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Workshop 8 Regression Analysis of Time Series

*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: Sat, 27 Nov 2010 11:39:05 +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/Nov/27/t1290857846vmmtep45uqbavux.htm/, Retrieved Sat, 27 Nov 2010 12:37:37 +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/Nov/27/t1290857846vmmtep45uqbavux.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 «

24 18 17 25 24 25 18 18 17 25 17 16 18 18 17 18 20 16 18 18 18 16 20 16 18 16 18 16 20 16 20 17 18 16 20 16 23 17 18 16 18 30 23 17 18 17 23 30 23 17 23 18 23 30 23 30 15 18 23 30 23 12 15 18 23 18 21 12 15 18 15 15 21 12 15 12 20 15 21 12 21 31 20 15 21 15 27 31 20 15 20 34 27 31 20 31 21 34 27 31 27 31 21 34 27 34 19 31 21 34 21 16 19 31 21 31 20 16 19 31 19 21 20 16 19 16 22 21 20 16 20 17 22 21 20 21 24 17 22 21 22 25 24 17 22 17 26 25 24 17 24 25 26 25 24 25 17 25 26 25 26 32 17 25 26 25 33 32 17 25 17 13 33 32 17 32 32 13 33 32 33 25 32 13 33 13 29 25 32 13 32 22 29 25 32 25 18 22 29 25 29 17 18 22 29 22 20 17 18 22 18 15 20 17 18 17 20 15 20 17 20 33 20 15 20 15 29 33 20 15 20 23 29 33 20 33 26 23 29 33 29 18 26 23 29 23 20 18 26 23 26 11 20 18 26 18 28 11 20 18 20 26 28 11 20 11 22 26 28 11 28 17 22 26 28 26 12 17 22 26 22 14 12 17 22 17 17 14 12 17 12 21 17 14 12 14 19 21 17 14 17 18 19 21 17 21 10 18 19 21 19 29 10 18 19 18 31 29 10 18 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	13 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Concernovermistakes[t] = -1.7562780158085e-14 + 1.53241564413974e-16Y1[t] -6.31065648645808e-18Y2[t] -1.77275820171837e-16Y3[t] + 1Y4[t] + 5.51714686945489e-16M1[t] + 8.53864962316541e-16M2[t] + 4.08923417553911e-16M3[t] + 5.83790269313932e-16M4[t] -4.12738543583127e-15M5[t] + 3.66459573819441e-16M6[t] + 1.39671603645796e-16M7[t] + 1.97031416598575e-16M8[t] + 7.66447169580341e-17M9[t] + 2.83259325707545e-17M10[t] + 1.64776501725111e-16M11[t] + 1.06828021625867e-17t + 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)	-1.7562780158085e-14	0	-5.1883	1e-06	0
Y1	1.53241564413974e-16	0	2.1325	0.03472	0.01736
Y2	-6.31065648645808e-18	0	-0.0879	0.930069	0.465035
Y3	-1.77275820171837e-16	0	-2.4778	0.014419	0.007209
Y4	1	0	13879196763174842	0	0
M1	5.51714686945489e-16	0	0.2885	0.773392	0.386696
M2	8.53864962316541e-16	0	0.4474	0.655309	0.327654
M3	4.08923417553911e-16	0	0.2125	0.832	0.416
M4	5.83790269313932e-16	0	0.3031	0.76226	0.38113
M5	-4.12738543583127e-15	0	-2.1356	0.034464	0.017232
M6	3.66459573819441e-16	0	0.1908	0.848924	0.424462
M7	1.39671603645796e-16	0	0.0733	0.941666	0.470833
M8	1.97031416598575e-16	0	0.1035	0.917697	0.458849
M9	7.66447169580341e-17	0	0.0408	0.967549	0.483774
M10	2.83259325707545e-17	0	0.0148	0.988207	0.494104
M11	1.64776501725111e-16	0	0.0857	0.931859	0.465929
t	1.06828021625867e-17	0	1.2539	0.211995	0.105998

Multiple Linear Regression - Regression Statistics
Multiple R	1
R-squared	1
Adjusted R-squared	1
F-TEST (value)	1.38555603953635e+31
F-TEST (DF numerator)	16
F-TEST (DF denominator)	139
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.7694682348403e-15
Sum Squared Residuals	3.16194798679795e-27

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	24	24	3.8833668017645e-15
2	25	25	4.45949864142709e-15
