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deterministische trend workshop 7

*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: Thu, 02 Dec 2010 23:47:54 +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/03/t1291333554ekl05mw28yl8kuu.htm/, Retrieved Fri, 03 Dec 2010 00:46:04 +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/03/t1291333554ekl05mw28yl8kuu.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 «

2 9 2 1 4 3 3 3 3 3 9 2 3 4 3 3 4 3 3 9 4 2 3 4 4 4 3 3 9 3 3 2 3 3 3 3 3 9 3 2 3 3 2 2 2 3 9 1 2 4 3 3 2 2 2 9 4 4 5 4 4 5 4 3 9 2 2 4 2 2 3 2 3 9 2 2 4 4 3 2 3 4 9 2 2 2 2 2 2 2 3 9 4 2 2 3 2 4 4 3 9 3 3 4 3 2 3 3 2 9 3 2 4 4 4 3 3 3 9 2 2 5 3 4 2 3 9 3 3 5 3 3 4 3 3 9 2 2 4 3 2 2 2 3 9 3 3 3 3 3 3 3 3 9 3 3 4 4 4 4 3 2 9 2 2 4 2 2 2 2 4 9 2 2 2 3 2 2 3 3 9 1 1 4 3 3 3 2 2 9 4 3 4 4 4 4 3 3 9 3 2 4 3 3 2 3 3 9 2 2 4 3 3 2 2 2 9 3 3 4 3 4 3 3 2 9 3 3 4 4 4 4 3 4 9 4 3 4 4 2 4 4 2 9 3 2 3 4 3 3 3 3 9 3 3 3 4 3 3 3 2 9 2 2 4 4 4 4 2 4 9 2 2 3 2 4 2 2 3 9 4 3 4 3 3 3 4 2 9 4 3 4 4 3 4 4 3 9 2 2 4 3 2 3 3 3 9 2 2 4 3 2 2 3 1 9 3 3 4 4 4 4 4 3 9 3 3 4 3 3 4 3 3 9 3 2 3 2 2 2 2 3 9 3 3 4 3 3 3 3 2 9 4 3 4 4 4 4 4 3 9 3 3 4 3 4 4 3 9 1 2 3 2 2 3 3 5 9 2 1 5 2 1 4 2 4 9 2 2 4 3 2 3 2 3 9 3 3 4 3 2 3 3 2 9 4 3 4 4 4 3 4 2 9 3 2 4 4 4 3 4 3 9 2 2 5 2 2 2 2 4 9 2 3 4 3 3 4 3 2 9 3 3 4 4 3 4 3 3 9 3 3 4 3 2 4 3 4 10 4 2 3 3 1 2 2 3 10 3 2 4 4 3 3 4 4 10 2 2 4 3 2 3 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	11 seconds
R Server	'George Udny Yule' @ 72.249.76.132
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Multiple Linear Regression - Estimated Regression Equation

Yt[t] = + 9.35251838680335 -0.640087609275249month[t] -0.0290741578293503X1t[t] + 0.995491703191262X2t[t] + 0.114642721332865X3t[t] + 0.00880269656895907X4t[t] -0.243179688101038X5t[t] -0.104457642439144X6t[t] -0.542200790326548X7t[t] -0.0331456040618912t + 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)	9.35251838680335	0.819016	11.4192	0	0
month	-0.640087609275249	0.068035	-9.4083	0	0
X1t	-0.0290741578293503	0.13013	-0.2234	0.823518	0.411759
X2t	0.995491703191262	0.141128	7.0538	0	0
X3t	0.114642721332865	0.117472	0.9759	0.330722	0.165361
X4t	0.00880269656895907	0.086423	0.1019	0.919011	0.459505
X5t	-0.243179688101038	0.063292	-3.8422	0.000181	9.1e-05
X6t	-0.104457642439144	0.102443	-1.0197	0.309572	0.154786
X7t	-0.542200790326548	0.047916	-11.3157	0	0
t	-0.0331456040618912	0.005988	-5.535	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.86415787561406
R-squared	0.746768833985806
Adjusted R-squared	0.731158693615068
F-TEST (value)	47.8387007579806
F-TEST (DF numerator)	9
F-TEST (DF denominator)	146
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.21870073244992
Sum Squared Residuals	216.843795390000

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2	2.31139229923516	-0.311392299235163
2	3	4.1647724591164	-1.1647724591164
3	3	2.72896712333966	0.271032876660345
4	3	3.94457929293671	-0.944579292936707
5	3	3.92042282788315	-0.92042282788315
6	3	3.81688857271178	-0.816888572711783
7	2	4.16999512337462	-2.16999512337462
8	3	3.85144255585159	-0.851442555851587
9	3	3.15497950893917	-0.154979508939173
10	4	3.66032354750122	0.339676452498781
11	3	2.28451545881821	0.715484541181793
12	3	4.15187959120835	-1.15187959120835
13	2	2.64568560432208	-0.645685604322078
14	3	2.85191182529259	0.148088174707414
15	9	9.28294974352176	-0.282949743521756
16	9	9.50548852544546	-0.505488525445463
17	9	7.46885481711649	1.53114518288351
18	9	8.8536674363732	0.146332563626806
19	9	8.74920820160038	0.250791798399624
20	9	7.27746506037623	1.72253493962377
21	9	10.3167460710351	-1.31674607103507
22	9	7.53879662052383	1.46120337947617
23	9	8.53772674186679	0.462273258133211
24	9	9.79132717984584	-0.79132717984584
