Repository of Reproducible Computations

Multiple Linear Regression - Estimated Regression Equation

Parameter[t] = + 28.2113145628771 -1.21076082808972Variable[t] -0.0662441512071265S.D.[t] + 0.219982378476394`T-STAT`[t] -0.138042493202293`2-tail`[t] -0.267683206546856`1-tail`[t] + 0.415179865256042MultipleLinearRegression[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)	28.2113145628771	14.945756	1.8876	0.060988	0.030494
Variable	-1.21076082808972	1.484819	-0.8154	0.416104	0.208052
S.D.	-0.0662441512071265	0.063225	-1.0478	0.296415	0.148207
`T-STAT`	0.219982378476394	0.112769	1.9507	0.052927	0.026464
`2-tail`	-0.138042493202293	0.105255	-1.3115	0.191667	0.095833
`1-tail`	-0.267683206546856	0.1315	-2.0356	0.043526	0.021763
MultipleLinearRegression	0.415179865256042	0.076265	5.4439	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.475107146524304
R-squared	0.225726800678466
Adjusted R-squared	0.195163384915774
F-TEST (value)	7.38552269259133
F-TEST (DF numerator)	6
F-TEST (DF denominator)	152
p-value	6.01600129268576e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.50327124217684
Sum Squared Residuals	1865.48222823202

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	26	24.0380116421254	1.96198835787455
2	23	25.3499030197419	-2.34990301974192
3	25	25.4754187312743	-0.475418731274257
4	23	23.1283877855251	-0.128387785525072
5	19	22.9502296744362	-3.95022967443618
6	29	24.0580491468969	4.94195085310306
7	25	24.7689434225897	0.231056577410302
8	21	22.5497602295545	-1.54976022955452
9	22	21.9587949609711	0.0412050390288867
10	25	22.4478041876181	2.55219581238185
11	24	20.1834857808795	3.81651421912048
12	18	19.7590757706424	-1.75907577064236
13	22	18.3723483201740	3.62765167982603
14	15	20.6720873616672	-5.67208736166723
15	22	23.4458223210569	-1.4458223210569
16	28	24.2571921190913	3.74280788090874
17	20	22.1748462508084	-2.17484625080836
18	12	19.0224880776687	-7.02248807766865
19	24	21.4521344910145	2.54786550898554
20	20	21.3877901376630	-1.38779013766305
21	21	23.2363704932754	-2.23637049327542
22	20	20.6606202172801	-0.660620217280076
23	21	19.1683613628413	1.83163863715866
24	23	21.0812378834395	1.91876211656055
25	28	21.9085377998056	6.09146220019442
26	24	21.8730095344099	2.12699046559012
27	24	23.4614246582104	0.538575341789579
28	24	20.3771366822311	3.62286331776894
29	23	21.9726643776973	1.02733562230274
30	23	22.6907025024683	0.30929749753174
31	29	24.2446853910721	4.75531460892793
32	24	21.9943008716901	2.00569912830986
33	18	25.0181996958846	-7.0181996958846
34	25	25.9629248535507	-0.962924853550714
35	21	22.5810225057866	-1.58102250578665
36	26	26.6953459132976	-0.695345913297585
37	22	25.1140100044524	-3.11401000445245
38	22	22.8253821301005	-0.825382130100459
39	22	22.5517548560342	-0.551754856034195
40	23	25.5973147716882	-2.59731477168816
41	30	22.89545874919	7.10454125081001
42	23	22.6639292293579	0.336070770642107
43	17	18.7115504081909	-1.71155040819089
44	23	23.7897978251764	-0.789797825176364
45	23	24.2514329548606	-1.25143295486061
46	25	22.3934967831105	2.60650321688952
47	24	20.7223871608150	3.27761283918504
48	24	27.4346766009058	-3.4346766009058
49	23	22.9639707423358	0.0360292576641574
50	21	23.8188359040196	-2.81883590401957
51	24	25.689268014907	-1.68926801490697
52	24	21.8119545661137	2.18804543388633
53	28	21.4842687769198	6.51573122308023
54	16	21.0236250829993	-5.0236250829993
55	20	19.7974410658806	0.202558934119395
56	29	23.4074704661304	5.59252953386964
57	27	23.8428596660418	3.15714033395823
58	22	23.1630373613017	-1.16303736130166
59	28	23.9455798738586	4.05442012614142
60	16	20.3525238918059	-4.35252389180595
61	25	22.8560551065421	2.14394489345793
62	24	23.4760680066282	0.523931993371768
63	28	23.6427953662461	4.35720463375388
64	24	24.2219104420497	-0.221910442049688
65	23	22.6726225365779	0.327377463422146
66	30	26.8922094115959	3.10779058840406
67	24	21.2840205804030	2.71597941959703
68	21	24.0987471132405	-3.09874711324051
69	25	23.2691731098696	1.73082689013040
