Home » date » 2009 » Nov » 20 »

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: Fri, 20 Nov 2009 06:56:36 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j.htm/, Retrieved Fri, 20 Nov 2009 14:57:46 +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/2009/Nov/20/t12587254534kiqlvup0iz641j.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

6.9 2.28 6.8 2.26 6.7 2.71 6.6 2.77 6.5 2.77 6.5 2.64 7.0 2.56 7.5 2.07 7.6 2.32 7.6 2.16 7.6 2.23 7.8 2.40 8.0 2.84 8.0 2.77 8.0 2.93 7.9 2.91 7.9 2.69 8.0 2.38 8.5 2.58 9.2 3.19 9.4 2.82 9.5 2.72 9.5 2.53 9.6 2.70 9.7 2.42 9.7 2.50 9.6 2.31 9.5 2.41 9.4 2.56 9.3 2.76 9.6 2.71 10.2 2.44 10.2 2.46 10.1 2.12 9.9 1.99 9.8 1.86 9.8 1.88 9.7 1.82 9.5 1.74 9.3 1.71 9.1 1.38 9.0 1.27 9.5 1.19 10.0 1.28 10.2 1.19 10.1 1.22 10.0 1.47 9.9 1.46 10.0 1.96 9.9 1.88 9.7 2.03 9.5 2.04 9.2 1.90 9.0 1.80 9.3 1.92 9.8 1.92 9.8 1.97 9.6 2.46 9.4 2.36 9.3 2.53 9.2 2.31 9.2 1.98 9.0 1.46 8.8 1.26 8.7 1.58 8.7 1.74 9.1 1.89 9.7 1.85 9.8 1.62 9.6 1.30 9.4 1.42 9.4 1.15 9.5 0.42 9.4 0.74 9.3 1.02 9.2 1.51 9.0 1.86 8.9 1.59 9.2 1.03 9.8 0.44 9.9 0.82 9.6 0.86 9.2 0.58 9.1 0.59 9.1 0.95 9.0 0.98 8.9 1.23 8.7 1.17 8.5 0.84 8.3 0.74 8.5 0.65 8.7 0.91 8.4 1.19 8.1 1.30 7.8 1.53 7.7 1.94 7.5 1.79 7.2 1.95 6.8 2.26 6.7 2.04 6.4 2.16 6.3 2. 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	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 10.1924266397789 -0.529300900085433X[t] -0.0745355431955221M1[t] -0.152394972116518M2[t] -0.292295981835693M3[t] -0.443765988554583M4[t] -0.610056420475866M5[t] -0.713284481199883M6[t] -0.221024193589143M7[t] + 0.151941828555044M8[t] + 0.203849248899061M9[t] + 0.108661512507523M10[t] -0.0302565182136459M11[t] -0.00633716687860314t + 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)	10.1924266397789	0.35697	28.5526	0	0
X	-0.529300900085433	0.107545	-4.9217	2e-06	1e-06
M1	-0.0745355431955221	0.351679	-0.2119	0.832412	0.416206
M2	-0.152394972116518	0.351625	-0.4334	0.665286	0.332643
M3	-0.292295981835693	0.351607	-0.8313	0.40699	0.203495
M4	-0.443765988554583	0.351626	-1.262	0.208705	0.104352
M5	-0.610056420475866	0.351592	-1.7351	0.084574	0.042287
M6	-0.713284481199883	0.351489	-2.0293	0.044023	0.022011
M7	-0.221024193589143	0.351439	-0.6289	0.530271	0.265136
M8	0.151941828555044	0.351401	0.4324	0.66602	0.33301
M9	0.203849248899061	0.351372	0.5802	0.562599	0.281299
M10	0.108661512507523	0.351365	0.3093	0.757515	0.378757
M11	-0.0302565182136459	0.351354	-0.0861	0.931479	0.46574
t	-0.00633716687860314	0.001387	-4.5687	1e-05	5e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.509219366095136
R-squared	0.259304362806332
Adjusted R-squared	0.201298077965864
F-TEST (value)	4.47028047942537
F-TEST (DF numerator)	13
F-TEST (DF denominator)	166
p-value	1.69466380439687e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.96219474589104
Sum Squared Residuals	153.685909017374

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	6.9	8.90474787751007	-2.00474787751007
2	6.8	8.83113729971214	-2.03113729971214
3	6.7	8.44671371807591	-1.74671371807591
4	6.6	8.25714849047329	-1.65714849047329
5	6.5	8.0845208916734	-1.58452089167340
6	6.5	8.04376478108189	-1.54376478108189
7	7	8.57203197382086	-1.57203197382086
8	7.5	9.19801827012831	-1.69801827012831
9	7.6	9.11126329857236	-1.51126329857236
10	7.6	9.09442653931589	-1.49442653931589
11	7.6	8.91212027871014	-1.31212027871014
12	7.8	8.84605847703066	-1.04605847703066
13	8	8.53229337091894	-0.532293370918943
14	8	8.48514783812533	-0.485147838125327
15	8	8.25422151751388	-0.254221517513876