3	17	17	9.24241541089069e-16
4	18	18	4.61125481661534e-15
5	18	18.0000000000001	-5.2838819902124e-14
6	16	16	1.42903065268707e-15
7	20	20	1.36495432382927e-15
8	16	16	8.62610667874181e-16
9	18	18	5.385162280699e-16
10	17	17	1.14134724725819e-15
11	23	23	6.77059428648565e-16
12	30	30	1.44269847361675e-15
13	23	23	9.23376994723665e-16
14	18	18	3.57872526570919e-16
15	15	15	1.60625699562735e-15
16	12	12	-3.13768077881969e-16
17	21	21	4.58122455760425e-15
18	15	15	1.10819056724008e-15
19	20	20	-3.00412238663075e-16
20	31	31	4.18079129209161e-16
21	27	27	-6.59870099632231e-16
22	34	34	1.50838782343258e-15
23	21	21	5.74856950270073e-16
24	31	31	1.91725469604935e-16
25	19	19	3.97360753177649e-16
26	16	16	1.82846371929563e-16
27	20	20	7.58688484990028e-16
28	21	21	-8.25587317799867e-17
29	22	22	4.77556542915548e-15
30	17	17	7.7268116238042e-17
31	24	24	3.23872723740033e-16
32	25	25	7.1858264967758e-16
33	26	26	-2.65699034964752e-16
34	25	25	2.39564313396915e-16
35	17	17	6.77955131316204e-18
36	32	32	-4.23274989947867e-16
37	33	33	7.19464650024768e-16
38	13	13	2.21002884148810e-16
39	32	32	-1.08317613326465e-15
40	25	25	-4.26204267647754e-17
41	29	29	4.03430405574265e-15
42	22	22	1.92733860855692e-16
43	18	18	1.22093747056774e-15
44	17	17	5.42641586692203e-16
45	20	20	-3.17490407277616e-17
46	15	15	4.49681474651189e-16
47	20	20	6.17884216224246e-17
48	33	33	-4.99447296271356e-17
49	29	29	-2.30636069946821e-16
50	23	23	-4.93557801480265e-16
51	26	26	4.67131380782594e-16
52	18	18	-5.51391905569948e-16
53	20	20	4.82041746905647e-15
54	11	11	5.62837511020103e-16
55	28	28	4.43682276802976e-16
56	26	26	4.53580448336131e-16
57	22	22	8.16383967145096e-16
58	17	17	1.04003494524507e-15
59	12	12	1.21575771263536e-15
60	14	14	1.05530801366609e-15
61	17	17	2.58244596485335e-16
62	21	21	4.11103018301472e-16
63	19	19	-6.23213761956564e-16
64	18	18	-2.49544840487703e-16
65	10	10	5.08633773046969e-15
66	29	29	2.18274583820431e-16
67	31	31	-1.39537572062567e-16
68	19	19	7.60050037056527e-17
69	9	9	2.07828696186418e-15
70	20	20	-4.24867113968091e-16
71	28	28	-4.95327202783598e-16
72	19	19	-2.56586669411225e-16
73	30	30	-2.94734700887257e-16
74	29	29	-2.24982440947062e-16
75	26	26	-1.54437400140707e-16
76	23	23	1.17018086590954e-16
77	13	13	4.59427953539157e-15
78	21	21	-2.78300564777496e-17
79	19	19	4.54335758518357e-16
80	28	28	-3.21432289026417e-16
81	23	23	2.8989312050447e-16
82	18	18	2.31657706169282e-16
83	21	21	1.05984757410361e-16
84	20	20	2.54946825848687e-16
85	23	23	-2.45313405579323e-17
86	21	21	-1.08898687193293e-15
87	21	21	1.91453368756590e-16
88	15	15	-1.26039559772029e-15
89	28	28	5.21634196147695e-15
90	19	19	-1.15787610935093e-16
91	26	26	-7.80520164552607e-16
92	10	10	7.45283462474208e-17
93	16	16	-6.85542411714772e-16
94	22	22	-4.17135619658525e-16
95	19	19	-5.58947702664968e-16
96	31	31	-2.48956073048628e-16
97	31	31	-1.37221574703373e-15
98	29	29	-1.14723453120047e-15
99	19	19	-2.08057630789501e-17
100	22	22	-6.76818886995344e-16
101	23	23	4.47765782721385e-15
102	15	15	1.73801391999369e-16
103	20	20	-2.42404276582120e-16
104	18	18	-1.74542254220035e-16
105	23	23	-5.0088390501433e-16
106	25	25	-3.80313282769418e-16
107	21	21	-2.37904433571677e-16
108	24	24	2.00275718784968e-16
109	25	25	-1.91431027897035e-15
