Multiple Linear Regression - Estimated Regression Equation

X2[t] = -6.96454269613189 + 0.199329143390148Y[t] -0.0159718658230266X1[t] + 3.12164685974994X3[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)	-6.96454269613189	2.873907	-2.4234	0.016493	0.008246
Y	0.199329143390148	0.092443	2.1562	0.032558	0.016279
X1	-0.0159718658230266	0.048447	-0.3297	0.742075	0.371037
X3	3.12164685974994	0.176178	17.7187	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.911862202403
R-squared	0.831492676171251
Adjusted R-squared	0.828333163849462
F-TEST (value)	263.171208555511
F-TEST (DF numerator)	3
F-TEST (DF denominator)	160
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	13.5434760941342
Sum Squared Residuals	29348.1191539814

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	84	82.8320395688444	1.16796043115561
2	72	59.4856443807253	12.5143556192747
3	37	73.5432263475093	-36.5432263475093
4	85	78.2505628832759	6.74943711672414
5	30	44.148931800967	-14.148931800967
6	53	44.6876049089542	8.3123950910458
7	74	71.1495942870105	2.85040571298954
8	22	50.76351321671	-28.76351321671
9	68	58.1183493263268	9.88165067367325
10	47	62.2609188811597	-15.2609188811597
11	102	94.6165032704263	7.38349672957368
12	123	114.530322205757	8.46967779424266
13	69	69.7277608626508	-0.727760862650798
14	108	115.507699633367	-7.50769963336692
15	59	90.4586002085658	-31.4586002085658
16	122	114.31354166784	7.68645833215975
17	91	77.250620742807	13.749379257193
18	45	71.0456607908763	-26.0456607908763
19	53	58.1502930579728	-5.1502930579728
20	112	94.6567521143816	17.3432478856184
21	82	85.7224135535581	-3.7224135535581
22	92	89.250182642489	2.74981735751103
23	51	44.5399233342334	6.46007666576655
24	120	92.153637691734	27.846362308266
25	99	87.3842305874895	11.6157694125105
26	86	74.4906797494003	11.5093202505997
27	59	66.2661316795084	-7.26613167950842
28	98	85.4112813494068	12.5887186505932
29	71	64.0268722223384	6.97312777766155
30	100	96.443047651379	3.55695234862092
31	113	96.4027988074238	16.5972011925762
32	92	102.459003278156	-10.4590032781563
33	107	97.0403967227542	9.95960327724585
34	75	58.4576932909238	16.5423067090762
35	100	89.9798797815571	10.0201202184429
36	69	79.6548103581115	-10.6548103581115
37	106	99.910225700536	6.08977429946401
38	51	61.4469920829807	-10.4469920829807
39	18	21.9786048250522	-3.97860482505223
40	91	77.7911107456084	13.2088892543915
41	75	82.5565830675394	-7.5565830675394
42	63	76.8003148873573	-13.8003148873573
43	72	65.3819273821142	6.61807261788577
44	59	62.6794838160765	-3.67948381607649
45	29	62.9899776614325	-33.9899776614325
46	85	89.6079537265186	-4.60795372651865
47	66	77.9126984473828	-11.9126984473828
48	106	94.5768927852664	11.4231072147336
49	113	110.411826817943	2.58817318205653
50	101	93.2378094913137	7.76219050868632
51	65	55.554441052792	9.445558947208
52	7	6.5340239668463	0.465976033153707
53	111	100.820088323194	10.1799116768056
54	61	52.5415036413983	8.4584963586017
55	41	41.1940319941658	-0.194031994165767
56	70	64.6049530043723	5.39504699562765
57	136	114.454833206638	21.5451667933621
58	87	77.0972921204998	9.90270787950016
59	90	84.7608051806584	5.23919481934164
60	76	68.6709596536083	7.32904034639173
61	101	101.987311245866	-0.987311245866108
62	57	68.7219688634823	-11.7219688634823
