Multiple Linear Regression - Estimated Regression Equation

PS[t] = + 14.5514432169931 + 0.328382757651301x[t] + 1.08162089861099M1[t] + 0.406425419305482M2[t] + 1.80572354132149M3[t] + 1.63550358771727M4[t] + 1.03025002187994M5[t] + 1.85898982437003M6[t] + 2.36391663137686M7[t] + 2.76323282770756M8[t] + 2.13843125245325M9[t] + 1.45968193131887M10[t] + 0.411295472818057M11[t] -0.0112734900892955t + 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)	14.5514432169931	1.773089	8.2068	0	0
x	0.328382757651301	0.055901	5.8744	0	0
M1	1.08162089861099	1.486541	0.7276	0.468026	0.234013
M2	0.406425419305482	1.49262	0.2723	0.785786	0.392893
M3	1.80572354132149	1.486453	1.2148	0.226422	0.113211
M4	1.63550358771727	1.525793	1.0719	0.285544	0.142772
M5	1.03025002187994	1.527359	0.6745	0.501048	0.250524
M6	1.85898982437003	1.532393	1.2131	0.227053	0.113527
M7	2.36391663137686	1.522166	1.553	0.122604	0.061302
M8	2.76323282770756	1.518104	1.8202	0.070793	0.035396
M9	2.13843125245325	1.514019	1.4124	0.159969	0.079984
M10	1.45968193131887	1.512799	0.9649	0.336207	0.168104
M11	0.411295472818057	1.519187	0.2707	0.786981	0.39349
t	-0.0112734900892955	0.006674	-1.6891	0.09335	0.046675

Multiple Linear Regression - Regression Statistics
Multiple R	0.483105972728421
R-squared	0.233391380885874
Adjusted R-squared	0.164660952965297
F-TEST (value)	3.39575044048285
F-TEST (DF numerator)	13
F-TEST (DF denominator)	145
p-value	0.000140547979544881
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.85416881771716
Sum Squared Residuals	2153.91950494218

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	24	23.5029768091459	0.497023190854101
2	25	23.1448905974025	1.85510940259752
3	30	21.9058531681188	8.0941468318812
4	19	22.0527424820766	-3.05274248207656
5	22	21.4362154261499	0.56378457385005
6	22	21.5969162232482	0.40308377675185
7	25	23.4041005707709	1.59589942922912
8	23	22.4786122464071	0.52138775359292
9	17	22.4993026963661	-5.49930269636609
10	21	21.4808971274911	-0.4808971274911
11	19	22.3915337248088	-3.39153372480879
12	19	24.2676440654606	-5.26764406546056
13	15	23.0393121704231	-8.03931217042313
14	16	20.7109294127718	-4.71092941277183
15	23	21.1138057717446	1.88619422825536
16	27	19.9471640550972	7.05283594490278
17	22	22.2860818180323	-0.286081818032306
18	14	21.1332515845253	-7.1332515845253
19	22	23.2688186896993	-1.26881868969933
20	23	27.2690717301051	-4.26907173010505
21	23	25.3194656341562	-2.31946563415624
22	21	26.9281221264917	-5.92812212649167
23	19	21.5994863284347	-2.59948632843465
24	18	24.4607449420403	-6.46074494204031
25	20	21.5904992587464	-1.59049925874639
26	23	19.9188820163977	3.08111798360231
27	25	22.6204376789296	2.3795623210704
28	19	22.7673269928874	-3.76732699288738
29	24	22.4791826946121	1.52081730538794
30	22	21.6547352187564	0.345264781243643
31	25	24.447067839233	0.552932160767008
32	26	25.1634933031257	0.836506696874298
33	29	24.8558009954334	4.1441990045666
34	32	23.8373954265584	8.16260457344159
35	25	20.1506734167579	4.8493265832421
36	29	24.6538458186201	4.34615418137993
37	28	26.0525759847931	1.94742401520694
38	17	18.7984518623722	-1.79845186237224
39	28	26.4257488896737	1.57425111032633
40	29	23.9455761424210	5.05442385757896
41	26	24.6425801170996	1.35741988290038
42	25	23.1613671259413	1.83863287405868
43	14	22.3414894122536	-8.34148941225363
44	25	22.4011493608437	2.59885063915625
45	26	22.7502225684540	3.24977743154596
46	20	20.4182859689739	-0.418285968973859
47	18	21.0005398086403	-3.00053980864026
48	32	24.8469466951998	7.15305330480018
49	25	24.6037630731163	0.39623692688369
50	25	21.9469975578137	3.05300244218630
51	23	24.3201704626943	-1.32017046269432
52	21	21.5116149577904	-0.51161495779039
53	20	21.5518534171664	-1.55185341716637
54	15	19.4138749107055	-4.41387491070546
55	30	25.4900351076951	4.5099648923049
56	24	25.2213122986339	-1.22131229863391
57	26	23.2717062026851	2.7282937973149