16	7.9	8.10700036191809	-0.207000361918091
17	7.9	8.050818961137	-0.150818961137000
18	8	8.10533701256086	-0.105337012560865
19	8.5	8.48539995327591	0.0146000467240849
20	9.2	8.52915525948939	0.670844740510614
21	9.4	8.77056684598641	0.629433154013591
22	9.5	8.72197203272481	0.778027967275188
23	9.5	8.67728400614127	0.822715993858728
24	9.6	8.61122220446179	0.98877779553821
25	9.7	8.67855374641159	1.02144625358841
26	9.7	8.55201307860515	1.14798692139485
27	9.6	8.5063420730236	1.09365792697639
28	9.5	8.29560480941757	1.20439519058243
29	9.4	8.04358207560487	1.35641792439513
30	9.3	7.82815666798516	1.47184333201484
31	9.6	8.34054483372157	1.25945516627843
32	10.2	8.85008493201022	1.34991506798978
33	10.2	8.88506916747393	1.31493083252607
34	10.1	8.96350657023283	1.13649342976717
35	9.9	8.88706048964417	1.01293951035583
36	9.8	8.97978895799032	0.820211042009683
37	9.8	8.88833022991448	0.911669770085518
38	9.7	8.83589168812	0.86410831187999
39	9.5	8.73199758352907	0.768002416470934
40	9.3	8.59006943693413	0.709930563065865
41	9.1	8.59211113516244	0.507888864837557
42	9	8.54076900656922	0.45923099343078
43	9.5	9.06903619930819	0.430963800691808
44	10	9.3880279735661	0.611972026433913
45	10.2	9.4812353080392	0.718764691960809
46	10.1	9.36383137776649	0.736168622233514
47	10	9.08625095514535	0.913749044854645
48	9.9	9.11546331548125	0.784536684518748
49	10	8.76994015536441	1.23005984463559
50	9.9	8.72808763157165	1.17191236842835
51	9.7	8.50245431996105	1.19754568003895
52	9.5	8.3393541373627	1.16064586263730
53	9.2	8.24082866457478	0.95917133542522
54	9	8.1841935269807	0.815806473019297
55	9.3	8.60660053970259	0.693399460297413
56	9.8	8.97322939496817	0.826770605031828
57	9.8	8.99233460342931	0.807665396570687
58	9.6	8.63145225911731	0.96854774088269
59	9.4	8.53912715152608	0.860872848473918
60	9.3	8.4730653498466	0.8269346501534
61	9.2	8.50863883779127	0.691361162208729
62	9.2	8.59911153901986	0.600888460980135
63	9	8.72810983046651	0.271890169533488
64	8.8	8.6761628368861	0.123837163113896
65	8.7	8.33415895005888	0.365841049941119
66	8.7	8.13990557844259	0.560094421557408
67	9.1	8.54643356416191	0.553566435838086
68	9.7	8.93423445543091	0.765765544569084
69	9.8	9.10154391591598	0.698456084084022
70	9.6	9.16939530067317	0.430604699326824
71	9.4	8.96062399506315	0.439376004936848
72	9.4	9.12745458942126	0.272545410578739
73	9.5	9.4329715364095	0.0670284635904984
74	9.4	9.17939865258256	0.220601347417436
75	9.3	8.88495622396086	0.415043776039136
76	9.2	8.46779160932151	0.73220839067849
77	9	8.10990869549172	0.890091304508278
78	8.9	8.14325471091217	0.756745289087832
79	9.2	8.92558633569215	0.274413664307852
80	9.8	9.60450272200814	0.195497277991863
81	9.9	9.44893863344109	0.451061366558914
82	9.6	9.32624169416753	0.273758305832471
83	9.2	9.32919074859168	-0.129190748591678
84	9.1	9.34781709092587	-0.247817090925866
85	9.1	9.07639605682098	0.0236039431790155
86	9	8.97632043401882	0.0236795659811778
87	8.9	8.69775703239969	0.202242967600314
88	8.7	8.57170791280732	0.128292087192681
89	8.5	8.57374961103563	-0.0737496110356252
90	8.3	8.51711447344155	-0.217114473441548
91	8.5	9.05067467518137	-0.550674675181374
92	8.7	9.27968529642475	-0.579685296424747
93	8.4	9.17705129786624	-0.777051297866239
94	8.1	9.0173032955867	-0.9173032955867
95	7.8	8.75030889096728	-0.95030889096728
96	7.7	8.5572148732673	-0.857214873267293
97	7.5	8.55573729820598	-1.05573729820598
98	7.2	8.38685255839271	-1.18685255839271
99	6.8	8.07653110276845	-1.27653110276845
100	6.7	8.03517012718975	-1.33517012718975