63	61	96.7894200106946	-35.7894200106946
64	92	82.608433447322	9.39156655267802
65	80	75.1059157629845	4.89408423701553
66	35	45.6796774847961	-10.6796774847961
67	72	57.3516997668215	14.6483002331785
68	88	86.7856047985237	1.21439520147628
69	80	75.5441845349247	4.45581546507535
70	62	53.848643203705	8.151356796295
71	81	77.1274189573317	3.87258104266831
72	63	58.808435980235	4.19156401976496
73	91	77.3503867200587	13.6496132799413
74	65	75.5365177814108	-10.5365177814108
75	79	69.6881503774909	9.31184962250908
76	85	80.9223394352583	4.07766056474167
77	75	65.5211010334126	9.4788989665874
78	70	69.6875120186955	0.312487981304453
79	78	66.1199296334916	11.8800703665084
80	75	76.9836721649244	-1.98367216492445
81	55	54.1278316762103	0.872168323789716
82	80	100.763762983875	-20.7637629838749
83	83	68.2403576351819	14.7596423648181
84	38	77.7087961628837	-39.7087961628837
85	27	21.9945766908752	5.00542330912475
86	62	63.9470128932233	-1.94701289322331
87	82	66.5185879202719	15.4814120797281
88	88	78.691925267621	9.30807473237897
89	59	95.39018122465	-36.3901812246501
90	92	82.7797536413796	9.2202463586204
91	40	74.5155950863279	-34.5155950863279
92	91	78.6658313946746	12.3341686053254
93	63	64.0984264391444	-1.09842643914438
94	88	76.5088865202293	11.4911134797707
95	85	77.50553223718	7.49446776281993
96	76	62.2130032836906	13.7869967163094
97	67	62.9783761256051	4.02162387439488
98	69	77.6569457831012	-8.65694578310115
99	150	127.594352067996	22.4056479320043
100	77	74.3154247730292	2.68457522697085
101	103	97.371435575042	5.62856442495798
102	81	83.7092154715201	-2.70921547152008
103	37	59.6753916942155	-22.6753916942155
104	64	54.5150912382764	9.48490876172357
105	22	46.1179462567362	-24.1179462567362
106	35	64.3124507307668	-29.3124507307668
107	61	69.4209989884951	-8.42099898849515
108	80	77.2978979814807	2.70210201851927
109	54	56.0215599439733	-2.02155994397329
110	76	72.0993683875139	3.90063161248614
111	87	73.929644739667	13.0703552603331
112	75	84.2153064890659	-9.21530648906588
113	0	-2.8066396342713	2.8066396342713
114	61	74.0849930679015	-13.0849930679015
115	30	30.3628715531743	-0.36287155317434
116	66	81.7760795297104	-15.7760795297104
117	56	74.8099142547476	-18.8099142547476
118	0	-6.0241176889594	6.0241176889594
119	32	54.9129083551482	-22.9129083551482
120	9	19.4991290217415	-10.4991290217415
121	82	77.1062355916044	4.89376440839559
122	110	96.822002101136	13.177997898864
123	71	71.4061881212006	-0.406188121200624
124	50	59.1911224011923	-9.1911224011923
125	21	19.6582093211764	1.34179067882362
126	78	66.2956201575449	11.7043798424551
127	118	106.046927859179	11.9530721408211
128	102	103.017380223167	-1.01738022316683
129	109	102.562298415495	6.43770158450494
130	104	106.174064426968	-2.17406442696777
131	124	115.295492236559	8.7045077634413
132	76	65.996525036903	10.0034749630969
133	57	59.1911224011923	-2.19112240119231
134	91	75.4208845678774	15.5791154321226
135	101	97.290096717223	3.70990328277704
136	66	58.0194245189836	7.98057548101636
137	98	89.8993820936466	8.10061790635336
138	63	72.9369338050297	-9.9369338050297
139	85	83.0396738245437	1.9603261754563
140	74	80.5755315282606	-6.57553152826062
141	19	33.5311572928026	-14.5311572928026
142	57	71.050031120872	-14.050031120872
