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Multiple Lineair Regression en Seizoenaliteit

*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: Sun, 12 Dec 2010 12:49:29 +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/12/t12921581515bpedysd8wwvujj.htm/, Retrieved Sun, 12 Dec 2010 13:49:21 +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/12/t12921581515bpedysd8wwvujj.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 «

43880 43110 44496 44164 40399 36763 37903 35532 35533 32110 33374 35462 33508 36080 34560 38737 38144 37594 36424 36843 37246 38661 40454 44928 48441 48140 45998 47369 49554 47510 44873 45344 42413 36912 43452 42142 44382 43636 44167 44423 42868 43908 42013 38846 35087 33026 34646 37135 37985 43121 43722 43630 42234 39351 39327 35704 30466 28155 29257 29998 32529 34787 33855 34556 31348 30805 28353 24514 21106 21346 23335 24379 26290 30084 29429 30632 27349 27264 27474 24482 21453 18788 19282 19713 21917 23812 23785 24696 24562 23580 24939 23899 21454 19761 19815 20780 23462 25005 24725 26198 27543 26471 26558 25317 22896 22248 23406 25073 27691 30599 31948 32946 34012 32936 32974 30951 29812 29010 31068 32447 34844 35676 35387 36488 35652 33488 32914 29781 27951

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

OPENVAC[t] = + 31205.7 + 2878.75454545454M1[t] + 4617.02727272725M2[t] + 4437.20909090909M3[t] + 5506.93636363636M4[t] + 4582.02727272727M5[t] + 3309.75454545454M6[t] + 2771.75454545454M7[t] + 722.75454545454M8[t] -1622.33636363637M9[t] -3204.00000000001M10[t] -1396.80000000001M11[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)	31205.7	2460.797331	12.6811	0	0
M1	2878.75454545454	3400.080128	0.8467	0.398906	0.199453
M2	4617.02727272725	3400.080128	1.3579	0.177103	0.088551
M3	4437.20909090909	3400.080128	1.305	0.194443	0.097222
M4	5506.93636363636	3400.080128	1.6196	0.108	0.054
M5	4582.02727272727	3400.080128	1.3476	0.180383	0.090192
M6	3309.75454545454	3400.080128	0.9734	0.332346	0.166173
M7	2771.75454545454	3400.080128	0.8152	0.416613	0.208306
M8	722.75454545454	3400.080128	0.2126	0.832032	0.416016
M9	-1622.33636363637	3400.080128	-0.4771	0.634148	0.317074
M10	-3204.00000000001	3480.09296	-0.9207	0.35912	0.17956
M11	-1396.80000000001	3480.09296	-0.4014	0.688881	0.34444

Multiple Linear Regression - Regression Statistics
Multiple R	0.347257952103242
R-squared	0.120588085298937
Adjusted R-squared	0.0379083326347348
F-TEST (value)	1.45849596077890
F-TEST (DF numerator)	11
F-TEST (DF denominator)	117
p-value	0.156576377353524
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7781.72442733709
Sum Squared Residuals	7084962502.37273

