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*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, 19 Nov 2009 06:57:06 -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/19/t1258639081gobe752f93qazz2.htm/, Retrieved Wed, 22 May 2013 15:34:50 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t12585637133kpz1ucjg2abm6f (pk = 57535)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

3.88	153.3
3.98	154.5
3.29	155.2
2.88	156.9
3.22	157
3.62	157.4
3.82	157.2
3.54	157.5
2.53	158
2.22	158.5
2.85	159
2.78	159.3
2.28	160
2.26	160.8
2.71	161.9
2.77	162.5
2.77	162.7
2.64	162.8
2.56	162.9
2.07	163
2.32	164
2.16	164.7
2.23	164.8
2.4	164.9
2.84	165
2.77	165.8
2.93	166.1
2.91	167.2
2.69	167.7
2.38	168.3
2.58	168.6
3.19	168.9
2.82	169.1
2.72	169.5
2.53	169.6
2.7	169.7
2.42	169.8
2.5	170.4
2.31	170.9
2.41	171.9
2.56	171.9
2.76	172
2.71	172
2.44	172.4
2.46	173
2.12	173.7
1.99	173.8
1.86	173.8
1.88	173.9
1.82	174.6
1.74	175
1.71	175.9
1.38	176
1.27	175.1
1.19	175.6
1.28	175.9
1.19	176.7
1.22	176.1
1.47	176.1
1.46	176.2
1.96	176.3
1.88	177.8
2.03	178.5
2.04	179.4
1.9	179.5
1.8	179.6
1.92	179.7
1.92	179.7
1.97	179.8
2.46	179.9
2.36	180.2
2.53	180.4
2.31	180.4
1.98	181.3
1.46	181.9
1.26	182.5
1.58	182.7
1.74	183.1
1.89	183.6
1.85	183.7
1.62	183.8
1.3	183.9
1.42	184.1
1.15	184.4
0.42	184.5
0.74	185.9
1.02	186.6
1.51	187.6
1.86	187.8
1.59	187.9
1.03	188
0.44	188.3
0.82	188.4
0.86	188.5
0.58	188.5
0.59	188.6
0.95	188.6
0.98	189.4
1.23	190
1.17	191.9
0.84	192.5
0.74	193
0.65	193.5
0.91	193.9
1.19	194.2
1.3	194.9
1.53	194.9
1.94	194.9
1.79	194.9
1.95	195.5
2.26	196
2.04	196.2
2.16	196.2
2.75	196.2
2.79	196.2
2.88	197
3.36	197.7
2.97	198
3.1	198.2
2.49	198.5
2.2	198.6
2.25	199.5
2.09	200
2.79	201.3
3.14	202.2
2.93	202.9
2.65	203.5
2.67	203.5
2.26	204
2.35	204.1
2.13	204.3
2.18	204.5
2.9	204.8
2.63	205.1
2.67	205.7
1.81	206.5
1.33	206.9
0.88	207.1
1.28	207.8
1.26	208
1.26	208.5
1.29	208.6
1.1	209
1.37	209.1
1.21	209.7
1.74	209.8
1.76	209.9
1.48	210
1.04	210.8
1.62	211.4
1.49	211.7
1.79	212
1.8	212.2
1.58	212.4
1.86	212.9
1.74	213.4
1.59	213.7
1.26	214
1.13	214.3
1.92	214.8
2.61	215
2.26	215.9
2.41	216.4
2.26	216.9
2.03	217.2
2.86	217.5
2.55	217.9
2.27	218.1
2.26	218.6
2.57	218.9
3.07	219.3
2.76	220.4
2.51	220.9
2.87	221
3.14	221.8
3.11	222
3.16	222.2
2.47	222.5
2.57	222.9
2.89	223.1
2.63	223.4
2.38	224
1.69	225.1
1.96	225.5
2.19	225.9
1.87	226.3
1.6	226.5
1.63	227
1.22	227.3
1.21	227.8
1.49	228.1
1.64	228.4
1.66	228.5
1.77	228.8
1.82	229
1.78	229.1
1.28	229.3
1.29	229.6
1.37	229.9
1.12	230
1.51	230.2
2.24	230.8
2.94	231
3.09	231.7
3.46	231.9
3.64	233
4.39	235.1
4.15	236
5.21	236.9
5.8	237.1
5.91	237.5
5.39	238.2
5.46	238.9
4.72	239.1
3.14	240
2.63	240.2
2.32	240.5
1.93	240.7
0.62	241.1
0.6	241.4
-0.37	242.2
-1.1	242.9
-1.68	243.2
-0.78	243.9

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	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 2.46573628773672 -0.00180117407981777X[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	2.46573628773672	0.547683	4.5021	1.1e-05	5e-06
X	-0.00180117407981777	0.002751	-0.6547	0.513324	0.256662

Multiple Linear Regression - Regression Statistics
Multiple R	0.0438997676878124
R-squared	0.0019271896030439