25	9	8.75018517470813	0.249814825291873
26	9	7.50410102322497	1.49589897677503
27	9	7.79320635496386	1.20679364503614
28	9	7.2479700515979	1.7520299484021
29	9	7.72795108003321	1.27204891996679
30	9	8.14513801652115	0.854861983478854
31	9	7.91577543313089	1.08422456686911
32	9	7.76481799799154	1.23518200200846
33	9	7.06093463683492	1.93906536316508
34	9	8.56123032179124	0.438769678208761
35	9	9.85566598648348	-0.855665986483481
36	9	7.61038813049346	1.38961186950654
37	9	7.55825475096889	1.44174524903111
38	9	7.02606320228448	1.97393679771552
39	9	8.2773440212727	0.722655978727309
40	9	6.83771810497064	2.16228189502936
41	9	4.18127028933100	4.8187297106690
42	1	2.70804787348276	-1.70804787348276
43	2	3.49863886881370	-1.49863886881370
44	2	4.06026918370021	-2.06026918370021
45	3	3.24831392470118	-0.248313924701179
46	4	4.19676577839524	-0.196765778395242
47	3	4.69925014116946	-1.69925014116946
48	2	2.78986056742394	-0.789860567423937
49	2	3.23917692635544	-1.23917692635544
50	3	4.09706538304567	-1.09706538304566
51	3	2.30712692169396	0.692873078306045
52	4	3.15853230080606	0.84146769919394
53	3	3.73907536269955	-0.739075362699553
54	2	2.94343266465372	-0.943432664653717
55	2	2.22723104805192	-0.227231048051920
56	2	2.24723892614841	-0.247238926148405
57	2	3.19801039883331	-1.19801039883331
58	3	3.08577930884602	-0.0857793088460195
59	1	4.24669741149542	-3.24669741149542
60	5	2.99041394289289	2.00958605710711
61	2	3.58449565470304	-1.58449565470304
62	3	3.27176006530929	-0.271760065309288
63	4	3.00793947103092	0.992060528969082
64	4	3.8746306242901	0.125369375709896
65	2	1.85317484719415	0.146825152805854
66	3	2.53179117047571	0.468208829524285
67	3	2.23027461200778	0.769725387992216
68	3	2.94167425966029	0.0583257403397136
69	3	1.69661180314461	1.30338819685539
70	1	2.48719365208853	-1.48719365208853
71	3	2.40394000456457	0.596059995435434
72	3	2.12261987890132	0.877380121098683
73	3	3.5573324122704	-0.557332412270402
74	4	3.59494568350480	0.405054316495195
75	3	1.72193009141162	1.27806990858838
76	4	2.32887209662497	1.67112790337503
77	3	2.26665233473374	0.733347665266264
78	3	2.54863226450086	0.451367735499143
79	2	2.88609235365934	-0.88609235365934
80	1	1.75032218945756	-0.750322189457562
81	2	5.47052579962838	-3.47052579962838
82	3	3.60333003981734	-0.603330039817336
83	4	4.01857740741917	-0.0185774074191695
84	3	3.62456632683062	-0.624566326830624
85	4	4.36447074822967	-0.364470748229669
86	5	4.12620875290442	0.873791247095579
87	2	2.90754523970861	-0.907545239708607
88	2	3.11320207659631	-1.11320207659631
89	4	4.36190457337437	-0.36190457337437
90	4	3.34696790389116	0.653032096108835
91	3	3.64895493248490	-0.648954932484896
92	4	3.63746317200816	0.362536827991844
93	4	3.67970105255606	0.320298947443939
94	4	3.40441169358626	0.595588306413739
95	4	3.8278983163474	0.1721016836526
96	4	4.69810502848281	-0.698105028482812
97	2	6.36174231716034	-4.36174231716034
98	4	3.52963260165011	0.470367398349894
99	4	3.4331357190795	0.566864280920497
100	4	3.89774322745541	0.102256772544589
101	4	3.31007857762179	0.689921422378213
102	4	3.91563820051038	0.0843617994896166
103	5	5.60002621701524	-0.600026217015241
104	4	5.10377484538173	-1.10377484538173
105	4	2.02318558662111	1.97681441337889
106	4	4.36970425247812	-0.369704252478115
107	3	3.13232590526458	-0.132325905264584
108	4	4.38898160785785	-0.38898160785785
109	4	4.28258569573763	-0.282585695737626
110	4	5.03475522847652	-1.03475522847652
111	3	4.78262067462629	-1.78262067462629
112	3	4.83493222008425	-1.83493222008425
113	3	3.77722075500175	-0.77722075500175
114	3	3.74165683542197	-0.741656835421966
115	4	3.54821217479646	0.451787825203541
116	3	2.92305361220796	0.0769463877920404
117	3	2.88990800814607	0.110091991853932
118	4	4.02229490130181	-0.0222949013018123