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	43880	34084.4545454545	9795.5454545455
2	43110	35822.7272727273	7287.27272727272
3	44496	35642.9090909091	8853.09090909094
4	44164	36712.6363636364	7451.36363636363
5	40399	35787.7272727273	4611.27272727273
6	36763	34515.4545454546	2247.54545454545
7	37903	33977.4545454545	3925.54545454546
8	35532	31928.4545454546	3603.54545454545
9	35533	29583.3636363636	5949.63636363636
10	32110	28001.7	4108.3
11	33374	29808.9	3565.1
12	35462	31205.7	4256.3
13	33508	34084.4545454545	-576.454545454547
14	36080	35822.7272727273	257.272727272731
15	34560	35642.9090909091	-1082.90909090909
16	38737	36712.6363636364	2024.36363636364
17	38144	35787.7272727273	2356.27272727273
18	37594	34515.4545454545	3078.54545454546
19	36424	33977.4545454545	2446.54545454545
20	36843	31928.4545454545	4914.54545454545
21	37246	29583.3636363636	7662.63636363636
22	38661	28001.7	10659.3
23	40454	29808.9	10645.1
24	44928	31205.7	13722.3
25	48441	34084.4545454545	14356.5454545455
26	48140	35822.7272727273	12317.2727272727
27	45998	35642.9090909091	10355.0909090909
28	47369	36712.6363636364	10656.3636363636
29	49554	35787.7272727273	13766.2727272727
30	47510	34515.4545454545	12994.5454545455
31	44873	33977.4545454545	10895.5454545455
32	45344	31928.4545454545	13415.5454545455
33	42413	29583.3636363636	12829.6363636364
34	36912	28001.7	8910.3
35	43452	29808.9	13643.1
36	42142	31205.7	10936.3
37	44382	34084.4545454545	10297.5454545455
38	43636	35822.7272727273	7813.27272727273
39	44167	35642.9090909091	8524.0909090909
40	44423	36712.6363636364	7710.36363636364
41	42868	35787.7272727273	7080.27272727273
42	43908	34515.4545454545	9392.54545454545
43	42013	33977.4545454545	8035.54545454545
44	38846	31928.4545454545	6917.54545454545
45	35087	29583.3636363636	5503.63636363636
46	33026	28001.7	5024.3
47	34646	29808.9	4837.1
48	37135	31205.7	5929.3
49	37985	34084.4545454546	3900.54545454545
50	43121	35822.7272727273	7298.27272727273
51	43722	35642.9090909091	8079.0909090909
52	43630	36712.6363636364	6917.36363636364
53	42234	35787.7272727273	6446.27272727273
54	39351	34515.4545454545	4835.54545454545
55	39327	33977.4545454545	5349.54545454545
56	35704	31928.4545454545	3775.54545454546
57	30466	29583.3636363636	882.636363636364
58	28155	28001.7	153.300000000001
59	29257	29808.9	-551.899999999999
60	29998	31205.7	-1207.70000000001
61	32529	34084.4545454545	-1555.45454545455
62	34787	35822.7272727273	-1035.72727272727
63	33855	35642.9090909091	-1787.90909090909
64	34556	36712.6363636364	-2156.63636363636
65	31348	35787.7272727273	-4439.72727272727
66	30805	34515.4545454545	-3710.45454545454
67	28353	33977.4545454545	-5624.45454545455
68	24514	31928.4545454545	-7414.45454545455
69	21106	29583.3636363636	-8477.36363636363
70	21346	28001.7	-6655.7
71	23335	29808.9	-6473.9
72	24379	31205.7	-6826.7
73	26290	34084.4545454546	-7794.45454545455
74	30084	35822.7272727273	-5738.72727272727
75	29429	35642.9090909091	-6213.9090909091
76	30632	36712.6363636364	-6080.63636363636
77	27349	35787.7272727273	-8438.72727272727
78	27264	34515.4545454545	-7251.45454545454
79	27474	33977.4545454545	-6503.45454545455
80	24482	31928.4545454545	-7446.45454545455
81	21453	29583.3636363636	-8130.36363636363
82	18788	28001.7	-9213.7
83	19282	29808.9	-10526.9
84	19713	31205.7	-11492.7
85	21917	34084.4545454545	-12167.4545454545
86	23812	35822.7272727273	-12010.7272727273
87	23785	35642.9090909091	-11857.9090909091
88	24696	36712.6363636364	-12016.6363636364
89	24562	35787.7272727273	-11225.7272727273
90	23580	34515.4545454545	-10935.4545454545
91	24939	33977.4545454545	-9038.45454545455
92	23899	31928.4545454545	-8029.45454545455
93	21454	29583.3636363636	-8129.36363636363
94	19761	28001.7	-8240.7
95	19815	29808.9	-9993.9
96	20780	31205.7	-10425.7
97	23462	34084.4545454545	-10622.4545454545
98	25005	35822.7272727273	-10817.7272727273
99	24725	35642.9090909091	-10917.9090909091
100	26198	36712.6363636364	-10514.6363636364
101	27543	35787.7272727273	-8244.72727272727
102	26471	34515.4545454545	-8044.45454545454
103	26558	33977.4545454545	-7419.45454545454
104	25317	31928.4545454545	-6611.45454545455
105	22896	29583.3636363636	-6687.36363636364
106	22248	28001.7	-5753.7
107	23406	29808.9	-6402.9
108	25073	31205.7	-6132.70000000001
109	27691	34084.4545454546	-6393.45454545455
110	30599	35822.7272727273	-5223.72727272727
111	31948	35642.9090909091	-3694.90909090910
112	32946	36712.6363636364	-3766.63636363636
113	34012	35787.7272727273	-1775.72727272727
114	32936	34515.4545454545	-1579.45454545455
115	32974	33977.4545454545	-1003.45454545455
116	30951	31928.4545454545	-977.454545454545
117	29812	29583.3636363636	228.636363636365
118	29010	28001.7	1008.30000000000
119	31068	29808.9	1259.1
120	32447	31205.7	1241.30000000000
121	34844	34084.4545454545	759.545454545453
122	35676	35822.7272727273	-146.727272727269
123	35387	35642.9090909091	-255.909090909094
124	36488	36712.6363636364	-224.636363636361
125	35652	35787.7272727273	-135.727272727271
126	33488	34515.4545454545	-1027.45454545455
127	32914	33977.4545454545	-1063.45454545455
128	29781	31928.4545454545	-2147.45454545455
129	27951	29583.3636363636	-1632.36363636364