Adjusted R-squared	-0.00256863386721262
F-TEST (value)	0.428662205220865
F-TEST (DF numerator)	1
F-TEST (DF denominator)	222
p-value	0.513323876544774
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.02226417409436
Sum Squared Residuals	231.995337243375

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3.88	2.18961630130065	1.69038369869935
2	3.98	2.18745489240488	1.79254510759513
3	3.29	2.186194070549	1.103805929451
4	2.88	2.18313207461331	0.696867925386689
5	3.22	2.18295195720533	1.03704804279467
6	3.62	2.1822314875734	1.4377685124266
7	3.82	2.18259172238937	1.63740827761063
8	3.54	2.18205137016542	1.35794862983458
9	2.53	2.18115078312551	0.348849216874488
10	2.22	2.1802501960856	0.0397498039143977
11	2.85	2.17934960904569	0.670650390954306
12	2.78	2.17880925682175	0.601190743178252
13	2.28	2.17754843496588	0.102451565034124
14	2.26	2.17610749570202	0.0838925042979782
15	2.71	2.17412620421422	0.535873795785778
16	2.77	2.17304549976633	0.596954500233669
17	2.77	2.17268526495037	0.597314735049632
18	2.64	2.17250514754239	0.467494852457614
19	2.56	2.17232503013440	0.387674969865596
20	2.07	2.17214491272642	-0.102144912726423
21	2.32	2.17034373864660	0.149656261353395
22	2.16	2.16908291679073	-0.00908291679073216
23	2.23	2.16890279938275	0.0610972006172495
24	2.4	2.16872268197477	0.231277318025231
25	2.84	2.16854256456679	0.671457435433213
26	2.77	2.16710162530293	0.602898374697067
27	2.93	2.16656127307899	0.763438726921013
28	2.91	2.16457998159119	0.745420018408812
29	2.69	2.16367939455128	0.526320605448721
30	2.38	2.16259869010339	0.217401309896612
31	2.58	2.16205833787944	0.417941662120557
32	3.19	2.16151798565550	1.02848201434450
33	2.82	2.16115775083953	0.658842249160466
34	2.72	2.16043728120761	0.559562718792393
35	2.53	2.16025716379963	0.369742836200375
36	2.7	2.16007704639164	0.539922953608357
37	2.42	2.15989692898366	0.260103071016338
38	2.5	2.15881622453577	0.341183775464229
39	2.31	2.15791563749586	0.152084362504138
40	2.41	2.15611446341604	0.253885536583956
41	2.56	2.15611446341604	0.403885536583956
42	2.76	2.15593434600806	0.604065653991937
43	2.71	2.15593434600806	0.554065653991937
44	2.44	2.15521387637614	0.284786123623865
45	2.46	2.15413317192824	0.305866828071755
46	2.12	2.15287235007237	-0.0328723500723722
47	1.99	2.15269223266439	-0.162692232664391
48	1.86	2.15269223266439	-0.292692232664390
49	1.88	2.15251211525641	-0.272512115256409
50	1.82	2.15125129340054	-0.331251293400536
51	1.74	2.15053082376861	-0.410530823768609
52	1.71	2.14890976709677	-0.438909767096773
53	1.38	2.14872964968879	-0.768729649688792
54	1.27	2.15035070636063	-0.880350706360628
55	1.19	2.14945011932072	-0.959450119320719
56	1.28	2.14890976709677	-0.868909767096773
57	1.19	2.14746882783292	-0.95746882783292
58	1.22	2.14854953228081	-0.92854953228081
59	1.47	2.14854953228081	-0.67854953228081
60	1.46	2.14836941487283	-0.688369414872828
61	1.96	2.14818929746485	-0.188189297464846
62	1.88	2.14548753634512	-0.265487536345120
63	2.03	2.14422671448925	-0.114226714489247
64	2.04	2.14260565781741	-0.102605657817411
65	1.9	2.14242554040943	-0.242425540409429
66	1.8	2.14224542300145	-0.342245423001447
67	1.92	2.14206530559347	-0.222065305593466
68	1.92	2.14206530559347	-0.222065305593466