110	17	17	-5.58342749060412e-16
111	13	13	-1.40710916698716e-15
112	28	28	1.75995896134614e-16
113	21	21	4.03046582140411e-15
114	25	25	-4.82354893085692e-16
115	9	9	6.89065339052152e-16
116	16	16	-2.40086398543306e-16
117	19	19	1.47893093936049e-17
118	17	17	-5.9288506949058e-16
119	25	25	3.42323038189620e-16
120	20	20	-5.80880133139499e-16
121	29	29	-1.90678530886190e-16
122	14	14	-4.23766047950214e-16
123	22	22	-5.8728954152505e-16
124	15	15	-3.19402314866737e-16
125	19	19	3.86754219561692e-15
126	20	20	-1.92965636460651e-16
127	15	15	-1.19521799753211e-15
128	20	20	-1.01099848319274e-16
129	18	18	-3.70971395359309e-16
130	33	33	-3.75911377823661e-16
131	22	22	-1.03332081491370e-16
132	16	16	6.10360191008753e-16
133	17	17	-1.10274938207982e-15
134	16	16	-1.36236237856146e-16
135	21	21	-3.67959796887542e-16
136	26	26	-6.25967858144466e-16
137	18	18	3.98524618749881e-15
138	18	18	-1.09112738562669e-15
139	17	17	-9.73264151218723e-16
140	22	22	-7.98596428699453e-16
141	30	30	-9.5286344792078e-16
142	30	30	-1.28014199738019e-15
143	24	24	-1.08402396967233e-15
144	21	21	-7.67478554022456e-16
145	21	21	-1.05195774581381e-15
146	29	29	-1.55921676195035e-15
147	31	31	2.96219792594985e-16
148	20	20	-7.81800159129695e-16
149	16	16	3.36943713149333e-15
150	22	22	-1.85207110127491e-15
151	20	20	-8.65491491899326e-16
152	28	28	-1.51027061293384e-15
153	38	38	-2.70290251643311e-16
154	22	22	-1.13941904906277e-15
155	20	20	-5.05014469905607e-16
156	17	17	-1.42819354333347e-15

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
20	0	0	1
21	0.719856990206051	0.560286019587897	0.280143009793949
22	0.668870401777342	0.662259196445316	0.331129598222658
23	0.999999999399568	1.20086454992663e-09	6.00432274963313e-10
24	0.998127024127103	0.00374595174579384	0.00187297587289692
25	0.62458034082571	0.75083931834858	0.37541965917429
26	0.00339698979285965	0.0067939795857193	0.99660301020714
27	9.9767331149575e-06	1.9953466229915e-05	0.999990023266885
28	0.00181594095045590	0.00363188190091179	0.998184059049544
29	1	3.52060044205043e-42	1.76030022102521e-42
30	0.115222541835553	0.230445083671106	0.884777458164447
31	0.894510154171221	0.210979691657557	0.105489845828779
32	4.20093452951982e-07	8.40186905903964e-07	0.999999579906547
33	0.99916613784794	0.0016677243041197	0.00083386215205985
34	0.903931519865918	0.192136960268163	0.0960684801340816
35	3.50665838375945e-14	7.0133167675189e-14	0.999999999999965
36	0.00308144194247195	0.00616288388494389	0.996918558057528
37	0.999952602667514	9.47946649724211e-05	4.73973324862106e-05
38	1	2.51978653927511e-18	1.25989326963756e-18
39	0.999999369193811	1.26161237711984e-06	6.30806188559922e-07
40	5.4032760369708e-08	1.08065520739416e-07	0.99999994596724
41	1.00468160381728e-50	2.00936320763456e-50	1
42	0.242501733381911	0.485003466763822	0.757498266618089
43	1	2.02689835650921e-31	1.01344917825461e-31
44	1.31080341509135e-07	2.62160683018271e-07	0.999999868919659
45	1.68024958632601e-36	3.36049917265202e-36	1
46	1	4.71401815579007e-47	2.35700907789503e-47
47	1.32996657080606e-12	2.65993314161213e-12	0.99999999999867
48	0.858851306803598	0.282297386392804	0.141148693196402
49	1	1.61790360674534e-15	8.0895180337267e-16
50	0.430176854985172	0.860353709970344	0.569823145014828
51	1.91053786076928e-11	3.82107572153855e-11	0.999999999980895
