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Multiple Regression interaction effects minitutorial

*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: Tue, 23 Nov 2010 23:36:51 +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/24/t1290555423c1518buuuc81nf1.htm/, Retrieved Wed, 24 Nov 2010 00:37:13 +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/24/t1290555423c1518buuuc81nf1.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 «

7 7 1 7 7 1 7 7 4 5 2 5 6 2 5 6 5 6 1 5 5 1 5 5 7 7 1 7 7 1 7 6 6 6 2 5 6 1 4 5 5 4 1 7 7 1 4 7 5 6 2 5 6 2 5 6 5 6 1 6 7 1 6 7 6 7 1 7 5 1 6 7 5 6 2 5 6 3 6 6 6 7 1 5 6 1 5 7 7 7 1 7 7 1 6 7 6 7 1 3 7 2 7 7 3 7 1 7 7 1 6 7 6 6 1 6 6 1 5 6 3 3 1 5 5 1 4 4 4 6 1 5 6 1 4 5 6 7 1 7 6 1 6 7 6 7 1 3 6 1 6 6 5 5 1 7 6 1 5 6 6 6 1 7 7 1 7 7 6 6 1 7 6 1 6 6 3 4 1 7 7 1 4 7 4 5 3 4 3 3 4 5 5 6 2 6 7 2 6 6 4 4 1 5 5 1 6 7 5 7 1 7 7 0 5 7 6 6 2 6 6 2 5 5 2 5 1 4 5 1 2 6 5 7 1 5 7 1 5 5 3 6 1 7 7 2 5 7 7 7 1 7 7 1 7 7 6 5 1 7 6 1 6 5 6 6 1 7 6 2 7 5 6 5 1 7 6 1 6 5 7 3 1 6 5 1 6 6 5 6 1 3 6 1 5 7 5 5 1 4 6 2 4 5 7 6 1 5 6 1 5 6 5 4 3 7 7 3 6 7 5 5 1 5 5 1 6 6 2 6 3 6 7 2 4 7 5 4 4 5 3 6 5 1 6 7 1 6 7 1 6 6 5 6 1 7 7 1 5 7 1 4 1 7 7 1 6 6 5 7 1 7 6 1 5 6 5 3 2 7 7 1 6 7 5 7 1 6 7 1 5 7 6 4 1 7 6 1 5 4 6 5 1 6 7 1 7 6 6 7 1 7 6 1 5 6 5 6 2 7 6 2 5 6 6 6 1 6 6 2 6 6 5 6 4 6 6 4 3 6 5 6 1 5 7 1 6 7 6 6 2 5 6 2 5 6 6 6 1 6 7 1 6 7 4 6 2 5 6 2 4 5 5 6 1 6 6 2 6 6 4 5 1 3 5 1 6 5 6 7 1 7 7 2 5 6 6 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	9 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Q1_22[t] = + 1.61968772478699 -0.00918828791935026Q1_2[t] + 0.340656368476894Q1_3[t] + 0.356234894492118Q1_5[t] -0.159352120836570Q1_7[t] + 0.484170885364494Q1_8[t] -0.300030003511608Q1_12[t] + 0.097133273108172Q1_16[t] + 0.0248399368734786Q1_2v[t] -0.0351115015876335Q1_3v[t] + 0.331622895188286Q1_5v[t] -0.128426182123679Q1_7v[t] + 0.142269832219955Q1_8v[t] -0.0451005706686726Q1_12v[t] + 0.0428633491152994Q1_16v[t] -0.141230731472698Q1_22v[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)	1.61968772478699	0.877904	1.8449	0.068528	0.034264
Q1_2	-0.00918828791935026	0.104501	-0.0879	0.930143	0.465071
Q1_3	0.340656368476894	0.098087	3.473	0.000812	0.000406
Q1_5	0.356234894492118	0.130262	2.7348	0.007596	0.003798
Q1_7	-0.159352120836570	0.082334	-1.9354	0.056263	0.028132
Q1_8	0.484170885364494	0.094273	5.1358	2e-06	1e-06
Q1_12	-0.300030003511608	0.116909	-2.5664	0.01203	0.006015
Q1_16	0.097133273108172	0.114969	0.8449	0.40056	0.20028
Q1_2v	0.0248399368734786	0.109294	0.2273	0.820754	0.410377
Q1_3v	-0.0351115015876335	0.107443	-0.3268	0.744629	0.372315
Q1_5v	0.331622895188286	0.228915	1.4487	0.151108	0.075554
Q1_7v	-0.128426182123679	0.125192	-1.0258	0.30788	0.15394
Q1_8v	0.142269832219955	0.157977	0.9006	0.370361	0.18518
Q1_12v	-0.0451005706686726	0.138402	-0.3259	0.745327	0.372663
Q1_16v	0.0428633491152994	0.155632	0.2754	0.783665	0.391833
Q1_22v	-0.141230731472698	0.147537	-0.9573	0.341153	0.170577

Multiple Linear Regression - Regression Statistics
Multiple R	0.658977147434301
R-squared	0.434250880840649
Adjusted R-squared	0.334412800988998
F-TEST (value)	4.34955160882404
F-TEST (DF numerator)	15
F-TEST (DF denominator)	85
p-value	5.89831236164073e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.87092238918393
Sum Squared Residuals	64.4729936784568

