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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: Fri, 24 Dec 2010 18:43:14 +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/24/t129321610683d2ts7nk3a8qyg.htm/, Retrieved Fri, 24 Dec 2010 19:41:49 +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/24/t129321610683d2ts7nk3a8qyg.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 3 4 4 4 2 2 4 4 2 3 3 4 3 5 4 4 2 5 4 2 4 4 3 4 4 4 2 4 2 2 2 3 2 2 1 5 2 5 4 2 4 4 2 3 4 2 2 3 4 3 1 1 2 2 1 3 3 2 3 5 2 3 4 4 3 4 2 2 4 1 1 3 2 2 4 4 5 4 2 4 4 2 2 4 3 5 4 2 3 3 4 1 1 2 4 3 3 2 1 4 2 2 4 4 4 2 2 2 2 2 1 5 2 3 2 4 1 2 2 2 2 4 4 4 4 2 2 3 4 1 2 4 2 3 4 2 4 1 4 4 2 3 2 4 4 2 4 2 4 2 3 2 4 1 4 3 4 5 3 4 4 2 2 5 2 2 2 2 4 5 2 4 4 4 4 3 4 1 4 4 4 4 4 3 4 5 1 3 2 2 2 3 4 5 2 4 4 2 4 4 4 4 2 2 3 3 4 2 2 4 4 2 2 5 4 2 2 4 3 3 2 4 2 4 2 5 2 4 2 4 4 5 4 3 4 3 4 3 4 2 2 3 2 2 4 2 1 1 3 3 2 3 2 2 1 2 4 3 4 3 4 2 4 1 1 4 2 2 4 2 4 3 2 4 2 4 4 4 4 2 4 4 4 3 3 2 4 2 4 2 2 1 2 3 4 4 4 4 2 2 2 1 1

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation

Talk[t] = + 2.45451506198987 + 0.107073554497237Driver[t] + 0.00408452725909042M1[t] + 0.902963220784294M2[t] + 0.455762701774012M3[t] + 0.0304762330688719M4[t] + 0.684908072788722M5[t] + 0.163430441120555M6[t] + 1.05686793887865M7[t] + 1.00251923175277M8[t] + 0.51987770481297M9[t] + 0.883285710527861M10[t] + 0.422283179117521M11[t] -0.00330628375724843t + 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)	2.45451506198987	0.429083	5.7204	0	0
Driver	0.107073554497237	0.086789	1.2337	0.219403	0.109702
M1	0.00408452725909042	0.445175	0.0092	0.992693	0.496346
M2	0.902963220784294	0.445581	2.0265	0.044642	0.022321
M3	0.455762701774012	0.445736	1.0225	0.308336	0.154168
M4	0.0304762330688719	0.444821	0.0685	0.945476	0.472738
M5	0.684908072788722	0.44615	1.5352	0.127036	0.063518
M6	0.163430441120555	0.446501	0.366	0.714907	0.357454
M7	1.05686793887865	0.444976	2.3751	0.018919	0.00946
M8	1.00251923175277	0.446134	2.2471	0.026219	0.01311
M9	0.51987770481297	0.455759	1.1407	0.255977	0.127988
M10	0.883285710527861	0.454158	1.9449	0.053822	0.026911
M11	0.422283179117521	0.453669	0.9308	0.353573	0.176786
t	-0.00330628375724843	0.00206	-1.6047	0.110836	0.055418

Multiple Linear Regression - Regression Statistics
Multiple R	0.37294609650926
R-squared	0.139088790901494
Adjusted R-squared	0.0579884596096057
F-TEST (value)	1.7150212420329
F-TEST (DF numerator)	13
F-TEST (DF denominator)	138
p-value	0.0640730433665606
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.11110924197453
Sum Squared Residuals	170.369797168967

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2	2.77651396898342	-0.776513968983421
2	4	3.77915993324862	0.220840066751383
3	4	3.11450602148661	0.885493978513386
4	2	2.9000603780187	-0.900060378018698
5	4	3.33703882498683	0.662961175013173
6	3	2.91932846405865	0.080671535941352
7	4	3.8094596780595	0.190540321940502
8	5	3.85887824167361	1.14112175832639
9	4	3.15878332198208	0.841216678017919
10	5	3.7330321529342	1.2669678470658
11	2	3.26872333776661	-1.26872333776661
12	4	2.7360603203946	1.2639396796054
13	4	2.84391211839368	1.15608788160632
14	4	3.52533741916716	0.474662580832837
15	4	3.07483061639963	0.925169383600367
16	2	2.64623786393724	-0.646237863937244
17	3	3.29736341989985	-0.297363419899845
18	2	2.66550594997719	-0.665505949977194
19	5	3.66271071847528	1.33728928152472
20	5	3.81920283658663	1.18079716341337