52	0.999999999638577	7.22845374287005e-10	3.61422687143502e-10
53	0.712952108494549	0.574095783010902	0.287047891505451
54	0.307355318673353	0.614710637346707	0.692644681326646
55	1	2.73867528362786e-16	1.36933764181393e-16
56	1	1.12434355453661e-17	5.62171777268305e-18
57	1	1.52666504243120e-66	7.63332521215599e-67
58	0.99863790538146	0.00272418923707972	0.00136209461853986
59	0.000283076853401514	0.000566153706803028	0.999716923146599
60	1	2.18763530392175e-20	1.09381765196088e-20
61	1.02792430928911e-29	2.05584861857822e-29	1
62	1.28437643878008e-11	2.56875287756016e-11	0.999999999987156
63	1	2.37120455812057e-57	1.18560227906028e-57
64	0.354664205572054	0.709328411144109	0.645335794427946
65	0.0136950251553873	0.0273900503107746	0.986304974844613
66	3.09346679149556e-11	6.18693358299111e-11	0.999999999969065
67	0.999999992484456	1.50310883626835e-08	7.51554418134173e-09
68	1	1.02180632946562e-25	5.10903164732808e-26
69	0.0122180544654663	0.0244361089309326	0.987781945534534
70	0.981104316176566	0.0377913676468685	0.0188956838234343
71	3.70882949261692e-12	7.41765898523383e-12	0.999999999996291
72	1.77388725673243e-05	3.54777451346485e-05	0.999982261127433
73	3.42208057123584e-23	6.84416114247167e-23	1
74	1.72198694246963e-15	3.44397388493927e-15	0.999999999999998
75	1	3.77256458762366e-18	1.88628229381183e-18
76	0.0105993927445892	0.0211987854891783	0.98940060725541
77	0.00362220890052868	0.00724441780105737	0.996377791099471
78	1.89346081350575e-07	3.7869216270115e-07	0.999999810653919
79	0.384076802648202	0.768153605296404	0.615923197351798
80	0.0342575623939318	0.0685151247878636	0.965742437606068
81	1.64100341945322e-07	3.28200683890644e-07	0.999999835899658
82	0.999999999999998	3.80363030273808e-15	1.90181515136904e-15
83	0.984263639358605	0.031472721282791	0.0157363606413955
84	0.90247669302579	0.19504661394842	0.09752330697421
85	0.0152873495505228	0.0305746991010455	0.984712650449477
86	1	4.45540391287694e-22	2.22770195643847e-22
87	0.638792714037468	0.722414571925064	0.361207285962532
88	0.000395111760299482	0.000790223520598963	0.9996048882397
89	0.419853947315491	0.839707894630982	0.580146052684509
90	0.999497027680232	0.00100594463953648	0.00050297231976824
91	1	4.80783924920889e-21	2.40391962460444e-21
92	0.0790120652116307	0.158024130423261	0.920987934788369
93	2.23324791439416e-23	4.46649582878832e-23	1
94	1.82338215052376e-41	3.64676430104752e-41	1
95	1	4.38157791146543e-20	2.19078895573271e-20
96	0.999886216870355	0.000227566259290242	0.000113783129645121
97	1	2.13189876735798e-36	1.06594938367899e-36
98	0.925768372685205	0.148463254629590	0.0742316273147949
99	1	1.49716268527926e-20	7.48581342639629e-21
100	2.41685087831017e-22	4.83370175662034e-22	1
101	1.23616848682666e-06	2.47233697365332e-06	0.999998763831513
102	0.999999999996624	6.75230777931435e-12	3.37615388965717e-12
103	1	1.60221162372101e-19	8.01105811860506e-20
104	1	1.33355724651577e-18	6.66778623257883e-19
105	0.00634129466547553	0.0126825893309511	0.993658705334524
106	0.99999952409785	9.51804297828143e-07	4.75902148914072e-07
107	0.00353903279235668	0.00707806558471336	0.996460967207643
108	0.257775165039960	0.515550330079919	0.74222483496004
109	2.37044670337765e-09	4.7408934067553e-09	0.999999997629553
