Multiple Linear Regression - Estimated Regression Equation

y[t] = + 13.4283031142472 + 0.832897843710754x[t] -1.31091204200039M1[t] -0.365009421819613M2[t] + 0.926100187197648M3[t] -0.866154643520036M4[t] -0.348823451910686M5[t] -1.49822113977123M6[t] + 0.49863090992441M7[t] -0.431904701871787M8[t] + 0.983814030091073M9[t] -0.844090480737548M10[t] -0.261872578116706M11[t] -0.00539532330297578t + 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)	13.4283031142472	0.923422	14.5419	0	0
x	0.832897843710754	0.367901	2.2639	0.025033	0.012516
M1	-1.31091204200039	0.86543	-1.5148	0.131968	0.065984
M2	-0.365009421819613	0.864442	-0.4222	0.673456	0.336728
M3	0.926100187197648	0.864388	1.0714	0.285736	0.142868
M4	-0.866154643520036	0.86529	-1.001	0.318461	0.159231
M5	-0.348823451910686	0.864331	-0.4036	0.687107	0.343554
M6	-1.49822113977123	0.86528	-1.7315	0.085449	0.042724
M7	0.49863090992441	0.880616	0.5662	0.572095	0.286048
M8	-0.431904701871787	0.881885	-0.4898	0.625035	0.312517
M9	0.983814030091073	0.880066	1.1179	0.265427	0.132713
M10	-0.844090480737548	0.880495	-0.9587	0.339296	0.169648
M11	-0.261872578116706	0.881806	-0.297	0.766903	0.383452
t	-0.00539532330297578	0.003778	-1.428	0.155389	0.077694

Multiple Linear Regression - Regression Statistics
Multiple R	0.391457433269082
R-squared	0.153238922061618
Adjusted R-squared	0.0788612598102736
F-TEST (value)	2.06028150688278
F-TEST (DF numerator)	13
F-TEST (DF denominator)	148
p-value	0.0197505101968209
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.24355168996005
Sum Squared Residuals	744.961579457345

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	14	13.7777914363653	0.222208563634675
2	18	14.7182987332431	3.28170126675690
3	11	16.0040130189574	-5.00401301895738
4	12	13.3734650212260	-1.37346502122596
5	16	14.7182987332431	1.28170126675691
6	18	13.5635057220796	4.43649427792042
7	14	15.5549624484722	-1.55496244847224
8	14	14.6190315133731	-0.619031513373067
9	15	16.0293549220330	-1.02935492203295
10	15	14.1960550879014	0.803944912098647
11	17	13.9399798235085	3.06002017649153
12	19	15.0293549220330	3.97064507796705
13	10	12.8801497130188	-2.88014971301883
14	16	14.6535548536074	1.34644514639261
15	18	15.9392691393217	2.06073086067833
16	14	13.3087211415903	0.691278858409743
17	14	13.8206570098966	0.179342990103369
18	17	13.4987618424439	3.50123815755613
19	14	14.6573207251258	-0.657320725125775
20	16	14.5542876337374	1.44571236626264
21	18	15.1317131986865	2.86828680131351
22	11	14.1313112082656	-3.13131120826564
23	14	14.7081337875835	-0.70813378758351
24	12	14.9646110423972	-2.96461104239724
25	17	12.8154058333831	4.18459416661688
26	9	14.5888109739717	-5.58881097397168
27	16	15.0416274159752	0.958372584024793
28	14	14.0768751056653	-0.0768751056653012
29	15	14.5888109739717	0.411189026028324
30	11	12.6011201190974	-1.60112011909740
31	16	15.4254746892008	0.57452531079918
32	13	13.6566459103909	-0.656645910390893
33	17	15.8998671627615	1.10013283723847
34	15	14.0665673286299	0.933432671370065
35	14	13.8104920642370	0.189507935762953
36	16	14.0669693190508	1.93303068094922
37	9	12.7506619537474	-3.75066195374741
38	15	13.6911692506252	1.30883074937479
39	17	15.8097813800503	1.19021861994975
40	13	13.1792333823188	-0.179233382318837
41	15	13.6911692506252	1.30883074937479
42	16	13.3692740831724	2.63072591682755
43	16	14.5278329658544	1.47216703414564
44	12	13.5919020307552	-1.59190203075518
45	12	15.8351232831258	-3.83512328312582
46	11	14.0018234489942	-3.00182344899422
47	15	14.5786460283121	0.421353971687908
48	15	14.8351232831258	0.164876716874178
49	17	13.5188159178225	3.48118408217755
50	13	13.6264253709895	-0.626425370989503
51	16	15.7450375004145	0.254962499585457
52	14	13.1144895026831	0.885510497316871
53	11	13.6264253709895	-2.62642537098950
54	12	13.3045302035367	-1.30453020353674
55	12	14.4630890862186	-2.46308908621865
56	15	14.3600559948302	0.639944005169771
57	16	15.7703794034901	0.229620596509888