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
15	0.419400469801491	0.838800939602982	0.580599530198509
16	0.296608458157425	0.593216916314851	0.703391541842575
17	0.180107080666569	0.360214161333138	0.819892919333431
18	0.100058027923094	0.200116055846189	0.899941972076906
19	0.0528790465493201	0.105758093098640	0.94712095345068
20	0.0266697637060665	0.0533395274121329	0.973330236293934
21	0.0133679820071521	0.0267359640143043	0.986632017992848
22	0.0110777938969308	0.0221555877938616	0.98892220610307
23	0.0100247601763844	0.0200495203527688	0.989975239823616
24	0.0141930758681792	0.0283861517363583	0.98580692413182
25	0.0258927916084047	0.0517855832168095	0.974107208391595
26	0.0335615016427235	0.0671230032854471	0.966438498357276
27	0.0319846673259047	0.0639693346518094	0.968015332674095
28	0.0295755678602766	0.0591511357205532	0.970424432139723
29	0.0499397705302862	0.0998795410605725	0.950060229469714
30	0.0768030737113999	0.153606147422800	0.9231969262886
31	0.0843792229846574	0.168758445969315	0.915620777015343
32	0.113218709818599	0.226437419637199	0.8867812901814
33	0.123255519939747	0.246511039879494	0.876744480060253
34	0.105850200047341	0.211700400094682	0.894149799952659
35	0.130349070783093	0.260698141566185	0.869650929216907
36	0.127457695410999	0.254915390821999	0.872542304589
37	0.129623646820544	0.259247293641088	0.870376353179456
38	0.117565947313457	0.235131894626914	0.882434052686543
39	0.112636940799808	0.225273881599615	0.887363059200192
40	0.104187740868303	0.208375481736607	0.895812259131697
41	0.0948510465275977	0.189702093055195	0.905148953472402
42	0.102266381483421	0.204532762966841	0.89773361851658
43	0.101436002240300	0.202872004480599	0.8985639977597
44	0.0968807915129872	0.193761583025974	0.903119208487013
45	0.0958980875795421	0.191796175159084	0.904101912420458
46	0.0931939788933405	0.186387957786681	0.90680602110666
47	0.100024295551257	0.200048591102513	0.899975704448743
48	0.112988277010628	0.225976554021256	0.887011722989372
49	0.125757945939527	0.251515891879055	0.874242054060473
50	0.148831578145936	0.297663156291872	0.851168421854064
51	0.192025139823858	0.384050279647716	0.807974860176142
52	0.23357203751077	0.46714407502154	0.76642796248923
53	0.280921135839277	0.561842271678553	0.719078864160723
54	0.314576403627139	0.629152807254279	0.68542359637286
55	0.355676791839831	0.711353583679662	0.644323208160169
56	0.397742804578513	0.795485609157025	0.602257195421487
57	0.452815208214664	0.905630416429327	0.547184791785336
58	0.49921052470871	0.99842104941742	0.50078947529129
59	0.576525883313703	0.846948233372594	0.423474116686297
60	0.666093742281051	0.667812515437897	0.333906257718949
61	0.732426120914428	0.535147758171144	0.267573879085572
62	0.774135057281969	0.451729885436063	0.225864942718031
63	0.810173463494215	0.379653073011569	0.189826536505785
64	0.841063160447952	0.317873679104096	0.158936839552048
65	0.876001636134635	0.247996727730731	0.123998363865365
66	0.893990079396511	0.212019841206979	0.106009920603489
67	0.916075183891415	0.167849632217171	0.0839248161085854
68	0.945357546071085	0.109284907857830	0.0546424539289149
69	0.968582838101137	0.0628343237977258	0.0314171618988629
70	0.97419639949545	0.0516072010090976	0.0258036005045488
71	0.978754096748082	0.0424918065038354	0.0212459032519177
72	0.982808638857154	0.0343827222856922	0.0171913611428461
73	0.986129198388798	0.0277416032224036	0.0138708016112018
