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MR 2 no seasonal dummies

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 29 Dec 2010 17:35:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn.htm/, Retrieved Wed, 29 Dec 2010 18:34:13 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

34420 34070 33978 34484 34645 34410 34534 35019 35508 35488 35709 36534 36066 35724 35727 36281 36017 35780 36003 36285 36419 36413 36663 37451 37063 36613 36564 37064 36817 36621 36798 36967 36926 36975 37324 38159 37776 37465 37451 37944 37737 37603 37813 37960 37934 37975 38241 39176 39137 38797 38730 39031 38851 38727 39291 39407 39326 39326 39617 40458 40425 40092 39939 40174 40065 39922 40107 40163 40116 40118 40416 41215 40852 40497 40430 40766 40626 40442 40590 40673 40660 40736 41082 41873 41507 41104 40963 41227 41063 40873 41016 41433 41345 41375 41597 42225 41937 41642 41551 41866 41744 41615 41764 41828 41786 41852 42183 42937 42635 42292 42202 42577 42600 42433 42584 42660 42659 42712 43039 43664 43397 43110 43005 43159 43066 42977 43139 43226 43242 43348 43605 44225 43983 43754 43632 43868 43864 43808 43954 44032 44090 44210 44435 44919 44785 44616 44 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Multiple Linear Regression - Estimated Regression Equation

Coins[t] = + 36021.7926972397 + 51.9257782124659t + 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)	36021.7926972397	117.172507	307.4253	0	0
t	51.9257782124659	0.940667	55.201	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.96678107994094
R-squared	0.934665656531772
Adjusted R-squared	0.934358922524879
F-TEST (value)	3047.15367558689
F-TEST (DF numerator)	1
F-TEST (DF denominator)	213
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	856.048172662384
Sum Squared Residuals	156090334.944663