69	1.97	2.14188518818548	-0.171885188185484
70	2.46	2.14170507077750	0.318294929222498
71	2.36	2.14116471855356	0.218835281446443
72	2.53	2.14080448373759	0.389195516262407
73	2.31	2.14080448373759	0.169195516262407
74	1.98	2.13918342706576	-0.159183427065757
75	1.46	2.13810272261787	-0.678102722617867
76	1.26	2.13702201816998	-0.877022018169976
77	1.58	2.13666178335401	-0.556661783354012
78	1.74	2.13594131372209	-0.395941313722085
79	1.89	2.13504072668218	-0.245040726682176
80	1.85	2.13486060927419	-0.284860609274195
81	1.62	2.13468049186621	-0.514680491866213
82	1.3	2.13450037445823	-0.834500374458231
83	1.42	2.13414013964227	-0.714140139642268
84	1.15	2.13359978741832	-0.983599787418322
85	0.42	2.13341967001034	-1.71341967001034
86	0.74	2.13089802629860	-1.39089802629860
87	1.02	2.12963720444272	-1.10963720444272
88	1.51	2.12783603036291	-0.617836030362905
89	1.86	2.12747579554694	-0.267475795546942
90	1.59	2.12729567813896	-0.53729567813896
91	1.03	2.12711556073098	-1.09711556073098
92	0.44	2.12657520850703	-1.68657520850703
93	0.82	2.12639509109905	-1.30639509109905
94	0.86	2.12621497369107	-1.26621497369107
95	0.58	2.12621497369107	-1.54621497369107
96	0.59	2.12603485628309	-1.53603485628309
97	0.95	2.12603485628309	-1.17603485628309
98	0.98	2.12459391701923	-1.14459391701923
99	1.23	2.12351321257134	-0.893513212571343
100	1.17	2.12009098181969	-0.95009098181969
101	0.84	2.1190102773718	-1.27901027737180
102	0.74	2.11810969033189	-1.37810969033189
103	0.65	2.11720910329198	-1.46720910329198
104	0.91	2.11648863366005	-1.20648863366005
105	1.19	2.11594828143611	-0.925948281436108
106	1.3	2.11468745958024	-0.814687459580235
107	1.53	2.11468745958024	-0.584687459580235
108	1.94	2.11468745958024	-0.174687459580236
109	1.79	2.11468745958024	-0.324687459580235
110	1.95	2.11360675513234	-0.163606755132345
111	2.26	2.11270616809244	0.147293831907564
112	2.04	2.11234593327647	-0.0723459332764724
113	2.16	2.11234593327647	0.0476540667235277
114	2.75	2.11234593327647	0.637654066723528
115	2.79	2.11234593327647	0.677654066723528
116	2.88	2.11090499401262	0.769095005987382
117	3.36	2.10964417215675	1.25035582784325
118	2.97	2.1091038199328	0.8608961800672
119	3.1	2.10874358511684	0.991256414883163
120	2.49	2.10820323289289	0.381796767107109
121	2.2	2.10802311548491	0.0919768845150904
122	2.25	2.10640205881307	0.143597941186926
123	2.09	2.10550147177316	-0.0155014717731650
124	2.79	2.1031599454694	0.686840054530598
125	3.14	2.10153888879757	1.03846111120243
126	2.93	2.10027806694169	0.829721933058307
127	2.65	2.09919736249380	0.550802637506197
128	2.67	2.09919736249380	0.570802637506197
129	2.26	2.09829677545389	0.161703224546106
130	2.35	2.09811665804591	0.251883341954088
131	2.13	2.09775642322995	0.0322435767700515
132	2.18	2.09739618841398	0.0826038115860153
133	2.9	2.09685583619004	0.80314416380996
134	2.63	2.09631548396609	0.533684516033906
135	2.67	2.09523477951820	0.574765220481796
136	1.81	2.09379384025435	-0.283793840254349
137	1.33	2.09307337062242	-0.763073370622422
138	0.88	2.09271313580646	-1.21271313580646
139	1.28	2.09145231395059	-0.811452313950586
140	1.26	2.09109207913462	-0.831092079134623
141	1.26	2.09019149209471	-0.830191492094714