101	6.4	7.79902642037962	-1.39902642037962
102	6.3	7.37717366172659	-1.07717366172659
103	6.8	7.84192474645531	-1.04192474645531
104	7.3	8.1609165207132	-0.860916520713206
105	7.1	7.95242234213761	-0.852422342137612
106	7	8.05732478990079	-1.05732478990079
107	6.8	7.84326047528991	-1.04326047528991
108	6.6	8.19005337567707	-1.59005337567707
109	6.3	8.26267792662772	-1.96267792662772
110	6.1	8.15201628582385	-2.05201628582385
111	6.1	8.09046625323974	-1.99046625323974
112	6.3	7.56214844958244	-1.26214844958244
113	6.3	7.20426553575265	-0.904265535752654
114	6	7.20585349716798	-1.20585349716798
115	6.2	7.83998086992403	-1.63998086992403
116	6.4	8.19602370718791	-1.79602370718791
117	6.8	8.45860732968835	-1.65860732968835
118	7.5	8.30944534541052	-0.80944534541052
119	7.5	8.28063634582954	-0.780636345829543
120	7.6	8.27809065216031	-0.678090652160314
121	7.6	7.81612129402468	-0.216121294024677
122	7.4	7.87483594124815	-0.474835941248144
123	7.3	7.70742572864695	-0.40742572864695
124	7.1	8.00481732912293	-0.904817329122929
125	6.9	8.08625416236405	-1.18625416236405
126	6.8	8.21487433979988	-1.41487433979988
127	7.5	8.48907710049784	-0.989077100497838
128	7.6	8.86629197376513	-1.26629197376513
129	7.8	8.91186222723054	-1.11186222723055
130	8	8.79445829695784	-0.794458296957842
131	8.1	8.7497702703743	-0.649770270374302
132	8.2	8.63077837868628	-0.430778378686278
133	8.3	8.63459381262582	-0.33459381262582
134	8.2	8.26986773978094	-0.069867739780943
135	8	8.11304354518146	-0.113043545181456
136	7.9	8.10344062360788	-0.203440623607883
137	7.6	8.16370542084559	-0.563705420845588
138	7.6	7.74714567119342	-0.147145671193417
139	8.3	8.30187790893666	-0.00187790893665934
140	8.4	8.50971649417662	-0.109716494176614
141	8.4	8.54999373864117	-0.149993738641174
142	8.4	8.56491503338983	-0.164915033389828
143	8.4	8.27145558376614	0.128544416233866
144	8.6	8.35889104311143	0.241108956888570
145	8.9	8.35741346805012	0.542586531949882
146	8.8	8.44788616927871	0.352113830721288
147	8.3	8.37045710969204	-0.0704571096920402
148	7.5	7.79450222502706	-0.294502225027055
149	7.2	7.25665700516822	-0.0566570051682201
150	7.4	7.3323470925955	0.0676529074044981
151	8.8	7.73887507831482	1.06112492168518
152	9.3	8.18489906859322	1.11510093140678
153	9.3	8.35220852907829	0.947791470921714
154	8.7	7.81136387873724	0.888636121262764
155	8.2	7.83019196016395	0.369808039836051
156	8.3	8.00231556352291	0.297684436477089
157	8.5	7.92673586244964	0.573264137550359
158	8.6	7.67845598762356	0.921544012376442
159	8.5	7.26756736098306	1.23243263901694
160	8.2	7.27384346641205	0.926156533587945
161	8.1	7.23354109263353	0.866458907366473
162	7.9	6.93342754100015	0.96657245899985
163	8.6	7.27643941870922	1.32356058129078
164	8.7	7.65894730097737	1.04105269902263
165	8.7	7.67805250943851	1.02194749056149
166	8.5	7.94174522722732	0.558254772772683
167	8.4	7.743559939619	0.656440060380998
168	8.5	7.5981030029267	0.901896997073294
169	8.7	7.6548485268748	1.04515147312521
170	8.7	7.70297715609655	0.997022843903447
171	8.6	7.92195660055772	0.678043399442277
172	8.5	7.62123818393716	0.878761816062838
173	8.3	7.32687137811763	0.973128621882374
174	8	7.38668243854235	0.613317561457654
175	8.2	8.01551680229755	0.18448319770245
176	8.1	8.36626663056057	-0.266266630560571
177	8.1	8.62885025306101	-0.528850253061013
178	8	8.53261835879172	-0.532618358791725
179	7.9	8.23915890916803	-0.339158909168032
180	7.9	8.18368312549026	-0.283683125490259

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	3.58770505602729e-05	7.17541011205459e-05	0.99996412294944