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	34420	36073.7184754523	-1653.7184754523
2	34070	36125.6442536646	-2055.64425366463
3	33978	36177.5700318771	-2199.57003187713
4	34484	36229.4958100896	-1745.49581008959
5	34645	36281.4215883021	-1636.42158830206
6	34410	36333.3473665145	-1923.34736651452
7	34534	36385.273144727	-1851.27314472699
8	35019	36437.1989229395	-1418.19892293946
9	35508	36489.1247011519	-981.124701151922
10	35488	36541.0504793644	-1053.05047936439
11	35709	36592.9762575769	-883.976257576855
12	36534	36644.9020357893	-110.90203578932
13	36066	36696.8278140018	-630.827814001786
14	35724	36748.7535922143	-1024.75359221425
15	35727	36800.6793704267	-1073.67937042672
16	36281	36852.6051486392	-571.605148639183
17	36017	36904.5309268517	-887.53092685165
18	35780	36956.4567050641	-1176.45670506412
19	36003	37008.3824832766	-1005.38248327658
20	36285	37060.308261489	-775.308261489048
21	36419	37112.2340397015	-693.234039701514
22	36413	37164.159817914	-751.159817913978
23	36663	37216.0855961264	-553.085596126445
24	37451	37268.0113743389	182.988625661089
25	37063	37319.9371525514	-256.937152551377
26	36613	37371.8629307638	-758.862930763843
27	36564	37423.7887089763	-859.788708976309
28	37064	37475.7144871888	-411.714487188775
29	36817	37527.6402654012	-710.64026540124
30	36621	37579.5660436137	-958.566043613706
31	36798	37631.4918218262	-833.491821826172
32	36967	37683.4176000386	-716.417600038638
33	36926	37735.3433782511	-809.343378251104
34	36975	37787.2691564636	-812.26915646357
35	37324	37839.194934676	-515.194934676036
36	38159	37891.1207128885	267.879287111499
37	37776	37943.046491101	-167.046491100967
38	37465	37994.9722693134	-529.972269313433
39	37451	38046.8980475259	-595.8980475259
40	37944	38098.8238257384	-154.823825738365
41	37737	38150.7496039508	-413.749603950831
42	37603	38202.6753821633	-599.675382163297
43	37813	38254.6011603758	-441.601160375763
44	37960	38306.5269385882	-346.526938588229
45	37934	38358.4527168007	-424.452716800694
46	37975	38410.3784950132	-435.378495013161
47	38241	38462.3042732256	-221.304273225627
48	39176	38514.2300514381	661.769948561908
49	39137	38566.1558296506	570.844170349442
50	38797	38618.081607863	178.918392136976
51	38730	38670.0073860755	59.9926139245098
52	39031	38721.933164288	309.066835712044
53	38851	38773.8589425004	77.1410574995779
54	38727	38825.7847207129	-98.7847207128878
55	39291	38877.7104989254	413.289501074646
56	39407	38929.6362771378	477.363722862181
57	39326	38981.5620553503	344.437944649715
58	39326	39033.4878335628	292.512166437248
59	39617	39085.4136117752	531.586388224783
60	40458	39137.3393899877	1320.66061001232
61	40425	39189.2651682002	1235.73483179985
62	40092	39241.1909464126	850.809053587385
63	39939	39293.1167246251	645.883275374919
64	40174	39345.0425028375	828.957497162453
65	40065	39396.96828105	668.031718949987
66	39922	39448.8940592625	473.105940737522
67	40107	39500.819837475	606.180162525055
68	40163	39552.7456156874	610.25438431259
69	40116	39604.6713938999	511.328606100124
70	40118	39656.5971721123	461.402827887658
71	40416	39708.5229503248	707.477049675192
72	41215	39760.4487285373	1454.55127146273
73	40852	39812.3745067497	1039.62549325026
74	40497	39864.3002849622	632.699715037794
75	40430	39916.2260631747	513.773936825328
76	40766	39968.1518413871	797.848158612862
77	40626	40020.0776195996	605.922380400396
78	40442	40072.0033978121	369.996602187931
79	40590	40123.9291760245	466.070823975465
80	40673	40175.854954237	497.145045762999
81	40660	40227.7807324495	432.219267550533
82	40736	40279.7065106619	456.293489338067
83	41082	40331.6322888744	750.367711125601
84	41873	40383.5580670869	1489.44193291314
85	41507	40435.4838452993	1071.51615470067
86	41104	40487.4096235118	616.590376488203
87	40963	40539.3354017243	423.664598275738
88	41227	40591.2611799367	635.738820063272
89	41063	40643.1869581492	419.813041850806
90	40873	40695.1127363617	177.88726363834
91	41016	40747.0385145741	268.961485425874
92	41433	40798.9642927866	634.035707213408
93	41345	40850.8900709991	494.109929000942
94	41375	40902.8158492115	472.184150788476
95	41597	40954.741627424	642.25837257601
96	42225	41006.6674056365	1218.33259436354
97	41937	41058.5931838489	878.406816151079
98	41642	41110.5189620614	531.481037938613
99	41551	41162.4447402739	388.555259726147
100	41866	41214.3705184863	651.629481513681
101	41744	41266.2962966988	477.703703301215
102	41615	41318.2220749113	296.777925088749
103	41764	41370.1478531237	393.852146876283
104	41828	41422.0736313362	405.926368663817
105	41786	41473.9994095486	312.000590451351
106	41852	41525.9251877611	326.074812238886
107	42183	41577.8509659736	605.14903402642
108	42937	41629.776744186	1307.22325581395