143	74	75.4643252058095	-1.46432520580952
144	78	67.1516126944933	10.8483873055067
145	91	96.5459072410357	-5.5459072410357
146	112	96.092507773181	15.907492226819
147	79	74.9461971047542	4.05380289524579
148	100	92.6588875393712	7.34111246062878
149	0	-6.96454269613186	6.96454269613186
150	0	-6.32694478080153	6.32694478080153
151	0	-6.9805145619549	6.9805145619549
152	0	-6.99648642777792	6.99648642777792
153	0	-6.96454269613186	6.96454269613186
154	0	-6.96454269613186	6.96454269613186
155	48	62.116533729957	-14.116533729957
156	55	86.3357344907562	-31.3357344907562
157	0	-6.96454269613186	6.96454269613186
158	0	-7.02843015942397	7.02843015942397
159	0	-6.6457437384667	6.6457437384667
160	13	10.9155331502292	2.08446684977077
161	4	-2.92610944854631	6.92610944854631
162	31	68.388677568698	-37.388677568698
163	0	-6.99648642777792	6.99648642777792
164	29	48.2352806460216	-19.2352806460216

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.932536130640171	0.134927738719658	0.067463869359829
8	0.929914669493504	0.140170661012993	0.0700853305064965
9	0.928411541514672	0.143176916970657	0.0715884584853284
10	0.885608600478933	0.228782799042135	0.114391399521067
11	0.850895292500891	0.298209414998217	0.149104707499109
12	0.787480631695425	0.425038736609151	0.212519368304575
13	0.710821690968906	0.578356618062187	0.289178309031094
14	0.663850506284224	0.672298987431552	0.336149493715776
15	0.873702608555383	0.252594782889235	0.126297391444617
16	0.851301378808482	0.297397242383037	0.148698621191518
17	0.890685432419365	0.218629135161269	0.109314567580635
18	0.967453020246052	0.0650939595078966	0.0325469797539483
19	0.952258645818171	0.0954827083636577	0.0477413541818288
20	0.96210903105563	0.0757819378887413	0.0378909689443707
21	0.945826185783024	0.108347628433952	0.0541738142169761
22	0.924535360367699	0.150929279264603	0.0754646396323013
23	0.918136817063533	0.163726365872934	0.081863182936467
24	0.9648221161803	0.0703557676394009	0.0351778838197004
25	0.960647824746956	0.078704350506089	0.0393521752530445
26	0.956852806902743	0.0862943861945145	0.0431471930972573
27	0.943452586842998	0.113094826314003	0.0565474131570017
28	0.937154621688883	0.125690756622234	0.062845378311117
29	0.924383791984299	0.151232416031402	0.075616208015701
30	0.901334968526385	0.19733006294723	0.098665031473615
31	0.899277095724123	0.201445808551754	0.100722904275877
32	0.897605613388999	0.204788773222002	0.102394386611001
33	0.877797227168466	0.244405545663069	0.122202772831534
34	0.895789727054611	0.208420545890778	0.104210272945389
35	0.877093280683118	0.245813438633763	0.122906719316882
36	0.868069695979508	0.263860608040984	0.131930304020492
37	0.839164518625017	0.321670962749966	0.160835481374983
38	0.818831381861646	0.362337236276707	0.181168618138354
39	0.784136508812847	0.431726982374307	0.215863491187153
40	0.775129356725707	0.449741286548586	0.224870643274293
41	0.750201537429597	0.499596925140806	0.249798462570403
42	0.748968240187005	0.50206351962599	0.251031759812995
43	0.71829666263214	0.56340667473572	0.28170333736786
44	0.674289213363038	0.651421573273923	0.325710786636962
45	0.846722000808656	0.306555998382688	0.153277999191344
46	0.823945778159549	0.352108443680902	0.176054221840451
47	0.812240630956972	0.375518738086057	0.187759369043028