142	1.29	2.09001137468673	-0.800011374686732
143	1.1	2.08929090505480	-0.989290905054805
144	1.37	2.08911078764682	-0.719110787646823
145	1.21	2.08803008319893	-0.878030083198932
146	1.74	2.08784996579095	-0.347849965790951
147	1.76	2.08766984838297	-0.327669848382969
148	1.48	2.08748973097499	-0.607489730974987
149	1.04	2.08604879171113	-1.04604879171113
150	1.62	2.08496808726324	-0.464968087263242
151	1.49	2.08442773503930	-0.594427735039297
152	1.79	2.08388738281535	-0.293887382815352
153	1.8	2.08352714799939	-0.283527147999388
154	1.58	2.08316691318342	-0.503166913183424
155	1.86	2.08226632614352	-0.222266326143515
156	1.74	2.08136573910361	-0.341365739103607
157	1.59	2.08082538687966	-0.490825386879661
158	1.26	2.08028503465572	-0.820285034655716
159	1.13	2.07974468243177	-0.94974468243177
160	1.92	2.07884409539186	-0.158844095391862
161	2.61	2.0784838605759	0.531516139424102
162	2.26	2.07686280390406	0.183137196095938
163	2.41	2.07596221686415	0.334037783135847
164	2.26	2.07506162982424	0.184938370175755
165	2.03	2.0745212776003	-0.0445212776002994
166	2.86	2.07398092537635	0.786019074623646
167	2.55	2.07326045574443	0.476739544255573
168	2.27	2.07290022092846	0.197099779071537
169	2.26	2.07199963388855	0.188000366111445
170	2.57	2.07145928166461	0.498540718335391
171	3.07	2.07073881203268	0.999261187967318
172	2.76	2.06875752054488	0.691242479455118
173	2.51	2.06785693350497	0.442143066495026
174	2.87	2.06767681609699	0.802323183903008
175	3.14	2.06623587683314	1.07376412316686
176	3.11	2.06587564201717	1.04412435798283
177	3.16	2.06551540720121	1.09448459279879
178	2.47	2.06497505497726	0.405024945022735
179	2.57	2.06425458534534	0.505745414654662
180	2.89	2.06389435052937	0.826105649470626
181	2.63	2.06335399830543	0.566646001694571
182	2.38	2.06227329385754	0.317726706142462
183	1.69	2.06029200236974	-0.370292002369739
184	1.96	2.05957153273781	-0.0995715327378117
185	2.19	2.05885106310588	0.131148936894115
186	1.87	2.05813059347396	-0.188130593473957
187	1.6	2.05777035865799	-0.457770358657994
188	1.63	2.05686977161808	-0.426869771618085
189	1.22	2.05632941939414	-0.83632941939414
190	1.21	2.05542883235423	-0.84542883235423
191	1.49	2.05488848013029	-0.564888480130285
192	1.64	2.05434812790634	-0.41434812790634
193	1.66	2.05416801049836	-0.394168010498358
194	1.77	2.05362765827441	-0.283627658274413
195	1.82	2.05326742345845	-0.233267423458449
196	1.78	2.05308730605047	-0.273087306050468
197	1.28	2.05272707123450	-0.772727071234504
198	1.29	2.05218671901056	-0.762186719010559
199	1.37	2.05164636678661	-0.681646366786613
200	1.12	2.05146624937863	-0.931466249378631
201	1.51	2.05110601456267	-0.541106014562668
202	2.24	2.05002531011478	0.189974689885223
203	2.94	2.04966507529881	0.890334924701186
204	3.09	2.04840425344294	1.04159574655706
205	3.46	2.04804401862698	1.41195598137302
206	3.64	2.04606272713918	1.59393727286082
207	4.39	2.04228026157156	2.34771973842844
208	4.15	2.04065920489972	2.10934079510028
209	5.21	2.03903814822789	3.17096185177211
210	5.8	2.03867791341193	3.76132208658807
211	5.91	2.03795744378	3.87204255622
212	5.39	2.03669662192413	3.35330337807587
213	5.46	2.03543580006825	3.42456419993175
214	4.72	2.03507556525229	2.68492443474771