109	42635	41681.7025223985	953.297477601488
110	42292	41733.628300611	558.371699389022
111	42202	41785.5540788234	416.445921176556
112	42577	41837.4798570359	739.52014296409
113	42600	41889.4056352484	710.594364751624
114	42433	41941.3314134608	491.668586539158
115	42584	41993.2571916733	590.742808326692
116	42660	42045.1829698858	614.817030114226
117	42659	42097.1087480982	561.891251901761
118	42712	42149.0345263107	562.965473689295
119	43039	42200.9603045232	838.039695476829
120	43664	42252.8860827356	1411.11391726436
121	43397	42304.8118609481	1092.1881390519
122	43110	42356.7376391606	753.262360839431
123	43005	42408.663417373	596.336582626965
124	43159	42460.5891955855	698.4108044145
125	43066	42512.514973798	553.485026202034
126	42977	42564.4407520104	412.559247989568
127	43139	42616.3665302229	522.633469777102
128	43226	42668.2923084354	557.707691564636
129	43242	42720.2180866478	521.78191335217
130	43348	42772.1438648603	575.856135139704
131	43605	42824.0696430728	780.930356927238
132	44225	42875.9954212852	1349.00457871477
133	43983	42927.9211994977	1055.07880050231
134	43754	42979.8469777102	774.15302228984
135	43632	43031.7727559226	600.227244077375
136	43868	43083.6985341351	784.301465864909
137	43864	43135.6243123476	728.375687652443
138	43808	43187.55009056	620.449909439977
139	43954	43239.4758687725	714.524131227511
140	44032	43291.401646985	740.598353015045
141	44090	43343.3274251974	746.672574802579
142	44210	43395.2532034099	814.746796590113
143	44435	43447.1789816224	987.821018377647
144	44919	43499.1047598348	1419.89524016518
145	44785	43551.0305380473	1233.96946195272
146	44616	43602.9563162597	1013.04368374025
147	44496	43654.8820944722	841.117905527783
148	44600	43706.8078726847	893.192127315318
149	44463	43758.7336508971	704.266349102852
150	44232	43810.6594291096	421.340570890386
151	44248	43862.5852073221	385.41479267792
152	44282	43914.5109855345	367.489014465454
153	44311	43966.436763747	344.563236252988
154	44362	44018.3625419595	343.637458040523
155	44617	44070.2883201719	546.711679828057
156	45022	44122.2140983844	899.78590161559
157	44882	44174.1398765969	707.860123403125
158	44594	44226.0656548093	367.934345190659
159	44502	44277.9914330218	224.008566978193
160	44752	44329.9172112343	422.082788765727
161	44690	44381.8429894467	308.157010553261
162	44533	44433.7687676592	99.2312323407953
163	44604	44485.6945458717	118.305454128329
164	44646	44537.6203240841	108.379675915864
165	44652	44589.5461022966	62.4538977033977
166	44718	44641.4718805091	76.528119490932
167	44928	44693.3976587215	234.602341278466
168	45285	44745.323436934	539.676563066
169	45183	44797.2492151465	385.750784853534
170	44964	44849.1749933589	114.825006641068
171	44875	44901.1007715714	-26.1007715713972
172	45071	44953.0265497839	117.973450216137
173	44985	45004.9523279963	-19.9523279963296
174	44854	45056.8781062088	-202.878106208795
175	44925	45108.8038844213	-183.803884421262
176	44970	45160.7296626337	-190.729662633727
177	45011	45212.6554408462	-201.655440846193
178	45107	45264.5812190587	-157.581219058658
179	45306	45316.5069972711	-10.5069972711249
180	45773	45368.4327754836	404.567224516409
181	45625	45420.3585536961	204.641446303944
182	45391	45472.2843319085	-81.284331908523
183	45325	45524.210110121	-199.210110120989
184	45430	45576.1358883335	-146.135888333454
185	45321	45628.0616665459	-307.06166654592
186	45238	45679.9874447584	-441.987444758386
187	45246	45731.9132229708	-485.913222970852
188	45281	45783.8390011833	-502.839001183318
189	45297	45835.7647793958	-538.764779395784
190	45349	45887.6905576082	-538.69055760825
191	45536	45939.6163358207	-403.616335820715
192	45903	45991.5421140332	-88.5421140331812
193	45716	46043.4678922456	-327.467892245647
194	45419	46095.3936704581	-676.393670458114
195	45237	46147.3194486706	-910.31944867058
196	45349	46199.245226883	-850.245226883045
197	45260	46251.1710050955	-991.17100509551
198	45139	46303.096783308	-1164.09678330798
199	45154	46355.0225615204	-1201.02256152044
200	45186	46406.9483397329	-1220.94833973291
201	45262	46458.8741179454	-1196.87411794537
202	45227	46510.7998961578	-1283.79989615784
203	45313	46562.7256743703	-1249.72567437031
204	45564	46614.6514525828	-1050.65145258277
205	45392	46666.5772307952	-1274.57723079524
206	45114	46718.5030090077	-1604.5030090077
207	44996	46770.4287872202	-1774.42878722017
208	45159	46822.3545654326	-1663.35456543264
209	45107	46874.2803436451	-1767.2803436451
210	44963	46926.2061218576	-1963.20612185757
211	45005	46978.13190007	-1973.13190007003
212	45024	47030.0576782825	-2006.0576782825
213	45025	47081.983456495	-2056.98345649497
214	45053	47133.9092347074	-2080.90923470743
215	45143	47185.8350129199	-2042.8350129199