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	7	7.02510077115959	-0.0251007711595910
2	5	5.54783555237797	-0.547835552377967
3	5	6.0677536234044	-1.06775362340440
4	6	6.01797505809933	-0.0179750580993263
5	7	5.95630522897426	1.04369477102574
6	7	6.179380437712	0.820619562287998
7	7	6.77713235996046	0.222867640039541
8	6	6.0307364032501	-0.0307364032501016
9	5	5.5928576028722	-0.592857602872204
10	6	6.57185863205907	-0.571858632059068
11	7	6.2076897231097	0.792310276890294
12	7	5.83499139042263	1.16500860957737
13	6	6.32919667972098	-0.329196679720977
14	7	7.1766137258019	-0.176613725801904
15	6	5.36537287291367	0.634627127086326
16	7	5.77458892228821	1.22541107771179
17	5	5.42472270607947	-0.42472270607947
18	5	5.40205998770025	-0.402059987700248
19	7	6.58180263645311	0.418197363546885
20	6	6.45823506137093	-0.458235061370928
21	6	5.69197489724246	0.308025102757538
22	1	3.5274586067484	-2.5274586067484
23	7	6.11090461584054	0.889095384159459
24	6	6.29225351175008	-0.292253511750077
25	7	6.83244107113154	0.16755892886846
26	6	5.94841062476645	0.0515893752335524
27	6	5.67797108188373	0.322028918116265
28	6	5.90519235513111	0.0948076448688896
29	6	6.03362670705345	-0.0336267070534526
30	5	5.88389040149457	-0.883890401494574
31	5	5.47653778082898	-0.476537780828981
32	7	6.36042560741858	0.639574392581419
33	3	4.11480699037853	-1.11480699037853
34	6	5.32912901792549	0.670870982074511
35	5	6.01244033580896	-1.01244033580896
36	6	6.51116425693954	-0.51116425693954
37	7	5.98317215615326	1.01682784384674
38	6	6.00779495383096	-0.00779495383096274
39	5	5.09821386264445	-0.0982138626444483
40	5	5.63048130696828	-0.630481306968277
41	6	6.61846262526562	-0.618462625265624
42	7	6.15445757578822	0.845542424211778
43	7	7.16687594170784	-0.166875941707837
44	5	5.03574347968164	-0.0357434796816424
45	7	6.13240279761086	0.867597202389142
46	5	5.10009225961324	-0.100092259613243
47	5	4.74443156940751	0.255568430592490
48	5	5.81703059448912	-0.817030594489116
49	6	5.98773128370064	0.0122687162993624
50	6	6.26785516890419	-0.267855168904186
51	7	6.02379073955894	0.976209260441064
52	7	5.18382260728762	1.81617739271238
53	7	7.26004004461387	-0.260040044613874
54	7	5.9895821040213	1.01041789597870
55	2	4.03936357270476	-2.03936357270476
56	6	6.46013827739038	-0.460138277390379
57	6	6.86771306664385	-0.867713066643847
58	6	6.2500319788534	-0.250031978853404
59	7	6.55721505189587	0.442784948104131
60	5	5.23799128921044	-0.237991289210440
61	7	5.55677257337146	1.44322742662854
62	6	5.91071428791703	0.0892857120829742
63	6	6.01039560496425	-0.0103956049642501
64	5	5.04900426128738	-0.0490042612873828
65	6	5.94276456519716	0.0572354348028417
66	7	7.44626638147139	-0.44626638147139
67	6	6.19641332492934	-0.196413324929339
68	7	6.96821001896168	0.0317899810383194
69	7	6.22120208594566	0.778797914054345
70	5	4.9588223213712	0.0411776786287946
71	6	5.41125311252739	0.588746887472612
72	7	6.86188845793416	0.138111542065842
73	7	5.95456908055571	1.04543091944429
74	7	6.06462171301128	0.935378286988723
75	7	6.10463371084172	0.895366289158283
76	7	4.67842065654389	2.32157934345611
77	6	5.83320515016348	0.166794849836516
78	5	6.62405535506921	-1.62405535506921
79	5	4.56772531860318	0.432274681396818
80	7	6.94983344312298	0.0501665568770206
81	6	6.17138743306102	-0.171387433061018
82	6	6.68936991494391	-0.689369914943912
83	6	6.09230677154743	-0.0923067715474307
84	6	6.27129245407138	-0.271292454071381
85	7	7.5988230436906	-0.598823043690594
86	6	6.7459773891937	-0.745977389193694
87	7	6.45503510749454	0.544964892505461
88	5	6.83014836372585	-1.83014836372585
89	5	6.21007851366726	-1.21007851366726
90	7	5.97128439764152	1.02871560235848
91	5	5.77700025918297	-0.777000259182974
92	7	6.45196134242997	0.548038657570027
93	7	6.73039886317847	0.269601136821530
94	5	5.6408353039171	-0.640835303917097
95	6	6.28937136758725	-0.289371367587252
96	7	5.83264405506736	1.16735594493264
97	6	6.42118057174751	-0.421180571747512
98	5	6.36495373368526	-1.36495373368526
99	5	5.92716409210019	-0.927164092100193
100	7	5.95218998396851	1.04781001603149
101	7	6.62055406828976	0.379445931710238