48	0.796401347105427	0.407197305789147	0.203598652894573
49	0.761198041123503	0.477603917752994	0.238801958876497
50	0.731134288171211	0.537731423657579	0.268865711828789
51	0.719994138860814	0.560011722278373	0.280005861139186
52	0.692199673310334	0.615600653379332	0.307800326689666
53	0.663475220591289	0.673049558817422	0.336524779408711
54	0.645835916187634	0.708328167624731	0.354164083812365
55	0.600934874565159	0.798130250869682	0.399065125434841
56	0.562953865907343	0.874092268185314	0.437046134092657
57	0.609712666162202	0.780574667675596	0.390287333837798
58	0.585733016364206	0.828533967271588	0.414266983635794
59	0.544962143990027	0.910075712019946	0.455037856009973
60	0.512555618383971	0.97488876323206	0.48744438161603
61	0.472062435859282	0.944124871718563	0.527937564140718
62	0.459624041394342	0.919248082788685	0.540375958605658
63	0.738263952726593	0.523472094546815	0.261736047273407
64	0.717414176921968	0.565171646156064	0.282585823078032
65	0.6826396177304	0.634720764539199	0.317360382269599
66	0.659698844940127	0.680602310119746	0.340301155059873
67	0.672276459198322	0.655447081603356	0.327723540801678
68	0.631255754474171	0.737488491051657	0.368744245525829
69	0.592287463880065	0.815425072239871	0.407712536119935
70	0.567996600762792	0.864006798474416	0.432003399237208
71	0.526337228683344	0.947325542633313	0.473662771316656
72	0.486857921177142	0.973715842354284	0.513142078822858
73	0.487509985370632	0.975019970741264	0.512490014629368
74	0.46884171280348	0.93768342560696	0.53115828719652
75	0.446126833068895	0.89225366613779	0.553873166931105
76	0.405713551876274	0.811427103752548	0.594286448123726
77	0.385969217723299	0.771938435446597	0.614030782276701
78	0.343366368396744	0.686732736793488	0.656633631603256
79	0.335684709331996	0.671369418663991	0.664315290668004
80	0.296196987872717	0.592393975745434	0.703803012127283
81	0.258580858775478	0.517161717550956	0.741419141224522
82	0.31387887758446	0.627757755168921	0.68612112241554
83	0.323490826877178	0.646981653754355	0.676509173122822
84	0.648586116728698	0.702827766542604	0.351413883271302
85	0.614065119766125	0.771869760467751	0.385934880233875
86	0.570462364832061	0.859075270335877	0.429537635167939
87	0.585204927319001	0.829590145361997	0.414795072680999
88	0.568241252767596	0.863517494464809	0.431758747232405
89	0.806795219404487	0.386409561191026	0.193204780595513
90	0.791656786010377	0.416686427979246	0.208343213989623
91	0.924563862112359	0.150872275775283	0.0754361378876414
92	0.922376236508937	0.155247526982126	0.077623763491063
93	0.904188495086744	0.191623009826512	0.095811504913256
94	0.899837744808096	0.200324510383809	0.100162255191904
95	0.886142572611614	0.227714854776772	0.113857427388386
96	0.887979299775304	0.224041400449392	0.112020700224696
97	0.866781138006886	0.266437723986228	0.133218861993114
98	0.849536728265335	0.30092654346933	0.150463271734665
99	0.902769843584894	0.194460312830212	0.0972301564151058
100	0.88383678412099	0.232326431758019	0.11616321587901
101	0.867104931292236	0.265790137415528	0.132895068707764
102	0.840469025200773	0.319061949598454	0.159530974799227
103	0.87710481198568	0.24579037602864	0.12289518801432
104	0.865529046763408	0.268941906473184	0.134470953236592
105	0.91180527459634	0.17638945080732	0.0881947254036602