70	25	23.9181929748787	1.08180702512133
71	22	20.7820340168568	1.21796598314317
72	23	22.4275211010603	0.57247889893972
73	26	22.8262932570107	3.17370674298933
74	23	21.6022183253514	1.3977816746486
75	25	23.0639597509677	1.93604024903234
76	21	21.2855363232984	-0.285536323298390
77	25	23.6404111344227	1.35958886557731
78	24	22.1445809202261	1.85541907977393
79	29	23.5121022672524	5.48789773274761
80	22	23.6475211919108	-1.64752119191078
81	27	23.5679562571882	3.43204374281183
82	26	19.6293304628626	6.37066953713738
83	22	21.3047670242071	0.695232975792905
84	24	22.0326669603443	1.96733303965569
85	27	23.1055055643977	3.89449443560234
86	24	21.3535202379267	2.64647976207328
87	24	24.8501959300918	-0.850195930091759
88	29	24.355086122236	4.64491387776402
89	22	22.1422701689175	-0.142270168917533
90	21	20.5726565389056	0.427343461094374
91	24	20.4451088014099	3.55489119859013
92	24	21.7191549172559	2.28084508274409
93	23	21.940865263704	1.05913473629601
94	20	22.3033791385044	-2.30337913850444
95	27	21.3483864950151	5.65161350498487
96	26	23.4246262317058	2.57537376829417
97	25	21.9468890568043	3.05311094319566
98	21	20.0642106313397	0.935789368660327
99	21	20.7678540256853	0.232145974314726
100	19	20.3833782507911	-1.38337825079114
101	21	21.5815820263659	-0.581582026365927
102	21	21.2757289453639	-0.275728945363892
103	16	19.7626225329336	-3.76262253293362
104	22	20.6424782949367	1.35752170506331
105	29	21.7681419173125	7.23185808268746
106	15	21.7285300518644	-6.72853005186444
107	17	20.6914683311992	-3.69146833119921
108	15	19.9107210220628	-4.91072102206282
109	21	21.6461601660544	-0.646160166054349
110	21	21.0223978312602	-0.0223978312602254
111	19	19.2846170934275	-0.284617093427470
112	24	18.0610882808013	5.93891171919871
113	20	22.2498571897503	-2.24985718975033
114	17	25.0894942854413	-8.08949428544127
115	23	24.8187640667656	-1.81876406676557
116	24	22.3894676164898	1.61053238351019
117	14	22.0562702744901	-8.05627027449007
118	19	22.8524775017181	-3.85247750171813
119	24	22.1815265791481	1.81847342085194
120	13	20.4208948976005	-7.42089489760046
121	22	25.3600782782672	-3.36007827826717
122	16	21.1238596734177	-5.12385967341765
123	19	23.2284747086461	-4.22847470864615
124	25	22.7391461483101	2.26085385168991
125	25	24.1550100269908	0.844989973009183
126	23	21.4292185546407	1.57078144535926
127	24	23.5527023191067	0.44729768089329
128	26	23.5030131096226	2.49698689037737
129	26	21.4881687516386	4.51183124836138
130	25	24.1321460098712	0.867853990128754
131	18	22.2913902011632	-4.29139020116322
132	21	19.8685435422477	1.13145645775229
133	26	23.6496505606757	2.35034943932426
134	23	21.9637812000777	1.03621879992229
135	23	19.7573051646885	3.24269483531153
136	22	22.5981238379304	-0.59812383793039
137	20	22.3968907626009	-2.39689076260087
138	13	22.0661760017937	-9.0661760017937
139	24	21.3905331322975	2.60946686770245
140	15	21.5036713077125	-6.5036713077125
141	14	23.0937406475822	-9.09374064758223
142	22	24.0489169164051	-2.04891691640508
143	10	17.6456931542631	-7.64569315426309
144	24	24.4263784690027	-0.426378469002686
145	22	21.8302492712579	0.169750728742082
146	24	25.7876336500023	-1.78763365000229
147	19	21.6536043888869	-2.65360438888688
148	20	22.0851919634486	-2.08519196344857
149	13	17.1097811441646	-4.1097811441646
150	20	20.1003643180544	-0.100364318054432
151	22	23.1857601196823	-1.18576011968228
152	24	23.3827593263361	0.617240673663883
153	29	23.2737759886985	5.72622401130151
154	12	20.9758996574622	-8.97589965746221
155	20	20.9222146380677	-0.922214638067708
156	21	21.4451629067001	-0.445162906700133
157	24	23.6330070353948	0.366992964605206
158	22	21.8925934477462	0.107406552253809
159	20	17.7221746839407	2.27782531605929

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.527011339441507	0.945977321116986	0.472988660558493
11	0.562050758269062	0.875898483461875	0.437949241730938
12	0.488797048040875	0.97759409608175	0.511202951959125
13	0.540312608910688	0.919374782178624	0.459687391089312