215	3.14	2.03345450858045	1.10654549141955
216	2.63	2.03309427376449	0.59690572623551
217	2.32	2.03255392154055	0.287446078459455
218	1.93	2.03219368672458	-0.102193686724582
219	0.62	2.03147321709265	-1.41147321709265
220	0.6	2.03093286486871	-1.43093286486871
221	-0.37	2.02949192560485	-2.39949192560485
222	-1.1	2.02823110374898	-3.12823110374898
223	-1.68	2.02769075152504	-3.70769075152504
224	-0.78	2.02642992966916	-2.80642992966916

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.0236954574572773	0.0473909149145545	0.976304542542723
6	0.0263421566458947	0.0526843132917895	0.973657843354105
7	0.0209895500036243	0.0419791000072486	0.979010449996376
8	0.00810453254429183	0.0162090650885837	0.991895467455708
9	0.0113690764952041	0.0227381529904082	0.988630923504796
10	0.0135705068326868	0.0271410136653737	0.986429493167313
11	0.0059822296932875	0.011964459386575	0.994017770306713
12	0.00249861935549060	0.00499723871098121	0.99750138064451
13	0.00112659133450835	0.00225318266901670	0.998873408665492
14	0.000428956462365636	0.000857912924731271	0.999571043537634
15	0.000394548766369662	0.000789097532739324	0.99960545123363
16	0.000344888826394417	0.000689777652788834	0.999655111173606
17	0.000229908259012922	0.000459816518025845	0.999770091740987
18	0.000109666590394971	0.000219333180789941	0.999890333409605
19	4.62496788174078e-05	9.24993576348156e-05	0.999953750321183
20	2.27816817943743e-05	4.55633635887485e-05	0.999977218318206
21	8.89041313699628e-06	1.77808262739926e-05	0.999991109586863
22	3.28705710254488e-06	6.57411420508975e-06	0.999996712942897
23	1.22322372953518e-06	2.44644745907036e-06	0.99999877677627
24	5.3863705171531e-07	1.07727410343062e-06	0.999999461362948
25	7.27282898904727e-07	1.45456579780945e-06	0.999999272717101
26	7.59242130399879e-07	1.51848426079976e-06	0.99999924075787
27	1.10449402617948e-06	2.20898805235895e-06	0.999998895505974
28	1.46616329256213e-06	2.93232658512426e-06	0.999998533836707
29	9.6262399158567e-07	1.92524798317134e-06	0.999999037376008
30	4.15136974060486e-07	8.30273948120973e-07	0.999999584863026
31	2.2282354394207e-07	4.4564708788414e-07	0.999999777176456
32	5.81107959565134e-07	1.16221591913027e-06	0.99999941889204
33	4.0052781756108e-07	8.0105563512216e-07	0.999999599472182
34	2.25801325689048e-07	4.51602651378096e-07	0.999999774198674
35	1.01897199496772e-07	2.03794398993544e-07	0.9999998981028
36	5.35212206684752e-08	1.07042441336950e-07	0.99999994647878
37	2.2777168529579e-08	4.5554337059158e-08	0.999999977222831
38	9.89440945720025e-09	1.97888189144005e-08	0.99999999010559
39	4.11055167259240e-09	8.22110334518479e-09	0.999999995889448
40	1.71743974984819e-09	3.43487949969638e-09	0.99999999828256
41	8.07797449929404e-10	1.61559489985881e-09	0.999999999192203
42	5.22906459684762e-10	1.04581291936952e-09	0.999999999477094
43	2.92890082159423e-10	5.85780164318846e-10	0.99999999970711
44	1.21100704063667e-10	2.42201408127334e-10	0.999999999878899
45	5.06801656942499e-11	1.01360331388500e-10	0.99999999994932
46	2.21040036397904e-11	4.42080072795807e-11	0.999999999977896
47	1.10381679490933e-11	2.20763358981866e-11	0.999999999988962
48	6.72192675990233e-12	1.34438535198047e-11	0.999999999993278