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.0549372409375335	0.109874481875067	0.945062759062467
6	0.0183128918324124	0.0366257836648248	0.981687108167588
7	0.00532152195441303	0.0106430439088261	0.994678478045587
8	0.00354889780512894	0.00709779561025788	0.99645110219487
9	0.00554509208435277	0.0110901841687055	0.994454907915647
10	0.00245567023460622	0.00491134046921244	0.997544329765394
11	0.00106287473023133	0.00212574946046267	0.99893712526977
12	0.00344619151103306	0.00689238302206612	0.996553808488967
13	0.00147496475978487	0.00294992951956973	0.998525035240215
14	0.00172806509953107	0.00345613019906214	0.998271934900469
15	0.00207504434598116	0.00415008869196231	0.99792495565402
16	0.000975814207482918	0.00195162841496584	0.999024185792517
17	0.000831426183154772	0.00166285236630954	0.999168573816845
18	0.0016496157208112	0.0032992314416224	0.998350384279189
19	0.00157852557504939	0.00315705115009877	0.99842147442495
20	0.000992410145140803	0.00198482029028161	0.99900758985486
21	0.000585020979886249	0.0011700419597725	0.999414979020114
22	0.000388083669660425	0.00077616733932085	0.99961191633034
23	0.000211328304041309	0.000422656608082617	0.999788671695959
24	0.000237905770511763	0.000475811541023527	0.999762094229488
25	0.000122835084860213	0.000245670169720426	0.99987716491514
26	0.000160692154314418	0.000321384308628836	0.999839307845686
27	0.000266243667107506	0.000532487334215011	0.999733756332893
28	0.000164911996006421	0.000329823992012841	0.999835088003994
29	0.000184330151810452	0.000368660303620903	0.99981566984819
30	0.00040745582263442	0.00081491164526884	0.999592544177366
31	0.000549638943478401	0.0010992778869568	0.999450361056522
32	0.000563181176770979	0.00112636235354196	0.999436818823229
33	0.000707669018989101	0.0014153380379782	0.99929233098101
34	0.000891301866876671	0.00178260373375334	0.999108698133123
35	0.000719805331344479	0.00143961066268896	0.999280194668656
36	0.000797790548891189	0.00159558109778238	0.99920220945111
37	0.00056149382529596	0.00112298765059192	0.999438506174704
38	0.000570150733513184	0.00114030146702637	0.999429849266487
39	0.000675049580541061	0.00135009916108212	0.99932495041946
40	0.000501804296019584	0.00100360859203917	0.99949819570398
41	0.000484274816714109	0.000968549633428217	0.999515725183286
42	0.000687800935951787	0.00137560187190357	0.999312199064048
43	0.000747939506989505	0.00149587901397901	0.99925206049301
44	0.000742179997933647	0.00148435999586729	0.999257820002066
45	0.000868738092746553	0.00173747618549311	0.999131261907253
46	0.00109085419912022	0.00218170839824045	0.99890914580088
47	0.0010763440127353	0.00215268802547059	0.998923655987265
48	0.0018213599404302	0.0036427198808604	0.99817864005957
49	0.00210911146027766	0.00421822292055532	0.997890888539722
50	0.00177790308747826	0.00355580617495651	0.998222096912522
51	0.00159935376690341	0.00319870753380682	0.998400646233097
52	0.00133751371139819	0.00267502742279639	0.998662486288602
53	0.0012552490370721	0.00251049807414421	0.998744750962928
54	0.00155905625813539	0.00311811251627078	0.998440943741865
55	0.00132601290352586	0.00265202580705172	0.998673987096474
56	0.00111649943444531	0.00223299886889063	0.998883500565555
57	0.00094869504150158	0.00189739008300316	0.999051304958498
58	0.000847283205475424	0.00169456641095085	0.999152716794525
59	0.00069218841526475	0.0013843768305295	0.999307811584735
60	0.00163045085804078	0.00326090171608155	0.99836954914196
61	0.00230976076574823	0.00461952153149646	0.997690239234252
62	0.00182585615534715	0.00365171231069429	0.998174143844653
63	0.00140994791711388	0.00281989583422776	0.998590052082886
64	0.00104866983363785	0.00209733966727569	0.998951330166362
65	0.000803260003412615	0.00160652000682523	0.999196739996587
66	0.000767496087639225	0.00153499217527845	0.99923250391236
67	0.000635021893857642	0.00127004378771528	0.999364978106142
68	0.00053282355908282	0.00106564711816564	0.999467176440917
69	0.00052464754174074	0.00104929508348148	0.99947535245826
70	0.000579047449228774	0.00115809489845755	0.999420952550771
71	0.000461800464859928	0.000923600929719856	0.99953819953514
72	0.000513427351951904	0.00102685470390381	0.999486572648048
73	0.000356186050656141	0.000712372101312282	0.999643813949344