18	9.68040658815184e-07	1.93608131763037e-06	0.999999031959341
19	9.56176480925752e-07	1.91235296185150e-06	0.99999904382352
20	0.000109511872884483	0.000219023745768965	0.999890488127116
21	8.03770335346255e-05	0.000160754067069251	0.999919622966465
22	5.85043133439328e-05	0.000117008626687866	0.999941495686656
23	3.64563606760843e-05	7.29127213521686e-05	0.999963543639324
24	1.29613160842164e-05	2.59226321684328e-05	0.999987038683916
25	2.89121739568935e-06	5.78243479137869e-06	0.999997108782604
26	6.31090861442762e-07	1.26218172288552e-06	0.999999368909139
27	1.32526107355518e-07	2.65052214711035e-07	0.999999867473893
28	2.66492513926113e-08	5.32985027852227e-08	0.999999973350749
29	5.37702444247734e-09	1.07540488849547e-08	0.999999994622976
30	1.91603296836497e-09	3.83206593672994e-09	0.999999998083967
31	1.83825372805512e-09	3.67650745611025e-09	0.999999998161746
32	1.06003236228473e-09	2.12006472456946e-09	0.999999998939968
33	1.2880174001719e-09	2.5760348003438e-09	0.999999998711983
34	2.07754885372836e-09	4.15509770745673e-09	0.999999997922451
35	5.69951654562223e-09	1.13990330912445e-08	0.999999994300483
36	1.47282443944703e-08	2.94564887889406e-08	0.999999985271756
37	4.77954560682425e-08	9.5590912136485e-08	0.999999952204544
38	7.00640869837282e-08	1.40128173967456e-07	0.999999929935913
39	5.67945397821156e-08	1.13589079564231e-07	0.99999994320546
40	3.78144106377944e-08	7.56288212755888e-08	0.99999996218559
41	1.57124658892956e-08	3.14249317785912e-08	0.999999984287534
42	6.66111671499001e-09	1.33222334299800e-08	0.999999993338883
43	2.24786679980756e-09	4.49573359961512e-09	0.999999997752133
44	9.86896207590831e-10	1.97379241518166e-09	0.999999999013104
45	3.49107392064177e-10	6.98214784128354e-10	0.999999999650893
46	2.13803343435628e-10	4.27606686871257e-10	0.999999999786197
47	4.98707268975733e-10	9.97414537951466e-10	0.999999999501293
48	1.21895691412810e-09	2.43791382825621e-09	0.999999998781043
49	2.9611500593653e-08	5.9223001187306e-08	0.9999999703885
50	1.89419435423451e-07	3.78838870846901e-07	0.999999810580565
51	1.12796034184656e-06	2.25592068369313e-06	0.999998872039658
52	4.48071041743086e-06	8.96142083486172e-06	0.999995519289583
53	1.72856955070143e-05	3.45713910140286e-05	0.999982714304493
54	6.41699305350706e-05	0.000128339861070141	0.999935830069465
55	0.000262051905703878	0.000524103811407757	0.999737948094296
56	0.000857192571300918	0.00171438514260184	0.9991428074287
57	0.00268981702007736	0.00537963404015472	0.997310182979923
58	0.0121488063504327	0.0242976127008654	0.987851193649567
59	0.0313580225976921	0.0627160451953841	0.968641977402308
60	0.0647712605206154	0.129542521041231	0.935228739479385
61	0.0994333118671731	0.198866623734346	0.900566688132827
62	0.127780071726997	0.255560143453994	0.872219928273003
63	0.152157353821481	0.304314707642962	0.847842646178519
64	0.172302473151259	0.344604946302518	0.82769752684874
65	0.193071638524512	0.386143277049025	0.806928361475488
66	0.216127718132358	0.432255436264717	0.783872281867642
67	0.239771173758946	0.479542347517893	0.760228826241054
68	0.277825689984994	0.555651379969988	0.722174310015006
69	0.314602000209816	0.629204000419631	0.685397999790184
70	0.344255694856044	0.688511389712089	0.655744305143956
71	0.385880032537758	0.771760065075516	0.614119967462242
72	0.412770537414871	0.825541074829742	0.587229462585129
73	0.393472255700861	0.786944511401723	0.606527744299139
74	0.386095368314307	0.772190736628613	0.613904631685693
75	0.394093714650230	0.788187429300459	0.60590628534977