58	24	20.9397696032049	3.06023039679508
59	22	18.2381958663583	3.76180413364169
60	14	18.4723924187536	-4.47239241875355
61	24	20.5278881002292	3.47211189977085
62	24	21.1549501614396	2.84504983856044
63	24	21.8862092780637	2.11379072193634
64	24	21.3763330767188	2.62366692328116
65	19	18.1327439595818	0.867256040418188
66	31	25.1894826673573	5.81051733264267
67	22	26.3399014995775	-4.33990149957747
68	27	22.7873511140033	4.21264888599674
69	19	18.8674484721466	0.13255152785336
70	25	21.7896359950873	3.21036400491273
71	20	23.3570381077076	-3.35703810770758
72	21	19.9790243259385	1.02097567406149
73	27	24.6615820686245	2.33841793137548
74	23	23.6467303415784	-0.646730341578419
75	25	24.0496067005512	0.950393299448774
76	20	22.8829649839038	-2.88296498390381
77	21	18.9826103514642	2.01738964853583
78	22	22.4271387250754	-0.427138725075379
79	23	22.2640265266903	0.735973473309696
80	25	25.6075140517934	-0.607514051793423
81	25	23.3295251981933	1.67047480180669
82	17	20.9975885987131	-3.99758859871312
83	19	20.9230769230769	-1.92307692307692
84	25	20.1721252025183	4.82787479748173
85	19	22.2276208839939	-3.22762088399387
86	20	20.8843863992965	-0.884386399296465
87	26	22.2724110312232	3.72758896877682
88	23	20.1206210416218	2.87937895837815
89	27	23.7730698351621	3.22693016483786
90	17	21.6350913287012	-4.63509132870123
91	17	24.4274239491779	-7.42742394917786
92	19	19.5613425329985	-0.561342532998458
93	17	20.8955640135627	-3.89556401356266
94	22	22.1758377482468	-0.175837748246784
95	21	20.1310295267028	0.868970473297223
96	32	23.6490536556110	8.35094634438896
97	21	24.7194010641327	-3.71940106413273
98	21	23.3761665794353	-2.37616657943533
99	18	21.4803636348490	-3.48036363484903
100	18	22.2840184641094	-4.28401846410941
101	23	21.9958741658341	1.00412583416591
102	19	20.1862784170245	-1.18627841702448
103	20	22.3218455221985	-2.32184552219851
104	21	22.0531227131373	-1.05312271313732
105	20	23.0589614360502	-3.05896143605022
106	17	23.0257041401291	-6.02570414012914
107	18	20.6525131609338	-2.65251316093383
108	19	21.2150924709804	-2.21509247098038
109	22	22.6138226371534	-0.613822637153377
110	15	19.3002916065482	-4.30029160654817
111	14	19.3747852078697	-5.37478520786968
112	18	24.1190331289457	-6.11903312894567
113	24	21.2038267694599	2.79617323054006
114	35	23.3348241124659	11.6651758875341
115	29	18.5743533069627	10.4256466930373
116	21	21.2610753167632	-0.261075316763173
117	25	21.6101485243735	3.38985147562653
118	20	20.2633601978472	-0.263360197847188
119	22	21.8307623104675	0.169237689532508
120	13	19.7662795593036	-6.76627955930363
121	26	23.7920717866870	2.20792821331296
122	17	18.1798614525227	-1.17986145252272
123	25	22.1949481456598	2.80505185434016
124	20	19.7147753984072	0.285224601592786
125	19	20.4117793730858	-1.41177937308579
126	21	21.5576284431379	-0.557628443137896
127	22	20.4093679717989	1.59063202820108
128	24	22.4393244662968	1.56067553370317
129	21	21.1464838856506	-0.146483885650622
130	26	25.3822024391965	0.61779756080354
131	24	20.7103321564420	3.28966784355796
132	16	18.3174666476269	-2.31746664762688
133	23	19.7161968137999	3.28380318620012
134	18	18.7013450867538	-0.701345086753777
135	16	21.731283506937	-5.73128350693699
136	26	23.1917038515000	2.80829614850002
137	19	19.9481147343629	-0.948114734362946
138	21	20.7655810467637	0.234418953236252
139	21	20.9308516060300	0.0691483939700265
140	22	22.9608081005279	-0.96080810052789
141	23	24.9517950963947	-1.95179509639469
142	29	24.261772285171	4.73822771482899
143	21	21.2318157906731	-0.231815790673101
144	21	19.8240985548118	1.17590144518816
145	23	20.8944459633335	2.10555403666646
146	27	22.8350390551491	4.16496094485085
147	25	24.8798292023785	0.120170797621541
148	21	21.0861254245206	-0.086125424520628
149	10	19.1560673379888	-9.1560673379888
150	20	21.9438301962974	-1.94383019629741
151	26	21.7807179979123	4.21928200208767