14	0.741606301267104	0.516787397465791	0.258393698732896
15	0.654975316425638	0.690049367148725	0.345024683574363
16	0.624349814096279	0.751300371807441	0.375650185903721
17	0.538687106536784	0.922625786926432	0.461312893463216
18	0.676523849957848	0.646952300084304	0.323476150042152
19	0.6017877142567	0.796424571486599	0.398212285743300
20	0.58900929980256	0.82198140039488	0.41099070019744
21	0.525027626121064	0.949944747757872	0.474972373878936
22	0.455644610275878	0.911289220551755	0.544355389724122
23	0.404802514498525	0.80960502899705	0.595197485501475
24	0.409292695949612	0.818585391899223	0.590707304050388
25	0.571837157525294	0.856325684949412	0.428162842474706
26	0.510576212129371	0.978847575741258	0.489423787870629
27	0.443519562686604	0.887039125373209	0.556480437313396
28	0.437932035294218	0.875864070588435	0.562067964705782
29	0.373771831625193	0.747543663250386	0.626228168374807
30	0.313336025758918	0.626672051517836	0.686663974241082
31	0.347263297377554	0.694526594755107	0.652736702622446
32	0.296163153698190	0.592326307396379	0.70383684630181
33	0.521927365358015	0.95614526928397	0.478072634641985
34	0.47081292178791	0.94162584357582	0.52918707821209
35	0.432862899334543	0.865725798669087	0.567137100665457
36	0.375546236339169	0.751092472678338	0.624453763660831
37	0.348910287323424	0.697820574646848	0.651089712676576
38	0.297272496870143	0.594544993740286	0.702727503129857
39	0.249904028542292	0.499808057084583	0.750095971457708
40	0.22256082533694	0.44512165067388	0.77743917466306
41	0.375203931367904	0.750407862735809	0.624796068632096
42	0.323419485366194	0.646838970732388	0.676580514633806
43	0.291372184891437	0.582744369782873	0.708627815108563
44	0.247786889016576	0.495573778033151	0.752213110983424
45	0.211393904844777	0.422787809689554	0.788606095155223
46	0.191987017977891	0.383974035955782	0.80801298202211
47	0.179547882285089	0.359095764570178	0.820452117714911
48	0.164459892538351	0.328919785076702	0.83554010746165
49	0.134369240006066	0.268738480012131	0.865630759993934
50	0.124728456293019	0.249456912586039	0.875271543706981
51	0.102954440158644	0.205908880317288	0.897045559841356
52	0.0878329701028204	0.175665940205641	0.91216702989718
53	0.147392747581936	0.294785495163872	0.852607252418064
54	0.176759866229267	0.353519732458534	0.823240133770733
55	0.165314066746353	0.330628133492705	0.834685933253647
56	0.222746328051185	0.445492656102369	0.777253671948815
57	0.21518432489016	0.43036864978032	0.78481567510984
58	0.184195410631712	0.368390821263425	0.815804589368287
59	0.197396035986441	0.394792071972882	0.80260396401356
60	0.225127634390958	0.450255268781916	0.774872365609042
61	0.198905633976573	0.397811267953146	0.801094366023427
62	0.167144063564595	0.33428812712919	0.832855936435405
63	0.182384014069960	0.364768028139919	0.81761598593004
64	0.153297483576505	0.306594967153011	0.846702516423495
65	0.126476444675909	0.252952889351819	0.87352355532409
66	0.122928310183972	0.245856620367945	0.877071689816028
67	0.112290924195902	0.224581848391804	0.887709075804098
68	0.111389708749007	0.222779417498014	0.888610291250993
69	0.094797850547306	0.189595701094612	0.905202149452694
70	0.0773954034562743	0.154790806912549	0.922604596543726
71	0.0628992200876907	0.125798440175381	0.93710077991231
72	0.0496820132984475	0.099364026596895	0.950317986701552
73	0.0466400462749179	0.0932800925498359	0.953359953725082
74	0.0373621752075985	0.074724350415197	0.962637824792401
75	0.031051733020051	0.062103466040102	0.968948266979949
76	0.0238172017328579	0.0476344034657158	0.976182798267142
77	0.0187002305121636	0.0374004610243272	0.981299769487836
78	0.0149689403621707	0.0299378807243413	0.98503105963783
79	0.0224924007048702	0.0449848014097404	0.97750759929513
80	0.0179314270308470	0.0358628540616939	0.982068572969153
81	0.0175338942105030	0.0350677884210059	0.982466105789497
82	0.0313614803069281	0.0627229606138563	0.968638519693072
83	0.024186212215663	0.048372424431326	0.975813787784337
84	0.0201798986454488	0.0403597972908976	0.97982010135455
