Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 3.46094894308918 -1.35890812535706X[t] + 1.57594470852792Y1[t] -0.641364831745757Y2[t] + 0.301634497468656M1[t] + 0.112538207357399M2[t] + 0.0715051759643893M3[t] + 0.263299441206298M4[t] + 0.460167495643472M5[t] + 0.100278611311066M6[t] + 0.184482326076706M7[t] + 0.262352168000846M8[t] + 0.194356140873652M9[t] + 0.104842003651204M10[t] + 0.00988454894042862M11[t] -0.0031959243864679t + 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)	3.46094894308918	1.393426	2.4838	0.016975	0.008488
X	-1.35890812535706	0.527899	-2.5742	0.013576	0.006788
Y1	1.57594470852792	0.106811	14.7545	0	0
Y2	-0.641364831745757	0.104974	-6.1098	0	0
M1	0.301634497468656	0.539082	0.5595	0.578701	0.28935
M2	0.112538207357399	0.538915	0.2088	0.835572	0.417786
M3	0.0715051759643893	0.538747	0.1327	0.89503	0.447515
M4	0.263299441206298	0.538875	0.4886	0.627601	0.3138
M5	0.460167495643472	0.546463	0.8421	0.404401	0.2022
M6	0.100278611311066	0.545736	0.1837	0.855074	0.427537
M7	0.184482326076706	0.540479	0.3413	0.734517	0.367258
M8	0.262352168000846	0.539049	0.4867	0.628947	0.314473
M9	0.194356140873652	0.538981	0.3606	0.720165	0.360082
M10	0.104842003651204	0.538855	0.1946	0.84665	0.423325
M11	0.00988454894042862	0.538931	0.0183	0.985452	0.492726
t	-0.0031959243864679	0.016433	-0.1945	0.846713	0.423356

Multiple Linear Regression - Regression Statistics
Multiple R	0.997691270248974
R-squared	0.995387870731012
Adjusted R-squared	0.993778988427876
F-TEST (value)	618.682838882126
F-TEST (DF numerator)	15
F-TEST (DF denominator)	43
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.801038532138557
Sum Squared Residuals	27.5914973887398

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	54.8	55.7110417169253	-0.911041716925267
2	52.7	54.0124347512415	-1.31243475124146
3	50.9	51.4283597056483	-0.528359705648272
4	50.6	50.1271237178195	0.472876282180463
5	52.1	51.0024691324542	1.09753086754576
6	53.3	53.195710836051	0.104289163949020
7	53.9	54.205805029045	-0.305805029045017
8	54.3	54.4564079736045	-0.156407973604542
9	54.2	54.6307750064546	-0.430775006454585
10	54.2	54.1239245412946	0.076075458705416
11	53.5	54.0899076453719	-0.589907645371917
12	51.4	52.9736658760755	-1.57366587607547
13	50.5	50.411575943471	0.0884240565289558
14	50.3	50.1477996379643	0.152200362035715
15	49.8	50.3656100890504	-0.565610089050398
16	50.7	49.894509041991	0.805490958008976
17	52.8	51.8272138255898	0.972786174410244
18	55.3	54.1963845562083	1.10361544379167
19	57.3	56.8703879712412	0.429612028758775
20	57.5	58.4935392264703	-0.99353922647035
21	56.8	57.4548065531708	-0.654806553170764
22	56.4	56.1306622292431	0.269337770756858
23	56.3	55.8510863489568	0.448913651043235
24	56.4	55.9369573374754	0.463042662524625
25	57	56.4571268645849	0.542873135415067
26	57.9	57.1462649920294	0.75373500797061
27	58.9	58.1355673748776	0.764432625122414
28	58.8	59.3228820756898	-0.522882075689771
29	56.5	57.3586867777849	-0.858686777784864
30	51.9	53.4350656226264	-1.53506562262635
31	47.4	47.7418668667923	-0.341866866792309
32	44.9	43.6750678219848	1.22493217801519
33	43.9	42.5501558420072	1.34984415799276
34	43.4	42.4849131512348	0.915086848765203
35	42.9	42.2401522496193	0.65984775038065
36	42.6	41.7597818379014	0.840218162098634
37	42.2	41.9061194142981	0.293880585701941
38	41.2	41.2758587659129	-0.0758587659128922
39	40.2	39.9122310343038	0.287768965696208
40	39.3	39.1662494983771	0.133750501622929
41	38.5	38.5829362224984	-0.0829362224983919
42	38.3	37.5363239955284	0.763676004471629
43	37.9	37.8152347095986	0.0847652904014438
44	37.6	37.3878037100742	0.212196289925788
45	37.3	37.1003742787005	0.199625721299517
46	36	36.7272902540569	-0.727290254056906
47	34.5	34.7728182033971	-0.272818203397096
48	33.5	33.2295949485478	0.270405051452204
49	32.9	32.9141360607207	-0.0141360607206959
50	32.9	32.4176418528520	0.482358147148027
51	32.8	32.7582317961200	0.0417682038800483
52	31.9	32.7892356661226	-0.889235666122597
53	30.5	31.6286940416727	-1.12869404167275
54	29.2	29.636514989586	-0.436514989585965
55	28.7	28.5667054233229	0.133294576677107
56	28.4	28.6871812678661	-0.287181267866087
57	28	28.4638883196669	-0.463888319666924
58	27.4	27.9332098241706	-0.533209824170572
59	26.9	27.1460355526549	-0.246035552654873

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.383797704894620	0.767595409789241	0.61620229510538
20	0.568013989745888	0.863972020508224	0.431986010254112
21	0.6815781411301	0.6368437177398	0.3184218588699
22	0.586269251241131	0.827461497517738	0.413730748758869
23	0.63852569768549	0.722948604629019	0.361474302314510
24	0.94794680983037	0.104106380339259	0.0520531901696295
25	0.92680831872781	0.14638336254438	0.07319168127219
26	0.911565973819178	0.176868052361644	0.0884340261808222
27	0.887915898499298	0.224168203001403	0.112084101500702
28	0.946247825801261	0.107504348397477	0.0537521741987387
29	0.996880616804502	0.00623876639099515	0.00311938319549758
30	0.996250261413407	0.00749947717318505	0.00374973858659253
31	0.992202923661093	0.0155941526778141	0.00779707633890706
32	0.996809611615654	0.00638077676869291	0.00319038838434646
33	0.995674568773917	0.00865086245216501	0.00432543122608251
34	0.99144085436057	0.0171182912788613	0.00855914563943065
35	0.986701273914209	0.0265974521715826	0.0132987260857913
36	0.97041615209434	0.0591676958113213	0.0295838479056607
37	0.94654085466774	0.106918290664519	0.0534591453322594
38	0.948693143622374	0.102613712755252	0.0513068563776259
39	0.8953786598597	0.209242680280600	0.104621340140300
40	0.798217131403275	0.403565737193449	0.201782868596725

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	4	0.181818181818182	NOK
5% type I error level	7	0.318181818181818	NOK
10% type I error level	8	0.363636363636364	NOK