21	2	3.33325502588957	-1.33325502588957
22	4	3.47920963885274	0.520790361147258
23	3	3.22904793267963	-0.229047932679628
24	2	2.58931136081039	-0.589311360810385
25	3	2.8042367133067	0.1957632866933
26	3	3.37858845958294	-0.378588459582945
27	1	3.03515521131265	-2.03515521131265
28	2	2.49948890435303	-0.499488904353026
29	3	3.3647615693101	-0.364761569310101
30	2	2.83997765388469	-0.839977653884686
31	5	3.6230353133883	1.3769646866117
32	3	3.77952743149965	-0.779527431499645
33	4	3.18650606630536	0.813493933694645
34	4	3.43953423376576	0.560465766234239
35	2	3.18937252759265	-1.18937252759265
36	1	2.44256240122617	-1.44256240122617
37	3	2.55041419922525	0.449585800774754
38	2	3.66013371798767	-1.66013371798767
39	4	3.31670046971738	0.68329953028262
40	4	2.56688705376328	1.43311294623672
41	4	3.43215971872036	0.567840281279644
42	2	2.69322869430047	-0.693228694300468
43	4	3.69043346279855	0.309566537201445
44	5	3.73985202641266	1.26014797358734
45	2	3.14683066121837	-1.14683066121837
46	3	3.61400593767325	-0.614005937673253
47	1	2.82847645901396	-1.82847645901396
48	2	2.7241076596309	-0.724107659630896
49	3	2.6178123486355	0.382187651364499
50	2	3.29923764940898	-1.29923764940898
51	4	2.95580440113869	1.04419559886131
52	2	2.74135875767077	-0.741358757670774
53	4	3.39248431363338	0.607515686366625
54	2	2.65355328921349	-0.653553289213487
55	2	3.54368450321434	-1.54368450321434
56	2	3.37895595783397	-1.37895595783397
57	5	3.00008170163416	1.99991829836584
58	3	3.3601834235918	-0.360183423591799
59	4	2.78880105392697	1.21119894607303
60	2	2.47028514554944	-0.470285145549441
61	2	2.47106338905128	-0.471063389051283
62	4	3.58078290781371	0.419217092186288
63	4	3.13027610504618	0.869723894953818
64	2	2.48753624358932	-0.487536243589319
65	3	3.35280890854639	-0.352808908546394
66	1	2.61387788412651	-1.61387788412651
67	4	3.50400909812736	0.495990901872644
68	3	3.6605012162387	-0.660501216238702
69	2	3.17455340554165	-1.17455340554165
70	1	3.53465512749929	-2.53465512749929
71	4	2.85619920333723	1.14380079666277
72	3	2.43060974046246	0.56939025953754
73	4	2.64553509295878	1.35446490704122
74	2	3.54110750272673	-1.54110750272673
75	2	3.0906006999592	-1.0906006999592
76	2	2.55493439299957	-0.554934392999575
77	2	3.31313350345941	-1.31313350345941
78	1	2.788349588034	-1.788349588034
79	3	3.67848080203485	-0.678480802034848
80	5	3.51375225665448	1.48624774334552
81	4	3.13487800045467	0.865121999545333
82	2	3.28083261341784	-1.28083261341784
83	5	2.81652379825025	2.18347620174975
84	2	2.39093433537548	-0.390934335375479
85	2	2.60585968787179	-0.605859687871794
86	5	3.28728498864528	1.71271501135472
87	4	3.05092529487222	0.94907470512778
88	4	2.62233254240983	1.37766745759017
89	3	3.27345809837243	-0.273458098372432
90	1	2.74867418294702	-1.74867418294702
91	4	3.63880539694787	0.361194603052133
92	4	3.58115040606474	0.418849593935261
93	3	3.09520259536769	-0.0952025953676858
94	5	3.13408365383362	1.86591634616638
95	3	2.77684839316327	0.223151606836733
96	2	2.3512589302885	-0.351258930288498
97	3	2.56618428278481	0.433815717215187
98	5	3.24760958355829	1.75239041644171
99	4	3.01124988978524	0.988750110214762
100	2	2.58265713732285	-0.582657137322849
101	4	3.23378269328545	0.76621730671455
102	4	2.49485166886556	1.50514833113444
103	2	3.49205643736365	-1.49205643736365
104	3	3.54147500097776	-0.541475000977758
105	2	2.84138008128623	-0.841380081286232