85	0.0221020803926987	0.0442041607853974	0.977897919607301
86	0.0195896963605925	0.0391793927211851	0.980410303639407
87	0.0148920824096964	0.0297841648193928	0.985107917590304
88	0.0194432873314934	0.0388865746629869	0.980556712668507
89	0.0152908309903176	0.0305816619806352	0.984709169009682
90	0.0114418907049145	0.0228837814098291	0.988558109295085
91	0.0115015183841046	0.0230030367682091	0.988498481615895
92	0.0100556605744891	0.0201113211489783	0.98994433942551
93	0.00771186522967623	0.0154237304593525	0.992288134770324
94	0.00637459672667722	0.0127491934533544	0.993625403273323
95	0.0116799873633404	0.0233599747266807	0.98832001263666
96	0.0105781200811641	0.0211562401623283	0.989421879918836
97	0.0100612562765505	0.0201225125531011	0.98993874372345
98	0.00769911304184285	0.0153982260836857	0.992300886958157
99	0.00568082481582094	0.0113616496316419	0.99431917518418
100	0.0043489785681723	0.0086979571363446	0.995651021431828
101	0.00321348308435686	0.00642696616871373	0.996786516915643
102	0.00228647225577789	0.00457294451155579	0.997713527744222
103	0.00244472023349372	0.00488944046698744	0.997555279766506
104	0.00191524517799058	0.00383049035598116	0.99808475482201
105	0.0081144813593183	0.0162289627186366	0.991885518640682
106	0.0181618719205615	0.0363237438411230	0.981838128079439
107	0.0180245037378093	0.0360490074756186	0.98197549626219
108	0.0227179481921593	0.0454358963843186	0.97728205180784
109	0.0175277218388999	0.0350554436777997	0.9824722781611
110	0.0128020488841614	0.0256040977683228	0.987197951115839
111	0.0092686140169013	0.0185372280338026	0.990731385983099
112	0.0227283733594771	0.0454567467189542	0.977271626640523
113	0.0205971811202094	0.0411943622404189	0.97940281887979
114	0.0572002938414689	0.114400587682938	0.942799706158531
115	0.0484627048912369	0.0969254097824738	0.951537295108763
116	0.0392764367838186	0.0785528735676373	0.960723563216181
117	0.115731466764411	0.231462933528823	0.884268533235589
118	0.110887113341822	0.221774226683644	0.889112886658178
119	0.0983127910559482	0.196625582111896	0.901687208944052
120	0.171833930614441	0.343667861228882	0.82816606938556
121	0.163712493436824	0.327424986873648	0.836287506563176
122	0.195066967106405	0.39013393421281	0.804933032893595
123	0.188054053203408	0.376108106406815	0.811945946796592
124	0.187235424914874	0.374470849829747	0.812764575085126
125	0.170002447239331	0.340004894478663	0.829997552760669
126	0.138341398877432	0.276682797754865	0.861658601122568
127	0.108178568043679	0.216357136087359	0.89182143195632
128	0.111630464935294	0.223260929870589	0.888369535064706
129	0.160133500921297	0.320267001842594	0.839866499078703
130	0.137951852096966	0.275903704193931	0.862048147903034
131	0.120423104329633	0.240846208659267	0.879576895670366
132	0.104299007980801	0.208598015961602	0.8957009920192
133	0.0956741758549077	0.191348351709815	0.904325824145092
134	0.0781005925981872	0.156201185196374	0.921899407401813
135	0.106580435245780	0.213160870491559	0.89341956475422
136	0.0790287321188473	0.158057464237695	0.920971267881153
137	0.057635798250948	0.115271596501896	0.942364201749052
138	0.146870833753747	0.293741667507494	0.853129166246253
139	0.20813414994964	0.41626829989928	0.79186585005036
140	0.188534489726447	0.377068979452894	0.811465510273553
141	0.406055845705896	0.812111691411792	0.593944154294104
142	0.356404340277384	0.712808680554768	0.643595659722616
143	0.66603697563369	0.667926048732619	0.333963024366309
144	0.604830923460292	0.790338153079417	0.395169076539708
145	0.494206523128988	0.988413046257976	0.505793476871012
146	0.423316957865472	0.846633915730943	0.576683042134528
147	0.433611033957532	0.867222067915064	0.566388966042468
148	0.303307218142269	0.606614436284538	0.69669278185773
149	0.211421302306707	0.422842604613414	0.788578697693293

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	5	0.0357142857142857	NOK
5% type I error level	37	0.264285714285714	NOK
10% type I error level	44	0.314285714285714	NOK