74	0.000345231390722212	0.000690462781444423	0.999654768609278
75	0.000429908913955752	0.000859817827911505	0.999570091086044
76	0.00034301862298867	0.000686037245977341	0.999656981377011
77	0.000372789122815889	0.000745578245631778	0.999627210877184
78	0.000709819184143459	0.00141963836828692	0.999290180815857
79	0.00103965553187481	0.00207931106374963	0.998960344468125
80	0.00142072938478758	0.00284145876957516	0.998579270615212
81	0.0022322416509605	0.00446448330192101	0.99776775834904
82	0.0032944339820041	0.0065888679640082	0.996705566017996
83	0.00303330840315703	0.00606661680631406	0.996966691596843
84	0.00270935021186695	0.0054187004237339	0.997290649788133
85	0.00200134096848766	0.00400268193697533	0.997998659031512
86	0.00242620751472479	0.00485241502944957	0.997573792485275
87	0.00434105012332103	0.00868210024664206	0.99565894987668
88	0.00504536247640268	0.0100907249528054	0.994954637523597
89	0.00871890904220634	0.0174378180844127	0.991281090957794
90	0.0241614661683135	0.0483229323366271	0.975838533831686
91	0.0480373722047761	0.0960747444095523	0.951962627795224
92	0.0534203425735859	0.106840685147172	0.946579657426414
93	0.0702794678022042	0.140558935604408	0.929720532197796
94	0.0938445952397802	0.18768919047956	0.90615540476022
95	0.103313161656502	0.206626323313004	0.896686838343498
96	0.087038905163688	0.174077810327376	0.912961094836312
97	0.0806493394180245	0.161298678836049	0.919350660581975
98	0.102284117073634	0.204568234147267	0.897715882926367
99	0.151262196723594	0.302524393447188	0.848737803276406
100	0.166353276329268	0.332706552658536	0.833646723670732
101	0.2136282743366	0.4272565486732	0.7863717256634
102	0.319001403311483	0.638002806622967	0.680998596688517
103	0.41117238905566	0.82234477811132	0.58882761094434
104	0.507095996904514	0.985808006190973	0.492904003095486
105	0.636347620112586	0.727304759774828	0.363652379887414
106	0.75149570028802	0.497008599423959	0.24850429971198
107	0.78881616637836	0.422367667243282	0.211183833621641
108	0.761509155146148	0.476981689707704	0.238490844853852
109	0.747498214062162	0.505003571875676	0.252501785937838
110	0.795435944409875	0.40912811118025	0.204564055590125
111	0.865199779830814	0.269600440338373	0.134800220169186
112	0.876895167415447	0.246209665169107	0.123104832584553
113	0.891398155742776	0.217203688514448	0.108601844257224
114	0.929060273066106	0.141879453867789	0.0709397269338944
115	0.948932231535301	0.102135536929397	0.0510677684646986
116	0.963218826190044	0.0735623476199112	0.0367811738099556
117	0.97684108058166	0.0463178388366797	0.0231589194183398
118	0.98626521660888	0.0274695667822401	0.0137347833911201
119	0.987291203524986	0.0254175929500287	0.0127087964750144
120	0.984038362414021	0.0319232751719573	0.0159616375859786
121	0.980776134911255	0.0384477301774897	0.0192238650887448
122	0.983558221425123	0.032883557149755	0.0164417785748775
123	0.989527111836643	0.0209457763267143	0.0104728881633572
124	0.992062474996061	0.015875050007877	0.0079375250039385
125	0.995750743377623	0.00849851324475429	0.00424925662237714
126	0.998660663481695	0.00267867303661032	0.00133933651830516
127	0.999478360617714	0.00104327876457304	0.000521639382286521
128	0.999795614509302	0.000408770981396557	0.000204385490698279
129	0.99993895364209	0.000122092715819727	6.10463579098637e-05
130	0.99998025647517	3.94870496616349e-05	1.97435248308174e-05
131	0.999986849542137	2.63009157256793e-05	1.31504578628397e-05
132	0.999979505416362	4.09891672754179e-05	2.04945836377089e-05
133	0.999972004811906	5.5990376188287e-05	2.79951880941435e-05
134	0.99997856433138	4.28713372383467e-05	2.14356686191733e-05
135	0.999991390423714	1.72191525712501e-05	8.60957628562503e-06
136	0.999993198943003	1.36021139940315e-05	6.80105699701574e-06
137	0.999995470481097	9.05903780561825e-06	4.52951890280912e-06
138	0.999998071471193	3.85705761460636e-06	1.92852880730318e-06
139	0.99999878464318	2.43071363954196e-06	1.21535681977098e-06
140	0.999999132855328	1.7342893442472e-06	8.671446721236e-07
141	0.999999345678345	1.30864330900712e-06	6.54321654503559e-07
142	0.999999347407433	1.3051851335391e-06	6.52592566769548e-07
143	0.999998993082225	2.01383555096694e-06	1.00691777548347e-06