106	4	3.41562891223835	0.584371087761652
107	2	2.73717298807629	-0.737172988076286
108	5	2.52573063419599	2.47426936580401
109	2	2.31236176870336	-0.312361768703359
110	4	3.31500773296855	0.68499226703145
111	3	2.75742737570378	0.242572624296217
112	4	2.3288346232414	1.67116537675861
113	4	2.979960179204	1.020039820796
114	5	2.45517626377858	2.54482373622142
115	4	3.34530747777943	0.654692522220569
116	4	3.50179959589078	0.498200404109223
117	5	3.01585178519372	1.98414821480628
118	3	3.37595350715137	-0.375953507151366
119	3	2.91164469198378	0.0883553080162218
120	3	2.48605522910901	0.513944770890991
121	2	2.27268636361638	-0.272686363616378
122	3	3.16825877338433	-0.168258773384332
123	2	2.93189907961128	-0.931899079611275
124	2	2.18208566365718	-0.182085663657177
125	1	3.04735832861425	-2.04735832861425
126	3	2.4155008586916	0.5844991413084
127	3	3.30563207269245	-0.30563207269245
128	2	3.14090352731209	-1.14090352731209
129	2	2.97617638010674	-0.976176380106743
130	3	3.33627810206439	-0.336278102064385
131	3	2.8719692868968	0.128030713103203
132	2	2.44637982402203	-0.446379824022028
133	1	2.12593740403216	-1.12593740403216
134	4	3.12858336829735	0.871416631702649
135	2	2.89222367452429	-0.892223674524294
136	2	2.46363092206191	-0.463630922061906
137	3	2.90060936903003	0.0993906309699663
138	4	2.37582545360462	1.62417454639538
139	4	3.48010377659994	0.519896223400058
140	4	3.42244878571681	0.577551214283185
141	2	2.93650097501976	-0.936500975019761
142	4	3.2966026969774	0.703397303022596
143	3	2.72522032731258	0.274779672687421
144	2	2.40670441893505	-0.406704418935047
145	2	2.40748266243689	-0.407482662436889
146	2	3.08890796321037	-1.08890796321037
147	1	2.63840116044284	-1.63840116044284
148	3	2.42395551697492	0.576044483025076
149	4	3.07508107293753	0.924918927062474
150	4	2.33615004851764	1.66384995148236
151	2	3.22628126251849	-1.22628126251849
152	1	3.06155271713812	-2.06155271713812

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.316536868650861	0.633073737301723	0.683463131349138
18	0.194311093197877	0.388622186395755	0.805688906802123
19	0.15343945826852	0.30687891653704	0.84656054173148
20	0.0921133029321115	0.184226605864223	0.907886697067888
21	0.245907222682794	0.491814445365588	0.754092777317206
22	0.194993617844372	0.389987235688743	0.805006382155628
23	0.167691430030768	0.335382860061536	0.832308569969232
24	0.205306333486691	0.410612666973381	0.79469366651331
25	0.143715972963048	0.287431945926097	0.856284027036952
26	0.102480423087612	0.204960846175224	0.897519576912388
27	0.261486710161052	0.522973420322104	0.738513289838948
28	0.215168819828684	0.430337639657367	0.784831180171316
29	0.159913419401369	0.319826838802738	0.840086580598631
30	0.117381469203035	0.23476293840607	0.882618530796965
31	0.114825585476265	0.229651170952529	0.885174414523735
32	0.119977270242719	0.239954540485438	0.880022729757281
33	0.141010413149694	0.282020826299389	0.858989586850305
34	0.106193875735418	0.212387751470836	0.893806124264582
35	0.081036672571598	0.162073345143196	0.918963327428402
36	0.0891684376476727	0.178336875295345	0.910831562352327
37	0.0751098654301477	0.150219730860295	0.924890134569852
38	0.0700649409855357	0.140129881971071	0.929935059014464
39	0.0879975713451135	0.175995142690227	0.912002428654887
40	0.197235914464355	0.394471828928711	0.802764085535645
41	0.17404923089411	0.348098461788221	0.82595076910589
42	0.139147241374066	0.278294482748132	0.860852758625934