58	15	13.9370795693585	1.06292043064148
59	12	13.6810043049656	-1.68100430496563
60	12	14.7703794034901	-2.77037940349011
61	8	12.6211741944760	-4.62117419447599
62	13	13.5616814913538	-0.561681491353793
63	11	15.6802936207788	-4.68029362077883
64	14	13.8826434667582	0.117356533241827
65	15	14.3945793350645	0.605420664935452
66	10	12.4068884801903	-2.40688848019028
67	11	15.2312430502937	-4.23124305029369
68	12	13.4624142714838	-1.46241427148376
69	15	15.7056355238544	-0.705635523854403
70	15	13.0394378460121	1.96056215398795
71	14	13.6162604253299	0.383739574670082
72	16	14.7056355238544	1.29436447614560
73	15	13.3893281585510	1.61067184144897
74	15	13.4969376117181	1.50306238828192
75	13	14.7826518974324	-1.78265189743237
76	12	13.8178995871225	-1.81789958712246
77	17	14.3298354554288	2.67016454457116
78	13	13.1750424442653	-0.175042444265321
79	15	14.3336013269472	0.666398673052771
80	13	13.3976703918481	-0.397670391848056
81	15	14.8079938005079	0.192006199492061
82	16	12.9746939663763	3.02530603362366
83	15	14.3844143894050	0.615585610595036
84	16	13.8079938005079	2.19200619949206
85	15	13.3245842789153	1.67541572108468
86	14	14.2650915757931	-0.265091575793129
87	15	14.7179080177967	0.28209198220334
88	14	13.7531557074868	0.246844292513246
89	13	14.2650915757931	-1.26509157579313
90	7	13.1102985646296	-6.11029856462961
91	17	15.1017552910223	1.89824470897773
92	13	14.1658243559231	-1.1658243559231
93	15	15.5761477645830	-0.576147764582984
94	14	13.7428479304514	0.257152069548612
95	13	14.3196705097693	-1.31967050976925
96	16	14.5761477645830	1.42385223541702
97	12	13.2598403992796	-1.25984039927961
98	14	14.2003476961574	-0.200347696157419
99	17	14.6531641381610	2.34683586183905
100	15	12.8555139841403	2.14448601585971
101	17	14.2003476961574	2.79965230384258
102	12	12.2126568412831	-0.212656841283147
103	16	15.0370114113866	0.962988588613436
104	11	13.2681826325766	-2.26818263257664
105	15	15.5114038849473	-0.511403884947275
106	9	12.8452062071049	-3.84520620710493
107	16	14.2549266301335	1.74507336986646
108	15	13.6785060412365	1.32149395876348
109	10	12.3621986759332	-2.36219867593315
110	10	14.1356038165217	-4.13560381652171
111	15	15.421318102236	-0.421318102235996
112	11	13.6236679482153	-2.62366794821533
113	13	14.1356038165217	-1.13560381652171
114	14	12.1479129616474	1.85208703835256
115	18	14.9722675317509	3.02773246824915
116	16	13.2034387529409	2.79656124705907
117	14	15.4466600053116	-1.44666000531157
118	14	13.6133601711800	0.386639828820031
119	14	14.1901827504978	-0.190182750497835
120	14	14.4466600053116	-0.446660005311566
121	12	13.1303526400082	-1.13035264000819
122	14	14.070859936886	-0.0708599368860008
123	15	15.3565742226003	-0.356574222600287
124	15	13.5589240685796	1.44107593142037
125	15	14.070859936886	0.929140063113999
126	13	12.9160669257225	0.0839330742775167
127	17	14.0746258084044	2.92537419159561
128	17	13.9715927170160	3.02840728298403
129	19	15.3819161256759	3.61808387432414
130	15	13.5486162915443	1.45138370845574
131	13	13.2925410271514	-0.292541027151372
132	9	13.5490182819651	-4.5490182819651
133	15	13.0656087603725	1.93439123962751
134	15	13.1732182135395	1.82678178646046
135	15	14.4589324992538	0.541067500746177
136	16	13.4941801889439	2.50581981105608
137	11	13.1732182135395	-2.17321821353954
138	14	12.0184252023760	1.98157479762398
139	11	14.8427797724794	-3.84277977247944
140	15	13.9068488373803	1.09315116261974
141	13	14.4842744023294	-1.48427440232939
142	15	13.4838724119085	1.51612758809145
143	16	13.2277971475157	2.77220285248434
144	14	14.3171722460401	-0.317172246040147
145	15	12.1679670370260	2.83203296297398
146	16	13.9413721776146	2.05862782238542
147	16	15.2270864633289	0.772913536671132
148	11	12.5965384655975	-1.59653846559745
149	12	13.1084743339038	-1.10847433390383
150	9	11.9536813227403	-2.95368132274031
151	16	14.7780358928437	1.22196410715627
152	13	13.8421049577446	-0.842104957744553
153	16	14.4195305226937	1.58046947730632