144	0.999998842252387	2.31549522572649e-06	1.15774761286325e-06
145	0.999998265480286	3.46903942714078e-06	1.73451971357039e-06
146	0.999997159823344	5.68035331281885e-06	2.84017665640943e-06
147	0.999995893192903	8.21361419412628e-06	4.10680709706314e-06
148	0.999993682782145	1.26344357094565e-05	6.31721785472824e-06
149	0.99999216766745	1.56646650997879e-05	7.83233254989395e-06
150	0.999995525983235	8.9480335300844e-06	4.4740167650422e-06
151	0.99999772115333	4.55769334074381e-06	2.2788466703719e-06
152	0.999998895768244	2.20846351281334e-06	1.10423175640667e-06
153	0.999999507393674	9.85212651788826e-07	4.92606325894413e-07
154	0.999999775324646	4.49350707152423e-07	2.24675353576212e-07
155	0.999999751064321	4.9787135715197e-07	2.48935678575985e-07
156	0.999999598821285	8.02357430078012e-07	4.01178715039006e-07
157	0.999999351022525	1.29795494917798e-06	6.48977474588989e-07
158	0.999999440265093	1.11946981392263e-06	5.59734906961313e-07
159	0.999999714566464	5.70867072006816e-07	2.85433536003408e-07
160	0.99999966634236	6.673152799795e-07	3.3365763998975e-07
161	0.99999970341014	5.93179721523608e-07	2.96589860761804e-07
162	0.9999998930225	2.13955001442399e-07	1.06977500721199e-07
163	0.999999955898402	8.82031957487827e-08	4.41015978743914e-08
164	0.999999982220573	3.55588533109916e-08	1.77794266554958e-08
165	0.99999999458537	1.08292599318056e-08	5.41462996590282e-09
166	0.999999998170089	3.65982263546799e-09	1.82991131773399e-09
167	0.999999998258973	3.48205322008974e-09	1.74102661004487e-09
168	0.999999996500216	6.99956766452546e-09	3.49978383226273e-09
169	0.99999999340849	1.31830188792889e-08	6.59150943964447e-09
170	0.999999993555306	1.28893881373715e-08	6.44469406868576e-09
171	0.999999996665584	6.66883232629272e-09	3.33441616314636e-09
172	0.999999995884044	8.23191101319168e-09	4.11595550659584e-09
173	0.99999999696943	6.06113845854626e-09	3.03056922927313e-09
174	0.999999999367522	1.26495590788948e-09	6.3247795394474e-10
175	0.99999999985595	2.88100435943589e-10	1.44050217971794e-10
176	0.999999999971736	5.65271097595505e-11	2.82635548797753e-11
177	0.999999999995666	8.6680625215762e-12	4.3340312607881e-12
178	0.999999999998951	2.09738180787002e-12	1.04869090393501e-12
179	0.99999999999869	2.61907573639289e-12	1.30953786819645e-12
180	0.99999999999843	3.13951753885214e-12	1.56975876942607e-12
181	0.999999999996436	7.12835195765008e-12	3.56417597882504e-12
182	0.999999999990914	1.81718023646058e-11	9.08590118230288e-12
183	0.999999999982167	3.56655913368567e-11	1.78327956684284e-11
184	0.999999999951065	9.78697619828663e-11	4.89348809914331e-11
185	0.99999999990427	1.91460170576885e-10	9.57300852884423e-11
186	0.999999999893148	2.13704714447525e-10	1.06852357223762e-10
187	0.99999999988917	2.21660235145734e-10	1.10830117572867e-10
188	0.99999999986656	2.66880215666436e-10	1.33440107833218e-10
189	0.999999999836746	3.26507282489887e-10	1.63253641244943e-10
190	0.999999999725471	5.49058076430015e-10	2.74529038215007e-10
191	0.99999999909851	1.80297850544389e-09	9.01489252721946e-10
192	0.999999999911834	1.76332025940314e-10	8.8166012970157e-11
193	0.999999999979723	4.05540351048015e-11	2.02770175524007e-11
194	0.999999999933097	1.33805265658991e-10	6.69026328294955e-11
195	0.999999999776466	4.47068357836001e-10	2.23534178918e-10
196	0.999999999124513	1.75097416711196e-09	8.75487083555981e-10
197	0.999999996540457	6.91908654254711e-09	3.45954327127355e-09
198	0.999999992563943	1.48721142404587e-08	7.43605712022934e-09
199	0.999999984105778	3.17884437753088e-08	1.58942218876544e-08
200	0.99999996031426	7.93714818708659e-08	3.96857409354329e-08
201	0.999999842987621	3.14024757983366e-07	1.57012378991683e-07
202	0.999999466870647	1.06625870687649e-06	5.33129353438246e-07
203	0.99999752276979	4.95446042233546e-06	2.47723021116773e-06
204	0.999999279913754	1.44017249165886e-06	7.20086245829428e-07
205	0.999999921438488	1.57123024886822e-07	7.85615124434112e-08
206	0.99999945891175	1.0821765000731e-06	5.4108825003655e-07
207	0.99999606368865	7.87262269939151e-06	3.93631134969575e-06
208	0.999990273076273	1.945384745429e-05	9.72692372714502e-06
209	0.99999763701115	4.72597770138962e-06	2.36298885069481e-06
210	0.999927930219874	0.000144139560252029	7.20697801260144e-05