43	0.112088055812546	0.224176111625093	0.887911944187454
44	0.11123177459661	0.222463549193219	0.88876822540339
45	0.103305632460282	0.206611264920564	0.896694367539718
46	0.0942350843472674	0.188470168694535	0.905764915652733
47	0.0937115370798009	0.187423074159602	0.906288462920199
48	0.0735863810386564	0.147172762077313	0.926413618961344
49	0.0596433388790835	0.119286677758167	0.940356661120917
50	0.0526080388257768	0.105216077651554	0.947391961174223
51	0.059052034332514	0.118104068665028	0.940947965667486
52	0.0460949736187889	0.0921899472375777	0.953905026381211
53	0.0397364704597734	0.0794729409195468	0.960263529540227
54	0.0309222122488783	0.0618444244977565	0.969077787751122
55	0.0500728474584726	0.100145694916945	0.949927152541527
56	0.0571227264850604	0.114245452970121	0.94287727351494
57	0.146064004340411	0.292128008680821	0.85393599565959
58	0.118859754565946	0.237719509131892	0.881140245434054
59	0.209043079929441	0.418086159858881	0.79095692007056
60	0.177652897182419	0.355305794364839	0.822347102817581
61	0.14832889082245	0.296657781644901	0.85167110917755
62	0.139782830670743	0.279565661341486	0.860217169329257
63	0.12896691490674	0.25793382981348	0.87103308509326
64	0.106692820381361	0.213385640762722	0.893307179618639
65	0.0861606787252574	0.172321357450515	0.913839321274743
66	0.09991218963604	0.19982437927208	0.90008781036396
67	0.0829412960608948	0.16588259212179	0.917058703939105
68	0.0701084028142471	0.140216805628494	0.929891597185753
69	0.0701694617764548	0.14033892355291	0.929830538223545
70	0.165167104510032	0.330334209020064	0.834832895489968
71	0.202955879621606	0.405911759243212	0.797044120378394
72	0.191319140296455	0.382638280592909	0.808680859703545
73	0.218113156759861	0.436226313519721	0.78188684324014
74	0.254845853289674	0.509691706579349	0.745154146710326
75	0.249568012682605	0.499136025365209	0.750431987317395
76	0.229790032267832	0.459580064535664	0.770209967732168
77	0.246729718778746	0.493459437557492	0.753270281221254
78	0.390110285515343	0.780220571030687	0.609889714484657
79	0.36801407997603	0.73602815995206	0.63198592002397
80	0.40933768404624	0.81867536809248	0.59066231595376
81	0.3972186010843	0.7944372021686	0.6027813989157
82	0.448689175875223	0.897378351750447	0.551310824124777
83	0.605355423071365	0.78928915385727	0.394644576928635
84	0.580528984449833	0.838942031100334	0.419471015550167
85	0.550329400940566	0.899341198118867	0.449670599059434
86	0.611197300333057	0.777605399333886	0.388802699666943
87	0.596551928880298	0.806896142239404	0.403448071119702
88	0.616693074720702	0.766613850558596	0.383306925279298
89	0.584382791506264	0.831234416987472	0.415617208493736
90	0.88906332857254	0.22187334285492	0.11093667142746
91	0.863638127329935	0.27272374534013	0.136361872670065
92	0.83294319727758	0.334113605444839	0.167056802722419
93	0.803605980798787	0.392788038402426	0.196394019201213
94	0.87196166965719	0.25607666068562	0.12803833034281
95	0.841795106243104	0.316409787513792	0.158204893756896
96	0.822791814954097	0.354416370091806	0.177208185045903
97	0.786069888977695	0.42786022204461	0.213930111022305
98	0.814314001070947	0.371371997858106	0.185685998929053
99	0.808453482932942	0.383093034134116	0.191546517067058
100	0.840267378429263	0.319465243141474	0.159732621570737
101	0.810343404431652	0.379313191136695	0.189656595568348
102	0.824357125350682	0.351285749298637	0.175642874649318