152	24	24.7958227653642	-0.795822765364149
153	29	27.4435752765336	1.55642472346645
154	19	21.4994283428891	-2.49942834288906
155	24	19.7830028789963	4.21699712100365
156	19	18.3752856431351	0.624714356864907
157	24	23.0578433858211	0.942156614178902
158	22	20.4010778705185	1.59892212948151
159	17	24.7445473213069	-7.74454732130691

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.93874717849241	0.122505643015179	0.0612528215075893
18	0.912024638561513	0.175950722876974	0.0879753614384872
19	0.851669064270418	0.296661871459163	0.148330935729582
20	0.795824742323816	0.408350515352368	0.204175257676184
21	0.820051155885091	0.359897688229817	0.179948844114909
22	0.771324099258882	0.457351801482237	0.228675900741118
23	0.720179929029538	0.559640141940924	0.279820070970462
24	0.674673485662807	0.650653028674387	0.325326514337193
25	0.662532984301595	0.67493403139681	0.337467015698405
26	0.673968393098605	0.65206321380279	0.326031606901395
27	0.599061613273298	0.801876773453404	0.400938386726702
28	0.558445712908388	0.883108574183223	0.441554287091612
29	0.520247162580927	0.959505674838146	0.479752837419073
30	0.529093059151996	0.941813881696008	0.470906940848004
31	0.466376087612321	0.932752175224642	0.533623912387679
32	0.431558318984623	0.863116637969246	0.568441681015377
33	0.589968069285319	0.820063861429363	0.410031930714681
34	0.798624783665516	0.402750432668967	0.201375216334483
35	0.801231603544092	0.397536792911816	0.198768396455908
36	0.865277431564064	0.269445136871872	0.134722568435936
37	0.85864254968825	0.282714900623501	0.141357450311750
38	0.871505184299316	0.256989631401368	0.128494815700684
39	0.845304389275885	0.309391221448231	0.154695610724115
40	0.840310330024474	0.319379339951053	0.159689669975526
41	0.801359768315837	0.397280463368326	0.198640231684163
42	0.765953808361497	0.468092383277006	0.234046191638503
43	0.922251171493404	0.155497657013191	0.0777488285065957
44	0.901847414625894	0.196305170748211	0.0981525853741056
45	0.88270132229675	0.234597355406498	0.117298677703249
46	0.867222050810017	0.265555898379966	0.132777949189983
47	0.862519508803783	0.274960982392434	0.137480491196217
48	0.909719305274177	0.180561389451646	0.0902806947258229
49	0.885500005716966	0.228999988566068	0.114499994283034
50	0.863166065453693	0.273667869092614	0.136833934546307
51	0.876446274433753	0.247107451132493	0.123553725566247
52	0.860819944958613	0.278360110082775	0.139180055041387
53	0.848134442886428	0.303731114227145	0.151865557113572
54	0.860903957930008	0.278192084139985	0.139096042069992
55	0.864475481886133	0.271049036227734	0.135524518113867
56	0.84183425378702	0.31633149242596	0.15816574621298
57	0.815681165500488	0.368637668999023	0.184318834499512
58	0.78936770192333	0.421264596153339	0.210632298076670
59	0.772639269603574	0.454721460792852	0.227360730396426
60	0.797538854119588	0.404922291760824	0.202461145880412
61	0.780063589094086	0.439872821811828	0.219936410905914
62	0.750359834930401	0.499280330139198	0.249640165069599
63	0.728833844512606	0.542332310974788	0.271166155487394
64	0.699358969012784	0.601282061974432	0.300641030987216
65	0.656864712105634	0.686270575788732	0.343135287894366
66	0.68507065543135	0.6298586891373	0.31492934456865
67	0.718721433593516	0.562557132812967	0.281278566406484
68	0.712043591767296	0.575912816465409	0.287956408232704
69	0.672563590649973	0.654872818700054	0.327436409350027
70	0.65431021265736	0.691379574685279	0.345689787342640
71	0.662269182397974	0.675461635204052	0.337730817602026
72	0.616968126261803	0.766063747476395	0.383031873738198
73	0.577264991502798	0.845470016994405	0.422735008497202
74	0.543946557681907	0.912106884636185	0.456053442318093
75	0.526362029438142	0.947275941123717	0.473637970561858
76	0.526056768040518	0.947886463918964	0.473943231959482
77	0.493360008721391	0.986720017442781	0.506639991278609
78	0.446338033265781	0.892676066531562	0.553661966734219