119	3	3.81134173983772	-0.811341739837718
120	3	3.92191301493804	-0.92191301493804
121	3	3.75523561060766	-0.755235610607657
122	3	3.33017691887187	-0.330176918871873
123	3	3.33611682655029	-0.336116826550291
124	3	3.65338048290409	-0.653380482904092
125	4	2.98256558508484	1.01743441491516
126	3	1.88855614713285	1.11144385286715
127	4	3.66858639205128	0.331413607948717
128	3	4.09449133033031	-1.09449133033031
129	4	5.61821243768829	-1.61821243768829
130	1	2.12787971973257	-1.12787971973257
131	4	3.42136125447085	0.578638745529147
132	3	2.88407815692010	0.115921843079905
133	4	2.66834118284408	1.33165881715592
134	4	2.72575897578602	1.27424102421398
135	4	3.78013304792568	0.219866952074317
136	3	3.01487186157825	-0.0148718615782511
137	3	3.90386804574456	-0.903868045744562
138	3	2.42203943253142	0.577960567468577
139	4	3.16276724546616	0.837232754533836
140	3	4.36913535822434	-1.36913535822434
141	3	2.12348766849003	0.876512331509973
142	3	3.04899284641422	-0.0489928464142197
143	4	2.60504507574281	1.39495492425719
144	2	2.80008858136599	-0.800088581365988
145	3	2.74563558285058	0.254364417149421
146	3	4.35048760677309	-1.35048760677309
147	3	2.54794575100977	0.452054248990233
148	3	2.18872421831410	0.811275781685896
149	3	2.47710305081663	0.522896949183371
150	4	1.66756610733549	2.33243389266451
151	3	2.18893954904533	0.811060450954672
152	4	3.72978441137073	0.270215588629268
153	3	2.66726744676598	0.332732553234015
154	4	1.77816337918896	2.22183662081104
155	3	3.97798492972524	-0.97798492972524
156	3	1.68511763222667	1.31488236777333

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
13	0.0616555127202927	0.123311025440585	0.938344487279707
14	0.100259497640535	0.200518995281069	0.899740502359465
15	0.0425289853213626	0.0850579706427252	0.957471014678637
16	0.027196454946748	0.054392909893496	0.972803545053252
17	0.0210415891978975	0.0420831783957951	0.978958410802103
18	0.00881965371272902	0.0176393074254580	0.991180346287271
19	0.00453782900696995	0.0090756580139399	0.99546217099303
20	0.00212099003430079	0.00424198006860159	0.9978790099657
21	0.0148316771889884	0.0296633543779768	0.985168322811012
22	0.0410983105937388	0.0821966211874776	0.95890168940626
23	0.0281514497126312	0.0563028994252624	0.971848550287369
24	0.0246002460293221	0.0492004920586442	0.975399753970678
25	0.014162825211748	0.028325650423496	0.985837174788252
26	0.00969772900772784	0.0193954580154557	0.990302270992272
27	0.00534656731199019	0.0106931346239804	0.99465343268801
28	0.00314737426818994	0.00629474853637987	0.99685262573181
29	0.00181740465691262	0.00363480931382524	0.998182595343087
30	0.00125186623051176	0.00250373246102352	0.998748133769488
31	0.000816426955053716	0.00163285391010743	0.999183573044946
32	0.000424930523855343	0.000849861047710686	0.999575069476145
33	0.000247195403900381	0.000494390807800762	0.9997528045961
34	0.000664593544391008	0.00132918708878202	0.99933540645561
35	0.00168204014413316	0.00336408028826633	0.998317959855867
36	0.00130110254228499	0.00260220508456998	0.998698897457715
37	0.00132514813011119	0.00265029626022238	0.998674851869889
38	0.00144487542113027	0.00288975084226054	0.99855512457887
39	0.00266235190830484	0.00532470381660968	0.997337648091695
40	0.0138973978583106	0.0277947957166212	0.98610260214169
41	0.21148662850391	0.42297325700782	0.78851337149609
42	0.999582179922426	0.00083564015514822	0.00041782007757411
43	0.999972839900826	5.43201983487909e-05	2.71600991743954e-05
44	0.999995177124221	9.64575155755931e-06	4.82287577877966e-06
45	0.999994327716233	1.13445675339387e-05	5.67228376696933e-06
46	0.999993396544863	1.3206910274554e-05	6.603455137277e-06
47	0.999995929236925	8.14152615019874e-06	4.07076307509937e-06
48	0.999992703459289	1.45930814225348e-05	7.29654071126742e-06