154	12	13.4191285322728	-1.41912853227284
155	9	13.9959511115907	-4.99595111159071
156	13	14.2524283664044	-1.25242836640444
157	13	12.9361210011011	0.0638789988989338
158	14	13.8766282979789	0.123371702021128
159	19	15.1623425836932	3.83765741630684
160	13	13.3646924296725	-0.364692429672498
161	12	13.8766282979789	-1.87662829797887
162	13	12.7218352868154	0.278164713184645

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.775705067824097	0.448589864351806	0.224294932175903
18	0.746128161482611	0.507743677034777	0.253871838517389
19	0.687775784365806	0.624448431268388	0.312224215634194
20	0.573468452384091	0.853063095231818	0.426531547615909
21	0.663895747754116	0.672208504491767	0.336104252245884
22	0.779605055524588	0.440789888950823	0.220394944475412
23	0.78560816082384	0.428783678352319	0.214391839176160
24	0.90336718461727	0.193265630765461	0.0966328153827306
25	0.959230153041746	0.0815396939165085	0.0407698469582542
26	0.99343330600238	0.0131333879952384	0.00656669399761918
27	0.99009753291555	0.0198049341689004	0.00990246708445019
28	0.989604646725386	0.0207907065492291	0.0103953532746145
29	0.984265508843814	0.0314689823123727	0.0157344911561863
30	0.992827571666648	0.0143448566667038	0.00717242833335192
31	0.991407697786918	0.0171846044261647	0.00859230221308233
32	0.986865291940192	0.0262694161196157	0.0131347080598078
33	0.98148583112875	0.0370283377425002	0.0185141688712501
34	0.97819640356281	0.0436071928743788	0.0218035964371894
35	0.968925804442966	0.0621483911140675	0.0310741955570338
36	0.962294464023785	0.0754110719524299	0.0377055359762150
37	0.970217659857038	0.0595646802859232	0.0297823401429616
38	0.964650523317504	0.0706989533649929	0.0353494766824964
39	0.96099782766173	0.0780043446765415	0.0390021723382708
40	0.94684130970796	0.106317380584081	0.0531586902920403
41	0.933607973129286	0.132784053741427	0.0663920268707137
42	0.929821612639292	0.140356774721416	0.070178387360708
43	0.920914786358303	0.158170427283395	0.0790852136416974
44	0.905480484235834	0.189039031528331	0.0945195157641656
45	0.93162770613833	0.136744587723339	0.0683722938616693
46	0.927730672242662	0.144538655514675	0.0722693277573375
47	0.90891960232965	0.182160795340700	0.0910803976703502
48	0.88523040943257	0.229539181134859	0.114769590567430
49	0.933547654149544	0.132904691700912	0.0664523458504561
50	0.914576876045954	0.170846247908093	0.0854231239540463
51	0.893924306132448	0.212151387735103	0.106075693867552
52	0.875445194216066	0.249109611567869	0.124554805783934
53	0.88003564673837	0.239928706523258	0.119964353261629
54	0.876117969990171	0.247764060019658	0.123882030009829
55	0.866686648545383	0.266626702909235	0.133313351454617
56	0.84652124195997	0.306957516080058	0.153478758040029
57	0.817821392478256	0.364357215043488	0.182178607521744
58	0.808311969804006	0.383376060391988	0.191688030195994
59	0.787275925243038	0.425448149513924	0.212724074756962
60	0.791714693935467	0.416570612129067	0.208285306064533
61	0.858014885913894	0.283970228172211	0.141985114086106
62	0.82925053753759	0.341498924924819	0.170749462462410
63	0.882759227359489	0.234481545281023	0.117240772640512
64	0.860031789966087	0.279936420067827	0.139968210033913
65	0.838174420516746	0.323651158966508	0.161825579483254
66	0.834459391537125	0.33108121692575	0.165540608462875
67	0.880006995328139	0.239986009343722	0.119993004671861
68	0.862418422209325	0.275163155581350	0.137581577790675
69	0.836532983449763	0.326934033100474	0.163467016550237
70	0.849255047687933	0.301489904624134	0.150744952312067
71	0.822563971338465	0.35487205732307	0.177436028661535
72	0.809661338853261	0.380677322293478	0.190338661146739
73	0.809688247358831	0.380623505282337	0.190311752641169
74	0.80017428448782	0.39965143102436	0.19982571551218
75	0.790512725905708	0.418974548188584	0.209487274094292
76	0.771068819803299	0.457862360393403	0.228931180196701
77	0.797771230780874	0.404457538438252	0.202228769219126
78	0.76338431478437	0.47323137043126	0.23661568521563