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.298808483443559	0.597616966887118	0.701191516556441
20	0.270254644109751	0.540509288219501	0.72974535589025
21	0.155392934110984	0.310785868221967	0.844607065889016
22	0.348609607840317	0.697219215680635	0.651390392159683
23	0.275368127473243	0.550736254946487	0.724631872526757
24	0.188306823746288	0.376613647492577	0.811693176253712
25	0.146100293704662	0.292200587409323	0.853899706295338
26	0.0944792392154245	0.188958478430849	0.905520760784576
27	0.0629722593096512	0.125944518619302	0.93702774069035
28	0.100368106022247	0.200736212044494	0.899631893977753
29	0.0671683007510811	0.134336601502162	0.932831699248919
30	0.0663704723901064	0.132740944780213	0.933629527609894
31	0.0509332829101174	0.101866565820235	0.949066717089883
32	0.0391235803351982	0.0782471606703965	0.960876419664802
33	0.0334585817562925	0.066917163512585	0.966541418243708
34	0.0422555824143924	0.0845111648287848	0.957744417585608
35	0.0611042697136186	0.122208539427237	0.938895730286381
36	0.0592587300130289	0.118517460026058	0.940741269986971
37	0.0605836287992601	0.12116725759852	0.93941637120074
38	0.0546501124756634	0.109300224951327	0.945349887524337
39	0.0456269239382479	0.0912538478764958	0.954373076061752
40	0.0724785552548419	0.144957110509684	0.927521444745158
41	0.214891037314293	0.429782074628586	0.785108962685707
42	0.1995133642342	0.3990267284684	0.8004866357658
43	0.174297001238803	0.348594002477605	0.825702998761197
44	0.134335289895580	0.268670579791159	0.86566471010442
45	0.148628012573951	0.297256025147903	0.851371987426049
46	0.116610775203375	0.23322155040675	0.883389224796625
47	0.131737583026597	0.263475166053195	0.868262416973403
48	0.126564464612648	0.253128929225297	0.873435535387352
49	0.0973804339594581	0.194760867918916	0.902619566040542
50	0.0872817938536332	0.174563587707266	0.912718206146367
51	0.0946478315808648	0.189295663161730	0.905352168419135
52	0.338524215535318	0.677048431070637	0.661475784464682
53	0.408670513485931	0.817341026971862	0.591329486514069
54	0.386094527469081	0.772189054938162	0.613905472530919
55	0.537122298706111	0.925755402587779	0.462877701293889
56	0.503695875439141	0.992608249121718	0.496304124560859
57	0.483204920756455	0.96640984151291	0.516795079243545
58	0.418156309104462	0.836312618208924	0.581843690895538
59	0.351746715359801	0.703493430719603	0.648253284640199
60	0.288749648409777	0.577499296819554	0.711250351590223
61	0.288283135542555	0.576566271085109	0.711716864457445
62	0.231483220853061	0.462966441706122	0.768516779146939
63	0.180076208775864	0.360152417551728	0.819923791224136
64	0.165322676671074	0.330645353342148	0.834677323328926
65	0.123545425688593	0.247090851377185	0.876454574311407
66	0.0928326309044379	0.185665261808876	0.907167369095562
67	0.0655626933257484	0.131125386651497	0.934437306674252
68	0.0507263757390604	0.101452751478121	0.94927362426094
69	0.0472061667572856	0.0944123335145711	0.952793833242714
70	0.040293901566274	0.080587803132548	0.959706098433726
71	0.0292403701775057	0.0584807403550113	0.970759629822494
72	0.0267545696401430	0.0535091392802861	0.973245430359857
73	0.0474495250533333	0.0948990501066665	0.952550474946667
74	0.035631874920469	0.071263749840938	0.964368125079531
75	0.0411201981226624	0.0822403962453248	0.958879801877338
76	0.192211882660583	0.384423765321166	0.807788117339417
77	0.13306911074952	0.26613822149904	0.86693088925048
78	0.157501743855071	0.315003487710143	0.842498256144929
79	0.100645112428822	0.201290224857644	0.899354887571178
80	0.101144799952543	0.202289599905086	0.898855200047457
81	0.0657335647886768	0.131467129577354	0.934266435211323
82	0.0380556574351226	0.0761113148702452	0.961944342564877

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	0	0	OK
10% type I error level	12	0.1875	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/102ydh1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/102ydh1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/1dfgn1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/1dfgn1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/2dfgn1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/2dfgn1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/3dfgn1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/3dfgn1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/456fq1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/456fq1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/556fq1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/556fq1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/656fq1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/656fq1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/7ygfb1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/7ygfb1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/89pee1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/89pee1290555401.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/99pee1290555401.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290555423c1518buuuc81nf1/99pee1290555401.ps (open in new window)

Parameters (Session):

par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 8 ; 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')

}

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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