49	0.999992990781327	1.40184373455203e-05	7.00921867276013e-06
50	0.999988878665201	2.22426695974953e-05	1.11213347987477e-05
51	0.99998414266945	3.17146611003858e-05	1.58573305501929e-05
52	0.999993443606143	1.31127877147450e-05	6.55639385737252e-06
53	0.99999138388134	1.72322373218970e-05	8.61611866094849e-06
54	0.999989586592094	2.08268158118004e-05	1.04134079059002e-05
55	0.999988864637637	2.22707247254288e-05	1.11353623627144e-05
56	0.99998458877996	3.08224400774916e-05	1.54112200387458e-05
57	0.999981036455539	3.79270889223755e-05	1.89635444611877e-05
58	0.999969602574097	6.07948518050991e-05	3.03974259025495e-05
59	0.999988562292774	2.28754144524789e-05	1.14377072262394e-05
60	0.999998031906375	3.93618725056456e-06	1.96809362528228e-06
61	0.999998192913181	3.61417363735858e-06	1.80708681867929e-06
62	0.999997111342118	5.77731576456481e-06	2.88865788228241e-06
63	0.999998007004064	3.98599187270014e-06	1.99299593635007e-06
64	0.999997775960671	4.44807865786595e-06	2.22403932893297e-06
65	0.999997448458329	5.10308334164535e-06	2.55154167082268e-06
66	0.999995453784928	9.092430144955e-06	4.5462150724775e-06
67	0.999995211048303	9.577903395005e-06	4.7889516975025e-06
68	0.99999255583628	1.48883274412753e-05	7.44416372063764e-06
69	0.999987350258622	2.52994827566609e-05	1.26497413783304e-05
70	0.99999453476142	1.0930477160019e-05	5.4652385800095e-06
71	0.999991718630658	1.65627386838610e-05	8.28136934193048e-06
72	0.999986703602112	2.6592795775113e-05	1.32963978875565e-05
73	0.999982219130466	3.55617390673042e-05	1.77808695336521e-05
74	0.999990509025321	1.89819493579333e-05	9.49097467896665e-06
75	0.999985942737474	2.81145250521246e-05	1.40572625260623e-05
76	0.999993837355664	1.23252886719649e-05	6.16264433598246e-06
77	0.99999025004606	1.94999078792658e-05	9.7499539396329e-06
78	0.999993767939319	1.24641213626744e-05	6.23206068133722e-06
79	0.999996408270804	7.18345839182226e-06	3.59172919591113e-06
80	0.999998028809793	3.9423804145269e-06	1.97119020726345e-06
81	0.99999982263288	3.54734238467279e-07	1.77367119233640e-07
82	0.9999999940648	1.18704013228564e-08	5.93520066142819e-09
83	0.999999992306312	1.53873769384124e-08	7.69368846920621e-09
84	0.999999992315353	1.53692945259577e-08	7.68464726297886e-09
85	0.999999985038558	2.99228834373761e-08	1.49614417186881e-08
86	0.99999999319119	1.36176219658614e-08	6.8088109829307e-09
87	0.999999997786597	4.42680639566448e-09	2.21340319783224e-09
88	0.99999999988895	2.22099905898238e-10	1.11049952949119e-10
89	0.999999999750472	4.99056242188086e-10	2.49528121094043e-10
90	0.999999999511614	9.76771264705623e-10	4.88385632352812e-10
91	0.99999999962752	7.44959806899633e-10	3.72479903449816e-10
92	0.999999999155695	1.68860999890972e-09	8.44304999454859e-10
93	0.999999998329857	3.34028695548965e-09	1.67014347774483e-09
94	0.999999996308552	7.38289650533276e-09	3.69144825266638e-09
95	0.999999991848392	1.63032166361822e-08	8.1516083180911e-09
96	0.999999987025785	2.59484306393927e-08	1.29742153196963e-08
97	0.999999999949124	1.01752065724778e-10	5.08760328623891e-11
98	0.999999999885182	2.29636645250879e-10	1.14818322625440e-10
99	0.999999999762697	4.74606131269499e-10	2.37303065634749e-10
100	0.999999999421532	1.15693608705566e-09	5.78468043527831e-10
101	0.999999998829646	2.34070839120423e-09	1.17035419560212e-09
102	0.999999997231708	5.53658471037505e-09	2.76829235518752e-09
103	0.999999994603728	1.07925446692244e-08	5.3962723346122e-09
104	0.999999990178933	1.96421336230804e-08	9.8210668115402e-09
105	0.999999992723346	1.45533085816621e-08	7.27665429083103e-09
106	0.9999999826251	3.47498018212213e-08	1.73749009106106e-08
107	0.999999980319189	3.93616223626171e-08	1.96808111813086e-08
108	0.999999963318075	7.336385089326e-08	3.668192544663e-08
109	0.999999919276788	1.61446423345902e-07	8.07232116729508e-08
