	0.376399669694468
29	7.28	6.63360033030553	0.646399669694467
30	7.32	6.6241488734222	0.695851126577799
31	6.76	6.15843458770791	0.601565412292084
32	6.93	6.25557744485077	0.674422555149227
33	6.99	6.35843458770792	0.631565412292085
34	7.16	6.50272030199363	0.65727969800637
35	7.28	6.49557744485077	0.784422555149227
36	7.08	6.56129173056506	0.518708269434942
37	7.34	6.61113026424443	0.728869735755574
38	7.87	6.80488026424443	1.06511973575557
39	6.28	6.59883980181668	-0.318839801816680
40	6.3	6.66383980181668	-0.36383980181668
41	6.36	6.60383980181668	-0.24383980181668
42	6.28	6.59438834493335	-0.314388344933349
43	5.89	6.12867405921906	-0.238674059219063
44	6.04	6.22581691636192	-0.185816916361920
45	5.96	6.32867405921906	-0.368674059219063
46	6.1	6.47295977350478	-0.372959773504778
47	6.26	6.46581691636192	-0.205816916361921
48	6.02	6.53153120207621	-0.511531202076206
49	6.25	6.58136973575557	-0.331369735755574
50	6.41	6.77511973575557	-0.365119735755574
51	6.22	6.59883980181668	-0.378839801816681
52	6.57	6.66383980181668	-0.0938398018166798
53	6.18	6.60383980181668	-0.423839801816681
54	6.26	6.59438834493335	-0.334388344933350
55	6.1	6.12867405921906	-0.0286740592190635
56	6.02	6.22581691636192	-0.205816916361921
57	6.06	6.32867405921906	-0.268674059219064
58	6.35	6.47295977350478	-0.122959773504778
59	6.21	6.46581691636192	-0.255816916361921
60	6.48	6.53153120207621	-0.0515312020762056
61	6.74	6.58136973575557	0.158630264244426
62	6.53	6.77511973575557	-0.245119735755574
63	6.8	6.59883980181668	0.201160198183319
64	6.75	6.66383980181668	0.0861601981833199
65	6.56	6.60383980181668	-0.043839801816681
66	6.66	6.59438834493335	0.0656116550666509
67	6.18	6.12867405921906	0.0513259407809366
68	6.4	6.22581691636192	0.17418308363808
69	6.43	6.32867405921906	0.101325940780936
70	6.54	6.47295977350478	0.0670402264952225
71	6.44	6.46581691636192	-0.0258169163619203
72	6.64	6.53153120207621	0.108468797923794
73	6.82	6.58136973575557	0.238630264244426
74	6.97	6.77511973575557	0.194880264244425
75	7	6.59883980181668	0.401160198183319
76	6.91	6.66383980181668	0.24616019818332
77	6.74	6.60383980181668	0.136160198183320
78	6.98	6.59438834493335	0.385611655066651
79	6.37	6.12867405921906	0.241325940780937
80	6.56	6.22581691636192	0.334183083638079
81	6.63	6.32867405921906	0.301325940780937
82	6.87	6.47295977350478	0.397040226495222
83	6.68	6.46581691636192	0.214183083638079
84	6.75	6.53153120207621	0.218468797923794
85	6.84	6.58136973575557	0.258630264244425
86	7.15	6.77511973575557	0.374880264244426
87	7.09	6.59883980181668	0.491160198183319
88	6.97	6.66383980181668	0.306160198183320
89	7.15	6.60383980181668	0.54616019818332

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.961167742970396	0.0776645140592088	0.0388322570296044
17	0.956524335100293	0.0869513297994135	0.0434756648997067
18	0.932982036357404	0.134035927285191	0.0670179636425956
19	0.909120901517585	0.181758196964831	0.0908790984824153
20	0.90584378599655	0.188312428006899	0.0941562140034494
21	0.906600959674	0.186798080651999	0.0933990403259995
22	0.919226363785399	0.161547272429202	0.080773636214601
23	0.945198061213196	0.109603877573607	0.0548019387868035
24	0.954861335158464	0.0902773296830715	0.0451386648415358
25	0.97320700138261	0.05358599723478	0.02679299861739
26	0.986250165810947	0.0274996683781054	0.0137498341890527
27	0.988516967123464	0.0229660657530714	0.0114830328765357
28	0.991679710541762	0.0166405789164762	0.0083202894582381
29	0.996280826534161	0.0074383469316771	0.00371917346583855
30	0.998046043888163	0.00390791222367402	0.00195395611183701
31	0.998803430485996	0.00239313902800834	0.00119656951400417
32	0.999428071572352	0.00114385685529587	0.000571928427647933
33	0.99948759048088	0.00102481903824092	0.000512409519120458
34	0.99962945358399	0.000741092832020001	0.000370546416010001
35	0.999741312132082	0.000517375735836272	0.000258687867918136
36	0.9996895651044	0.00062086979119929	0.000310434895599645
37	0.99982890386142	0.000342192277161092	0.000171096138580546
38	0.999934560645022	0.000130878709955725	6.54393549778627e-05
39	0.999922215349602	0.000155569300795205	7.77846503976023e-05
40	0.999911100398303	0.000177799203394033	8.88996016970165e-05
41	0.999852413895521	0.000295172208957482	0.000147586104478741
42	0.999777185006173	0.000445629987654659	0.000222814993827329
43	0.99965246196488	0.000695076070239906	0.000347538035119953
44	0.999441315392751	0.00111736921449813	0.000558684607249067
45	0.999279573039939	0.00144085392012215	0.000720426960061074
46	0.999198145175555	0.00160370964888943	0.000801854824444714
47	0.998604601238998	0.00279079752200433	0.00139539876100217
48	0.998924473341832	0.00215105331633581	0.00107552665816791
49	0.99905072626754	0.00189854746492158	0.000949273732460788
50	0.999008693765053	0.00198261246989486	0.000991306234947432
51	0.999655501928708	0.000688996142583637	0.000344498071291818
52	0.999517590123939	0.000964819752122495	0.000482409876061247
53	0.999801491471973	0.000397017056055047	0.000198508528027524
54	0.9998853425444	0.000229314911201804	0.000114657455600902
55	0.999783435760103	0.000433128479793127	0.000216564239896563
56	0.999820796730918	0.000358406538164362	0.000179203269082181
57	0.999871351630633	0.000257296738734405	0.000128648369367203
58	0.999855080564574	0.00028983887085118	0.00014491943542559
59	0.999836132755845	0.000327734488309394	0.000163867244154697
60	0.999707505942432	0.000584988115136055	0.000292494057568027
61	0.99940143745418	0.00119712509163825	0.000598562545819123
62	0.99979679305533	0.000406413889338401	0.000203206944669201
63	0.999711498847728	0.000577002304544	0.000288501152272
64	0.99944860113786	0.00110279772427809	0.000551398862139043
65	0.999625572147108	0.000748855705784423	0.000374427852892211
66	0.999534799006222	0.000930401987556484	0.000465200993778242
67	0.998970053139428	0.00205989372114356	0.00102994686057178
68	0.997586505210017	0.00482698957996646	0.00241349478998323
69	0.994901690437582	0.0101966191248365	0.00509830956241825
70	0.99398915267443	0.0120216946511408	0.00601084732557041
71	0.988885367767393	0.0222292644652140	0.0111146322326070
72	0.96835318718541	0.0632936256291781	0.0316468128145891
73	0.908382929958021	0.183234140083957	0.0916170700419786

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	40	0.689655172413793	NOK
5% type I error level	46	0.793103448275862	NOK
10% type I error level	51	0.879310344827586	NOK