110	0.999999999482508	1.03498362521580e-09	5.17491812607898e-10
111	0.999707606127677	0.000584787744645187	0.000292393872322593
112	0.170623252776694	0.341246505553388	0.829376747223306
113	0.161903742947364	0.323807485894729	0.838096257052636
114	0.95189830244559	0.0962033951088213	0.0481016975544106
115	0.999978168890396	4.36622192074711e-05	2.18311096037356e-05
116	0.9999999402056	1.19588798993041e-07	5.97943994965203e-08
117	0.99996164468484	7.67106303215058e-05	3.83553151607529e-05
118	0.999999999937276	1.25448972025979e-10	6.27244860129895e-11
119	0.999999417559636	1.16488072826451e-06	5.82440364132257e-07
120	0.00087893690224204	0.00175787380448408	0.999121063097758
121	0.949546990736935	0.100906018526130	0.0504530092630648
122	0.99999966919095	6.61618098027346e-07	3.30809049013673e-07
123	0.0091841631868071	0.0183683263736142	0.990815836813193
124	0.999999999812117	3.75766265532907e-10	1.87883132766454e-10
125	0.996959455085392	0.00608108982921675	0.00304054491460837
126	0.191630952566376	0.383261905132751	0.808369047433624
127	0.898295505784387	0.203408988431227	0.101704494215613
128	0.99391987806349	0.0121602438730185	0.00608012193650925
129	0.999915373012127	0.000169253975745455	8.46269878727273e-05
130	0.998877998667253	0.00224400266549313	0.00112200133274657
131	0.998583293954154	0.00283341209169287	0.00141670604584644
132	0.999999900814988	1.98370023309739e-07	9.91850116548697e-08
133	0.99824187647966	0.0035162470406792	0.0017581235203396
134	0.933414984213413	0.133170031573174	0.0665850157865868
135	0.971044437128881	0.0579111257422374	0.0289555628711187
136	0.355913220742279	0.711826441484558	0.644086779257721

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	79	0.675213675213675	NOK
5% type I error level	88	0.752136752136752	NOK
10% type I error level	91	0.777777777777778	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/10c2p31290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/10c2p31290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/1yaad1290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/1yaad1290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/2yaad1290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/2yaad1290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/3yaad1290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/3yaad1290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/4rj9x1290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/4rj9x1290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/5rj9x1290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/5rj9x1290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/6rj9x1290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/6rj9x1290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/71s801290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/71s801290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/8c2p31290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/8c2p31290857931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/9c2p31290857931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290857846vmmtep45uqbavux/9c2p31290857931.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No 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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