110	0.999999986319302	2.7361396781573e-08	1.36806983907865e-08
111	0.999999967495858	6.50082845200863e-08	3.25041422600431e-08
112	0.999999919561134	1.60877731793766e-07	8.04388658968829e-08
113	0.999999844309113	3.11381773326921e-07	1.55690886663460e-07
114	0.999999702117931	5.95764137089438e-07	2.97882068544719e-07
115	0.999999566710002	8.6657999594454e-07	4.3328999797227e-07
116	0.99999926347283	1.47305434067613e-06	7.36527170338064e-07
117	0.999998817504675	2.36499065025434e-06	1.18249532512717e-06
118	0.999998657896366	2.68420726845118e-06	1.34210363422559e-06
119	0.999997199750597	5.60049880676308e-06	2.80024940338154e-06
120	0.99999341269478	1.31746104385961e-05	6.58730521929804e-06
121	0.99999052589359	1.89482128188405e-05	9.47410640942026e-06
122	0.999979699620572	4.06007588565986e-05	2.03003794282993e-05
123	0.999958443822713	8.31123545734825e-05	4.15561772867413e-05
124	0.999939971066504	0.000120057866991098	6.00289334955488e-05
125	0.999888915824107	0.000222168351786753	0.000111084175893377
126	0.999850272645582	0.000299454708835679	0.000149727354417839
127	0.999704738831897	0.00059052233620596	0.00029526116810298
128	0.999472705086915	0.00105458982617077	0.000527294913085385
129	0.998957945112243	0.00208410977551364	0.00104205488775682
130	0.999717900311586	0.000564199376828268	0.000282099688414134
131	0.999443457633082	0.00111308473383577	0.000556542366917884
132	0.998987305622193	0.00202538875561463	0.00101269437780732
133	0.998297612198668	0.00340477560266352	0.00170238780133176
134	0.997964419183825	0.00407116163235011	0.00203558081617506
135	0.998143338386383	0.00371332322723474	0.00185666161361737
136	0.99624092797065	0.00751814405869951	0.00375907202934976
137	0.994227634622225	0.0115447307555509	0.00577236537777543
138	0.99228134363106	0.0154373127378778	0.00771865636893891
139	0.989773401625974	0.0204531967480514	0.0102265983740257
140	0.97512159628305	0.0497568074339015	0.0248784037169508
141	0.962474556673016	0.0750508866539679	0.0375254433269840
142	0.91153269354424	0.176934612911519	0.0884673064557597
143	0.84966361174138	0.300672776517241	0.150336388258621

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	109	0.83206106870229	NOK
5% type I error level	121	0.923664122137405	NOK
10% type I error level	126	0.961832061068702	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/10bmq1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/10bmq1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/10puj11291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/10puj11291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/20bmq1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/20bmq1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/3blmt1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/3blmt1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/4blmt1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/4blmt1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/5blmt1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/5blmt1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/63clv1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/63clv1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/7elky1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/7elky1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/8elky1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/8elky1291333662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/9elky1291333662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291333554ekl05mw28yl8kuu/9elky1291333662.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal 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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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