106	0.964736180773787	0.0705276384524254	0.0352638192262127
107	0.957645214745156	0.0847095705096872	0.0423547852548436
108	0.946388913907082	0.107222172185836	0.0536110860929178
109	0.931731208502551	0.136537582994898	0.0682687914974489
110	0.915703427880697	0.168593144238606	0.0842965721193028
111	0.920225017014486	0.159549965971027	0.0797749829855135
112	0.908432118033938	0.183135763932123	0.0915678819660617
113	0.888098723726467	0.223802552547066	0.111901276273533
114	0.885787390147996	0.228425219704009	0.114212609852004
115	0.859499916399047	0.281000167201906	0.140500083600953
116	0.872456984751381	0.255086030497238	0.127543015248619
117	0.889224201935674	0.221551596128652	0.110775798064326
118	0.868019923132221	0.263960153735557	0.131980076867779
119	0.919693150495075	0.16061369900985	0.0803068495049252
120	0.915908423276718	0.168183153446563	0.0840915767232817
121	0.895937256582202	0.208125486835595	0.104062743417798
122	0.90012030890986	0.199759382180281	0.0998796910901404
123	0.873861069299382	0.252277861401236	0.126138930700618
124	0.85833912608006	0.283321747839879	0.141660873919939
125	0.825760965012173	0.348478069975653	0.174239034987827
126	0.820094611541592	0.359810776916815	0.179905388458408
127	0.825071883294557	0.349856233410886	0.174928116705443
128	0.788176205505847	0.423647588988305	0.211823794494153
129	0.764909163495177	0.470181673009647	0.235090836504823
130	0.719178263426447	0.561643473147106	0.280821736573553
131	0.721843491004177	0.556313017991646	0.278156508995823
132	0.726258435135382	0.547483129729235	0.273741564864618
133	0.673181836805764	0.653636326388471	0.326818163194236
134	0.721894347384774	0.556211305230452	0.278105652615226
135	0.730529327250965	0.538941345498069	0.269470672749035
136	0.693539104448814	0.612921791102372	0.306460895551186
137	0.730021842061827	0.539956315876346	0.269978157938173
138	0.68114335352374	0.637713292952521	0.31885664647626
139	0.621206227123714	0.757587545752571	0.378793772876286
140	0.556964040470658	0.886071919058683	0.443035959529342
141	0.55302516672786	0.893949666544281	0.44697483327214
142	0.492585625779483	0.985171251558967	0.507414374220517
143	0.432474592662284	0.864949185324568	0.567525407337716
144	0.494741993161276	0.989483986322552	0.505258006838724
145	0.476993349000881	0.953986698001761	0.523006650999119
146	0.859620762866983	0.280758474266033	0.140379237133017
147	0.913547171002058	0.172905657995885	0.0864528289979423
148	0.999999995514446	8.97110879753375e-09	4.48555439876688e-09
149	0.999999971465545	5.70689107304283e-08	2.85344553652141e-08
150	0.999999981953556	3.60928887154576e-08	1.80464443577288e-08
151	0.999999849854018	3.0029196350804e-07	1.5014598175402e-07
152	0.999998819607517	2.36078496498264e-06	1.18039248249132e-06
153	0.99999160930272	1.67813945613614e-05	8.39069728068071e-06
154	0.999944135842377	0.000111728315245271	5.58641576226356e-05
155	0.999996484036296	7.03192740758622e-06	3.51596370379311e-06
156	0.99995315143591	9.36971281800259e-05	4.6848564090013e-05
157	0.999338982455708	0.00132203508858351	0.000661017544291756

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	10	0.0662251655629139	NOK
5% type I error level	10	0.0662251655629139	NOK
10% type I error level	18	0.119205298013245	NOK