79	0.746359663275116	0.507280673449767	0.253640336724884
80	0.711375845891983	0.577248308216035	0.288624154108017
81	0.672508875852806	0.654982248294388	0.327491124147194
82	0.711957869223218	0.576084261553564	0.288042130776782
83	0.676336958887917	0.647326082224165	0.323663041112082
84	0.681335019470443	0.637329961059114	0.318664980529557
85	0.671432165325336	0.657135669349328	0.328567834674664
86	0.62575327341195	0.748493453176101	0.374246726588051
87	0.589044252375461	0.821911495249078	0.410955747624539
88	0.543314838660362	0.913370322679276	0.456685161339638
89	0.503252526963437	0.993494946073125	0.496747473036563
90	0.752453476560812	0.495093046878375	0.247546523439188
91	0.74579082256473	0.508418354870541	0.254209177435271
92	0.721066803438634	0.557866393122732	0.278933196561366
93	0.682609940792148	0.634780118415704	0.317390059207852
94	0.638425509761525	0.72314898047695	0.361574490238475
95	0.602588429207486	0.794823141585029	0.397411570792514
96	0.585129431772118	0.829741136455764	0.414870568227882
97	0.55071936788194	0.89856126423612	0.44928063211806
98	0.501075699707451	0.997848600585098	0.498924300292549
99	0.499404250461685	0.99880850092337	0.500595749538315
100	0.497843813947472	0.995687627894944	0.502156186052528
101	0.550549318162319	0.898901363675362	0.449450681837681
102	0.499188823631218	0.998377647262436	0.500811176368782
103	0.457277226433694	0.914554452867389	0.542722773566306
104	0.48074110271396	0.96148220542792	0.51925889728604
105	0.434443040619576	0.868886081239151	0.565556959380424
106	0.537196912721978	0.925606174556044	0.462803087278022
107	0.528555356746264	0.942889286507473	0.471444643253736
108	0.521048242264607	0.957903515470786	0.478951757735393
109	0.552687999976195	0.89462400004761	0.447312000023805
110	0.706095977352789	0.587808045294422	0.293904022647211
111	0.683074056428136	0.633851887143729	0.316925943571864
112	0.73090844998207	0.53818310003586	0.26909155001793
113	0.689991414814767	0.620017170370466	0.310008585185233
114	0.658529721148597	0.682940557702807	0.341470278851403
115	0.674207208843383	0.651585582313233	0.325792791156617
116	0.65684078436035	0.686318431279301	0.343159215639651
117	0.671411482753607	0.657177034492785	0.328588517246393
118	0.622219457023196	0.755561085953608	0.377780542976804
119	0.564167977514539	0.871664044970922	0.435832022485461
120	0.511241071257948	0.977517857484105	0.488758928742052
121	0.542704460216928	0.914591079566143	0.457295539783072
122	0.530109731518392	0.939780536963216	0.469890268481608
123	0.565338401823267	0.869323196353466	0.434661598176733
124	0.511117788407934	0.977764423184132	0.488882211592066
125	0.452975123840713	0.905950247681427	0.547024876159287
126	0.409366073569435	0.81873214713887	0.590633926430565
127	0.47077010991975	0.9415402198395	0.52922989008025
128	0.451670263406918	0.903340526813836	0.548329736593082
129	0.441577385010494	0.883154770020987	0.558422614989506
130	0.381072933333326	0.762145866666652	0.618927066666674
131	0.316276488085030	0.632552976170061	0.68372351191497
132	0.418826936106955	0.83765387221391	0.581173063893045
133	0.35437660924695	0.7087532184939	0.64562339075305
134	0.290611502722235	0.58122300544447	0.709388497277765
135	0.277946121308708	0.555892242617416	0.722053878691292
136	0.310059768236725	0.62011953647345	0.689940231763275
137	0.259378291935031	0.518756583870063	0.740621708064969
138	0.247872298225104	0.495744596450208	0.752127701774896
139	0.339946873949267	0.679893747898535	0.660053126050733
140	0.27575765560507	0.55151531121014	0.72424234439493
141	0.265822444003500	0.531644888007001	0.7341775559965
142	0.223806705780232	0.447613411560463	0.776193294219768
143	0.65103016033736	0.69793967932528	0.34896983966264
144	0.527406304056351	0.945187391887298	0.472593695943649
145	0.572119095440641	0.855761809118718	0.427880904559359

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	9	0.0697674418604651	NOK
10% type I error level	15	0.116279069767442	NOK