103	0.906974952417128	0.186050095165744	0.093025047582872
104	0.914567424973427	0.170865150053145	0.0854325750265727
105	0.907963677644116	0.184072644711768	0.0920363223558838
106	0.884336421634771	0.231327156730457	0.115663578365229
107	0.882428984278536	0.235142031442927	0.117571015721464
108	0.941562873293554	0.116874253412892	0.058437126706446
109	0.924192179726878	0.151615640546243	0.0758078202731217
110	0.901286778130256	0.197426443739488	0.0987132218697442
111	0.89617341943516	0.207653161129681	0.103826580564841
112	0.916163803576935	0.167672392846131	0.0838361964230654
113	0.918930443843356	0.162139112313288	0.081069556156644
114	0.932369479712735	0.135261040574529	0.0676305202872646
115	0.923107279450628	0.153785441098744	0.076892720549372
116	0.896980199774387	0.206039600451227	0.103019800225613
117	0.98306990078079	0.0338601984384209	0.0169300992192105
118	0.976011727820492	0.0479765443590162	0.0239882721795081
119	0.963947947835597	0.0721041043288052	0.0360520521644026
120	0.95799874758899	0.084002504822021	0.0420012524110105
121	0.947388228608616	0.105223542782768	0.0526117713913838
122	0.922064312977104	0.155871374045792	0.0779356870228959
123	0.892698204926431	0.214603590147138	0.107301795073569
124	0.891849527397142	0.216300945205716	0.108150472602858
125	0.985209257944197	0.029581484111606	0.014790742055803
126	0.989240263319242	0.0215194733615169	0.0107597366807584
127	0.980385228119905	0.0392295437601902	0.0196147718800951
128	0.966156834127446	0.067686331745108	0.033843165872554
129	0.941352384041516	0.117295231916968	0.0586476159584841
130	0.94145860778673	0.117082784426542	0.058541392213271
131	0.926967062312595	0.14606587537481	0.0730329376874052
132	0.876202132658159	0.247595734683682	0.123797867341841
133	0.8123913451343	0.375217309731399	0.187608654865699
134	0.922995933966104	0.154008132067791	0.0770040660338956
135	0.872045346470106	0.255909307059789	0.127954653529894

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	5	0.0420168067226891	OK
10% type I error level	11	0.092436974789916	OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/104sp11293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/104sp11293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/1f9sp1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/1f9sp1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/2f9sp1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/2f9sp1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/3pirs1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/3pirs1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/4pirs1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/4pirs1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/5pirs1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/5pirs1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/6ia9v1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/6ia9v1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/7t1qy1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/7t1qy1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/8t1qy1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/8t1qy1293216184.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/9t1qy1293216184.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t129321610683d2ts7nk3a8qyg/9t1qy1293216184.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

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