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	165	0.800970873786408	NOK
5% type I error level	179	0.868932038834951	NOK
10% type I error level	181	0.87864077669903	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/10xazs1293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/10xazs1293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/18rkh1293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/18rkh1293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/28rkh1293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/28rkh1293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/3j01k1293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/3j01k1293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/4j01k1293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/4j01k1293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/5j01k1293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/5j01k1293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/6u9041293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/6u9041293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/7u9041293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/7u9041293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/8m1z71293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/8m1z71293644142.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/9m1z71293644142.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293644043x4w03vzqzbzypsn/9m1z71293644142.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)

library(lmtest)

n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

if (n > n25) {

kp3 <- k + 3

nmkm3 <- n - k - 3

gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))

numgqtests <- 0

numsignificant1 <- 0

numsignificant5 <- 0

numsignificant10 <- 0

for (mypoint in kp3:nmkm3) {

j <- 0

numgqtests <- numgqtests + 1

for (myalt in c('greater', 'two.sided', 'less')) {

j <- j + 1

gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value

}

if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1

if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1

if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1

}

gqarr

}

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

qqline(mysum$resid)

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

if (n > n25) {

bitmap(file='test9.png')

plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')

grid()

dev.off()

}

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

if (n > n25) {

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-values',header=TRUE)

a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'breakpoint index',header=TRUE)

a<-table.element(a,'greater',header=TRUE)

a<-table.element(a,'2-sided',header=TRUE)

a<-table.element(a,'less',header=TRUE)

a<-table.row.end(a)

for (mypoint in kp3:nmkm3) {

a<-table.row.start(a)

a<-table.element(a,mypoint,header=TRUE)

a<-table.element(a,gqarr[mypoint-kp3+1,1])

a<-table.element(a,gqarr[mypoint-kp3+1,2])

a<-table.element(a,gqarr[mypoint-kp3+1,3])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable5.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Description',header=TRUE)

a<-table.element(a,'# significant tests',header=TRUE)

a<-table.element(a,'% significant tests',header=TRUE)

a<-table.element(a,'OK/NOK',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'1% type I error level',header=TRUE)

a<-table.element(a,numsignificant1)

a<-table.element(a,numsignificant1/numgqtests)

if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'5% type I error level',header=TRUE)

a<-table.element(a,numsignificant5)

a<-table.element(a,numsignificant5/numgqtests)

if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'10% type I error level',header=TRUE)

a<-table.element(a,numsignificant10)

a<-table.element(a,numsignificant10/numgqtests)

if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable6.tab')

}

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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