76	0.439575743920918	0.879151487841836	0.560424256079082
77	0.526183991613741	0.947632016772519	0.473816008386259
78	0.606607767169721	0.786784465660558	0.393392232830279
79	0.631930262984436	0.736139474031127	0.368069737015564
80	0.65451593505324	0.69096812989352	0.34548406494676
81	0.719993960750355	0.56001207849929	0.280006039249645
82	0.779799791542984	0.440400416914032	0.220200208457016
83	0.815673161047748	0.368653677904504	0.184326838952252
84	0.846541041632616	0.306917916734768	0.153458958367384
85	0.878020756526436	0.243958486947128	0.121979243473564
86	0.909792692097658	0.180414615804685	0.0902073079023424
87	0.947382933443596	0.105234133112808	0.0526170665564041
88	0.973532547344102	0.0529349053117951	0.0264674526558975
89	0.987504695510495	0.0249906089790104	0.0124953044895052
90	0.99508878717779	0.00982242564442001	0.00491121282221001
91	0.997585818034256	0.00482836393148898	0.00241418196574449
92	0.999390011027872	0.00121997794425675	0.000609988972128376
93	0.999884000455338	0.000231999089323051	0.000115999544661526
94	0.999977356009173	4.52879816542379e-05	2.26439908271190e-05
95	0.999995559892426	8.88021514794799e-06	4.44010757397400e-06
96	0.999999013281155	1.97343769007032e-06	9.8671884503516e-07
97	0.999999515457782	9.69084436239374e-07	4.84542218119687e-07
98	0.999999719023362	5.61953276777141e-07	2.80976638388570e-07
99	0.999999813232558	3.73534884673340e-07	1.86767442336670e-07
100	0.99999985392189	2.92156219809121e-07	1.46078109904561e-07
101	0.999999870037639	2.59924722556199e-07	1.29962361278099e-07
102	0.999999836529759	3.26940481982119e-07	1.63470240991059e-07
103	0.999999746065207	5.07869584997642e-07	2.53934792498821e-07
104	0.999999641500213	7.16999574036539e-07	3.58499787018270e-07
105	0.999999398628136	1.20274372830912e-06	6.01371864154561e-07
106	0.999998999203124	2.00159375206796e-06	1.00079687603398e-06
107	0.999998268384568	3.4632308639394e-06	1.7316154319697e-06
108	0.999997902529801	4.19494039736443e-06	2.09747019868222e-06
109	0.999999162768563	1.67446287298736e-06	8.37231436493682e-07
110	0.999999802438748	3.95122504999358e-07	1.97561252499679e-07
111	0.999999942375032	1.15249936398954e-07	5.76249681994768e-08
112	0.999999930426018	1.39147963649550e-07	6.95739818247749e-08
113	0.999999886500425	2.26999150449387e-07	1.13499575224693e-07
114	0.999999878203595	2.43592809229517e-07	1.21796404614758e-07
115	0.999999978637796	4.27244088501177e-08	2.13622044250589e-08
116	0.999999998094038	3.81192378726514e-09	1.90596189363257e-09
117	0.99999999963145	7.37099340044694e-10	3.68549670022347e-10
118	0.999999999298024	1.40395265048439e-09	7.01976325242196e-10
119	0.999999998477983	3.04403370315009e-09	1.52201685157504e-09
120	0.99999999678026	6.43947849272497e-09	3.21973924636249e-09
121	0.999999997832935	4.33413072900069e-09	2.16706536450034e-09
122	0.999999999264169	1.47166255075065e-09	7.35831275375327e-10
123	0.999999999797129	4.05742287200292e-10	2.02871143600146e-10
124	0.99999999983207	3.35861402095126e-10	1.67930701047563e-10
125	0.99999999981249	3.75021364664025e-10	1.87510682332012e-10
126	0.999999999771576	4.5684834849761e-10	2.28424174248805e-10
127	0.999999999809923	3.80154787742344e-10	1.90077393871172e-10
128	0.99999999990044	1.99119423603734e-10	9.9559711801867e-11
129	0.99999999991911	1.61780867582005e-10	8.08904337910023e-11
130	0.999999999807047	3.85906924161408e-10	1.92953462080704e-10
131	0.999999999455818	1.08836488604254e-09	5.44182443021268e-10
132	0.999999998463004	3.07399230006482e-09	1.53699615003241e-09
133	0.999999996242503	7.5149942767126e-09	3.7574971383563e-09