49	3.65571028703176e-12	7.31142057406351e-12	0.999999999996344
50	1.97235909230504e-12	3.94471818461009e-12	0.999999999998028
51	1.13206945921819e-12	2.26413891843639e-12	0.999999999998868
52	5.87584115527815e-13	1.17516823105563e-12	0.999999999999412
53	6.66870195959581e-13	1.33374039191916e-12	0.999999999999333
54	1.13372990081182e-12	2.26745980162363e-12	0.999999999998866
55	1.84731928932048e-12	3.69463857864097e-12	0.999999999998153
56	1.76203896775156e-12	3.52407793550313e-12	0.999999999998238
57	1.66231016200552e-12	3.32462032401104e-12	0.999999999998338
58	1.45806183779796e-12	2.91612367559592e-12	0.999999999998542
59	7.218944115413e-13	1.4437888230826e-12	0.999999999999278
60	3.49494451782893e-13	6.98988903565786e-13	0.99999999999965
61	1.51754314838830e-13	3.03508629677659e-13	0.999999999999848
62	6.6260214383419e-14	1.32520428766838e-13	0.999999999999934
63	3.83002821045388e-14	7.66005642090775e-14	0.999999999999962
64	2.44629732698592e-14	4.89259465397184e-14	0.999999999999976
65	1.16870386804490e-14	2.33740773608979e-14	0.999999999999988
66	4.86438718926842e-15	9.72877437853684e-15	0.999999999999995
67	2.33147176381711e-15	4.66294352763421e-15	0.999999999999998
68	1.08972739067170e-15	2.17945478134339e-15	0.999999999999999
69	5.44210719905558e-16	1.08842143981112e-15	1
70	1.07117816216937e-15	2.14235632433875e-15	0.999999999999999
71	1.33504704077367e-15	2.67009408154734e-15	0.999999999999999
72	2.80025129623952e-15	5.60050259247905e-15	0.999999999999997
73	2.51965353794073e-15	5.03930707588146e-15	0.999999999999998
74	1.22169793782694e-15	2.44339587565389e-15	0.999999999999999
75	5.11988412998345e-16	1.02397682599669e-15	1
76	2.56471645788598e-16	5.12943291577197e-16	1
77	9.76953000969466e-17	1.95390600193893e-16	1
78	3.97021609338788e-17	7.94043218677576e-17	1
79	1.97184130645294e-17	3.94368261290588e-17	1
80	9.07470982262487e-18	1.81494196452497e-17	1
81	3.38777907578339e-18	6.77555815156678e-18	1
82	1.44051492294481e-18	2.88102984588963e-18	1
83	5.3840032086916e-19	1.07680064173832e-18	1
84	2.66058013505788e-19	5.32116027011577e-19	1
85	1.45786345690265e-18	2.91572691380530e-18	1
86	1.36787507673527e-18	2.73575015347055e-18	1
87	6.27818394114343e-19	1.25563678822869e-18	1
88	2.75141541886039e-19	5.50283083772078e-19	1
89	2.36715310587458e-19	4.73430621174917e-19	1
90	1.10905747910266e-19	2.21811495820532e-19	1
91	4.79240554573309e-20	9.58481109146618e-20	1
92	8.28730124835647e-20	1.65746024967129e-19	1
93	4.62922803997995e-20	9.2584560799599e-20	1
94	2.36698748186838e-20	4.73397496373676e-20	1
95	2.22759967294803e-20	4.45519934589607e-20	1
96	1.95572092573719e-20	3.91144185147439e-20	1
97	8.78774865821209e-21	1.75754973164242e-20	1
98	3.78916603991302e-21	7.57833207982603e-21	1
99	1.66008521554054e-21	3.32017043108107e-21	1
100	7.912765781472e-22	1.5825531562944e-21	1
101	3.73676104537108e-22	7.47352209074215e-22	1
102	1.93691214507565e-22	3.87382429015131e-22	1
103	1.12529235505838e-22	2.25058471011676e-22	1
104	5.75441537698296e-23	1.15088307539659e-22	1
105	3.77244762453888e-23	7.54489524907776e-23	1
106	3.21770803017672e-23	6.43541606035344e-23	1
107	4.56252092101486e-23	9.12504184202971e-23	1
108	2.49705649948773e-22	4.99411299897545e-22	1