74	0.986307538006347	0.0273849239873069	0.0136924619936535
75	0.986318179684006	0.0273636406319885	0.0136818203159942
76	0.98589484314602	0.0282103137079584	0.0141051568539792
77	0.987602003425761	0.0247959931484771	0.0123979965742386
78	0.987332969723404	0.0253340605531914	0.0126670302765957
79	0.985889787458284	0.0282204250834313	0.0141102125417157
80	0.985366364502307	0.0292672709953863	0.0146336354976931
81	0.985728597186969	0.028542805626062	0.014271402813031
82	0.986850699682972	0.026298600634055	0.0131493003170275
83	0.989219389754567	0.0215612204908655	0.0107806102454327
84	0.9921047514434	0.0157904971131986	0.0078952485565993
85	0.994419994768123	0.0111600104637534	0.00558000523187671
86	0.995868011710495	0.00826397657901009	0.00413198828950504
87	0.996915079192241	0.00616984161551701	0.00308492080775850
88	0.997750611055921	0.00449877788815718	0.00224938894407859
89	0.998382892541384	0.00323421491723094	0.00161710745861547
90	0.998744814214404	0.00251037157119264	0.00125518578559632
91	0.998691709196913	0.00261658160617411	0.00130829080308706
92	0.998393946464532	0.00321210707093551	0.00160605353546776
93	0.99813866853923	0.00372266292153968	0.00186133146076984
94	0.997833571676196	0.00433285664760863	0.00216642832380432
95	0.99802076499219	0.00395847001562194	0.00197923500781097
96	0.998368566445649	0.00326286710870179	0.00163143355435090
97	0.998638026311078	0.00272394737784440	0.00136197368892220
98	0.998955266789101	0.00208946642179784	0.00104473321089892
99	0.999362549738607	0.00127490052278552	0.000637450261392762
100	0.999602276204925	0.000795447590149618	0.000397723795074809
101	0.999664336417353	0.000671327165293782	0.000335663582646891
102	0.99968768624347	0.000624627513059248	0.000312313756529624
103	0.999689547422994	0.000620905154011285	0.000310452577005643
104	0.999571019677614	0.000857960644771998	0.000428980322385999
105	0.999542463393905	0.000915073212189593	0.000457536606094797
106	0.999510735238978	0.000978529522044349	0.000489264761022174
107	0.999656868328848	0.00068626334230466	0.00034313167115233
108	0.999801617212088	0.000396765575824329	0.000198382787912165
109	0.999935551694428	0.000128896611143829	6.44483055719144e-05
110	0.999959483863386	8.10322732289427e-05	4.05161366144714e-05
111	0.999938656753207	0.000122686493586739	6.13432467933694e-05
112	0.999960842635412	7.83147291762603e-05	3.91573645881302e-05
113	0.999829974897045	0.000340050205909789	0.000170025102954895
114	0.998271783466299	0.00345643306740216	0.00172821653370108

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	29	0.29	NOK
5% type I error level	48	0.48	NOK
10% type I error level	56	0.56	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/10din11292158159.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/10din11292158159.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/17z871292158159.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/17z871292158159.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/2h8pa1292158159.png (open in new window)

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http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/9din11292158159.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t12921581515bpedysd8wwvujj/9din11292158159.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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')

}

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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