134	0.999999994460902	1.10781961961725e-08	5.53909809808623e-09
135	0.999999992019604	1.59607928181845e-08	7.98039640909224e-09
136	0.999999978750412	4.24991767907767e-08	2.12495883953884e-08
137	0.99999994276904	1.14461921183215e-07	5.72309605916075e-08
138	0.999999856467085	2.87065829431072e-07	1.43532914715536e-07
139	0.999999663962651	6.7207469722384e-07	3.3603734861192e-07
140	0.999999330932134	1.33813573136258e-06	6.69067865681289e-07
141	0.999998788087812	2.42382437661934e-06	1.21191218830967e-06
142	0.999996996169824	6.00766035122342e-06	3.00383017561171e-06
143	0.999993281065628	1.34378687440956e-05	6.71893437204782e-06
144	0.999987920789438	2.41584211246173e-05	1.20792105623087e-05
145	0.99998075541845	3.84891630994681e-05	1.92445815497340e-05
146	0.999967503502765	6.49929944696098e-05	3.24964972348049e-05
147	0.999923684830608	0.000152630338784012	7.63151693920061e-05
148	0.999937115505272	0.000125768989456038	6.28844947280191e-05
149	0.999993950276172	1.20994476555286e-05	6.0497238277643e-06
150	0.999998036150252	3.92769949555414e-06	1.96384974777707e-06
151	0.99999482677028	1.03464594396212e-05	5.17322971981059e-06
152	0.999997086594933	5.82681013371674e-06	2.91340506685837e-06
153	0.999999887023091	2.25953817226283e-07	1.12976908613141e-07
154	0.999999690542754	6.18914492868363e-07	3.09457246434182e-07
155	0.999998499692879	3.00061424287693e-06	1.50030712143847e-06
156	0.999996711968284	6.57606343217758e-06	3.28803171608879e-06
157	0.999988660068664	2.26798626712191e-05	1.13399313356096e-05
158	0.999956850238826	8.62995223489735e-05	4.31497611744868e-05
159	0.999955363512347	8.92729753052813e-05	4.46364876526406e-05
160	0.999928696507097	0.000142606985805397	7.13034929026985e-05
161	0.999597459423048	0.000805081153903527	0.000402540576951764
162	0.999964464401019	7.10711979629306e-05	3.55355989814653e-05
163	0.999938987141706	0.000122025716587644	6.1012858293822e-05

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	115	0.782312925170068	NOK
5% type I error level	117	0.795918367346939	NOK
10% type I error level	119	0.80952380952381	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/102xo11258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/102xo11258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/144dj1258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/144dj1258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/2zbcl1258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/2zbcl1258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/3656v1258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/3656v1258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/4gja71258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/4gja71258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/5so031258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/5so031258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/6a7pi1258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/6a7pi1258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/7c6251258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/7c6251258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/8o4ny1258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/8o4ny1258725386.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/9r53b1258725386.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t12587254534kiqlvup0iz641j/9r53b1258725386.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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.

FreeStatistics.org is powered by