109	5.61037606559084e-22	1.12207521311817e-21	1
110	2.09185596843676e-21	4.18371193687351e-21	1
111	2.35666851371155e-20	4.7133370274231e-20	1
112	7.4974012674133e-20	1.49948025348266e-19	1
113	2.82337494448655e-19	5.64674988897311e-19	1
114	8.69587339948773e-18	1.73917467989755e-17	1
115	1.58421723696279e-16	3.16843447392557e-16	1
116	2.66478373440962e-15	5.32956746881924e-15	0.999999999999997
117	1.90123127923443e-13	3.80246255846885e-13	0.99999999999981
118	1.50029435310632e-12	3.00058870621264e-12	0.9999999999985
119	1.23315057051500e-11	2.46630114103000e-11	0.999999999987669
120	1.83489696402606e-11	3.66979392805212e-11	0.99999999998165
121	1.63686795634679e-11	3.27373591269358e-11	0.999999999983631
122	1.55112326478565e-11	3.10224652957129e-11	0.999999999984489
123	1.18897969027219e-11	2.37795938054438e-11	0.99999999998811
124	2.83508563425677e-11	5.67017126851354e-11	0.99999999997165
125	1.35917832307751e-10	2.71835664615503e-10	0.999999999864082
126	3.38118260895138e-10	6.76236521790275e-10	0.999999999661882
127	4.62019465157659e-10	9.24038930315317e-10	0.99999999953798
128	6.1157759796389e-10	1.22315519592778e-09	0.999999999388422
129	4.7072710708555e-10	9.414542141711e-10	0.999999999529273
130	3.88204352634806e-10	7.76408705269613e-10	0.999999999611796
131	2.58380188375233e-10	5.16760376750466e-10	0.99999999974162
132	1.763802459699e-10	3.527604919398e-10	0.99999999982362
133	2.99962810909563e-10	5.99925621819126e-10	0.999999999700037
134	3.21685554667214e-10	6.43371109334429e-10	0.999999999678314
135	3.58438359732916e-10	7.16876719465831e-10	0.999999999641562
136	1.97464971275583e-10	3.94929942551167e-10	0.999999999802535
137	1.13805225229508e-10	2.27610450459016e-10	0.999999999886195
138	9.18897466638972e-11	1.83779493327794e-10	0.99999999990811
139	5.3818289180313e-11	1.07636578360626e-10	0.999999999946182
140	3.17423268435293e-11	6.34846536870586e-11	0.999999999968258
141	1.86804953976921e-11	3.73609907953842e-11	0.99999999998132
142	1.08074142954845e-11	2.16148285909689e-11	0.999999999989193
143	7.10265294409145e-12	1.42053058881829e-11	0.999999999992897
144	3.9727127676393e-12	7.9454255352786e-12	0.999999999996027
145	2.43130785146040e-12	4.86261570292079e-12	0.999999999997569
146	1.29098833688910e-12	2.58197667377820e-12	0.99999999999871
147	6.81934949504243e-13	1.36386989900849e-12	0.999999999999318
148	3.66557116544713e-13	7.33114233089426e-13	0.999999999999633
149	2.65849466091498e-13	5.31698932182996e-13	0.999999999999734
150	1.41665251706223e-13	2.83330503412445e-13	0.999999999999858
151	7.78382005985138e-14	1.55676401197028e-13	0.999999999999922
152	4.17546292645371e-14	8.35092585290743e-14	0.999999999999958
153	2.23348241256519e-14	4.46696482513038e-14	0.999999999999978
154	1.20815044096235e-14	2.4163008819247e-14	0.999999999999988
155	6.53774634278097e-15	1.30754926855619e-14	0.999999999999993
156	3.49574397272067e-15	6.99148794544134e-15	0.999999999999996
157	1.92473370065269e-15	3.84946740130538e-15	0.999999999999998
158	1.32097385037601e-15	2.64194770075202e-15	0.999999999999999
159	1.09181278003636e-15	2.18362556007272e-15	0.999999999999999
160	6.3764299876906e-16	1.27528599753812e-15	1
161	6.30728421728375e-16	1.26145684345675e-15	1