79	0.398254132889778	0.796508265779557	0.601745867110222
80	0.358086150796796	0.716172301593592	0.641913849203204
81	0.323565523840246	0.647131047680491	0.676434476159754
82	0.339749319372317	0.679498638744634	0.660250680627683
83	0.308213231992832	0.616426463985664	0.691786768007168
84	0.327052022762512	0.654104045525024	0.672947977237488
85	0.318205248014795	0.63641049602959	0.681794751985205
86	0.281884249592745	0.56376849918549	0.718115750407255
87	0.31564661802409	0.63129323604818	0.68435338197591
88	0.313640843664746	0.627281687329491	0.686359156335254
89	0.314196946701007	0.628393893402013	0.685803053298993
90	0.337475452417463	0.674950904834925	0.662524547582537
91	0.514096219446481	0.971807561107037	0.485903780553519
92	0.469652882115221	0.939305764230441	0.530347117884779
93	0.462025033993136	0.924050067986271	0.537974966006864
94	0.416231540505635	0.83246308101127	0.583768459494365
95	0.369872036382246	0.739744072764492	0.630127963617754
96	0.593389216736769	0.813221566526463	0.406610783263231
97	0.596430929510316	0.807138140979369	0.403569070489684
98	0.563577367694925	0.87284526461015	0.436422632305075
99	0.557436836681115	0.885126326637771	0.442563163318885
100	0.552833045513074	0.894333908973853	0.447166954486926
101	0.52700373070844	0.94599253858312	0.47299626929156
102	0.488194601162265	0.97638920232453	0.511805398837735
103	0.509554889951283	0.980890220097434	0.490445110048717
104	0.458604239687327	0.917208479374653	0.541395760312673
105	0.439276812079479	0.878553624158957	0.560723187920521
106	0.522643788168953	0.954712423662095	0.477356211831047
107	0.524116327792422	0.951767344415156	0.475883672207578
108	0.484088742390103	0.968177484780206	0.515911257609897
109	0.461803049888086	0.923606099776172	0.538196950111914
110	0.513953570720015	0.97209285855997	0.486046429279985
111	0.523009715689854	0.953980568620293	0.476990284310146
112	0.715902570966377	0.568194858067245	0.284097429033623
113	0.707786934430235	0.58442613113953	0.292213065569765
114	0.937065154207579	0.125869691584843	0.0629348457924215
115	0.986121743364264	0.027756513271472	0.013878256635736
116	0.979393154651758	0.0412136906964839	0.0206068453482420
117	0.979505853123624	0.0409882937527519	0.0204941468763760
118	0.970037672683585	0.0599246546328292	0.0299623273164146
119	0.964739683140257	0.070520633719485	0.0352603168597425
120	0.991142244811425	0.0177155103771499	0.00885775518857494
121	0.989844179900676	0.0203116401986479	0.0101558200993240
122	0.988320173383937	0.0233596532321261	0.0116798266160631
123	0.995344279280725	0.00931144143854968	0.00465572071927484
124	0.992162920810037	0.0156741583799254	0.0078370791899627
125	0.988709673103367	0.0225806537932662	0.0112903268966331
126	0.981881389369675	0.0362372212606498	0.0181186106303249
127	0.972201869633234	0.0555962607335321	0.0277981303667660
128	0.962163877146241	0.0756722457075179	0.0378361228537590
129	0.952022656204235	0.0959546875915294	0.0479773437957647
130	0.950152894430446	0.0996942111391073	0.0498471055695537
131	0.925668873635266	0.148662252729467	0.0743311263647336
132	0.92522383915043	0.149552321699139	0.0747761608495694
133	0.90338474241641	0.193230515167178	0.0966152575835892
134	0.869139249914396	0.261721500171207	0.130860750085604
135	0.822789421516752	0.354421156966497	0.177210578483248
136	0.750707428480774	0.498585143038453	0.249292571519227
137	0.792057547005877	0.415884905988245	0.207942452994123
138	0.72048748482212	0.559025030355761	0.279512515177880
139	0.689799759049551	0.620400481900897	0.310200240950449
140	0.561604075569739	0.876791848860522	0.438395924430261
141	0.481881591319332	0.963763182638665	0.518118408680668
142	0.475159026424130	0.950318052848261	0.524840973575870

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.00793650793650794	OK
5% type I error level	10	0.0793650793650794	NOK
10% type I error level	16	0.126984126984127	NOK