162	4.20529819092911e-16	8.41059638185822e-16	1
163	3.12765337027568e-16	6.25530674055137e-16	1
164	2.00660157108624e-16	4.01320314217248e-16	1
165	1.13894697995451e-16	2.27789395990903e-16	1
166	1.41574687198182e-16	2.83149374396363e-16	1
167	1.08847523556531e-16	2.17695047113062e-16	1
168	6.42195819033215e-17	1.28439163806643e-16	1
169	3.71582819678039e-17	7.43165639356078e-17	1
170	2.70219485893120e-17	5.40438971786241e-17	1
171	3.92834559583255e-17	7.8566911916651e-17	1
172	3.33498797793294e-17	6.66997595586588e-17	1
173	2.07411275934956e-17	4.14822551869911e-17	1
174	1.91118206242974e-17	3.82236412485947e-17	1
175	2.67728488543320e-17	5.35456977086641e-17	1
176	3.36614034616374e-17	6.73228069232749e-17	1
177	4.4516111608991e-17	8.9032223217982e-17	1
178	2.32363302392274e-17	4.64726604784549e-17	1
179	1.2958721346035e-17	2.591744269207e-17	1
180	1.03504346619356e-17	2.07008693238711e-17	1
181	5.92444864873863e-18	1.18488972974773e-17	1
182	2.71638592133124e-18	5.43277184266247e-18	1
183	1.16628127119406e-18	2.33256254238812e-18	1
184	4.62303607501425e-19	9.24607215002851e-19	1
185	1.85607209828709e-19	3.71214419657418e-19	1
186	7.2842296375152e-20	1.45684592750304e-19	1
187	3.26553332375291e-20	6.53106664750582e-20	1
188	1.45278782248971e-20	2.90557564497942e-20	1
189	1.05320896569686e-20	2.10641793139373e-20	1
190	8.3664793259896e-21	1.67329586519792e-20	1
191	4.93072289647008e-21	9.86144579294016e-21	1
192	2.64178857212926e-21	5.28357714425852e-21	1
193	1.49450617286886e-21	2.98901234573772e-21	1
194	8.21245835982006e-22	1.64249167196401e-21	1
195	4.71194758998378e-22	9.42389517996757e-22	1
196	3.20005011823829e-22	6.40010023647657e-22	1
197	6.37980548625264e-22	1.27596109725053e-21	1
198	2.00456137319741e-21	4.00912274639481e-21	1
199	9.95121432803607e-21	1.99024286560721e-20	1
200	3.40946330220314e-19	6.81892660440627e-19	1
201	1.94862094207815e-17	3.89724188415630e-17	1
202	6.4641573420457e-16	1.29283146840914e-15	1
203	2.78593368647831e-14	5.57186737295662e-14	0.999999999999972
204	4.20382126599161e-12	8.40764253198323e-12	0.999999999995796
205	9.24059878849942e-09	1.84811975769988e-08	0.999999990759401
206	0.000222414208901255	0.00044482841780251	0.999777585791099
207	0.0170756732595167	0.0341513465190334	0.982924326740483
208	0.483583335912164	0.967166671824328	0.516416664087836
209	0.746797096459466	0.506405807081069	0.253202903540534
210	0.835769396076116	0.328461207847769	0.164230603923884
211	0.845909515978057	0.308180968043887	0.154090484021943
212	0.815502915811535	0.368994168376930	0.184497084188465
213	0.87906992314691	0.241860153706182	0.120930076853091
214	0.900457066322482	0.199085867355036	0.099542933677518
215	0.878865660598207	0.242268678803586	0.121134339401793
216	0.833450051534579	0.333099896930842	0.166549948465421
217	0.816311849506288	0.367376300987425	0.183688150493712
218	0.845371619647841	0.309256760704317	0.154628380352159
219	0.715540146423523	0.568919707152953	0.284459853576477

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	195	0.906976744186046	NOK
5% type I error level	202	0.93953488372093	NOK
10% type I error level	203	0.944186046511628	NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')
}