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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, 20 Nov 2009 04:56:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt.htm/, Retrieved Fri, 20 Nov 2009 12:59:16 +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/2009/Nov/20/t1258718344qd2wt1onp84z0mt.htm/},
    year = {2009},
}
@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 = {2009},
    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:

ws7 link 4

Dataseries X:

» Textbox « » Textfile « » CSV «

6.3 101.9 1,7 1 1,2 1,4 6 106.2 6.3 1,7 1 1,2 6.2 81 6 6.3 1,7 1 6.4 94.7 6.2 6 6.3 1,7 6.8 101 6.4 6.2 6 6.3 7.5 109.4 6.8 6.4 6.2 6 7.5 102.3 7.5 6.8 6.4 6.2 7.6 90.7 7.5 7.5 6.8 6.4 7.6 96.2 7.6 7.5 7.5 6.8 7.4 96.1 7.6 7.6 7.5 7.5 7.3 106 7.4 7.6 7.6 7.5 7.1 103.1 7.3 7.4 7.6 7.6 6.9 102 7.1 7.3 7.4 7.6 6.8 104.7 6.9 7.1 7.3 7.4 7.5 86 6.8 6.9 7.1 7.3 7.6 92.1 7.5 6.8 6.9 7.1 7.8 106.9 7.6 7.5 6.8 6.9 8 112.6 7.8 7.6 7.5 6.8 8.1 101.7 8 7.8 7.6 7.5 8.2 92 8.1 8 7.8 7.6 8.3 97.4 8.2 8.1 8 7.8 8.2 97 8.3 8.2 8.1 8 8 105.4 8.2 8.3 8.2 8.1 7.9 102.7 8 8.2 8.3 8.2 7.6 98.1 7.9 8 8.2 8.3 7.6 104.5 7.6 7.9 8 8.2 8.3 87.4 7.6 7.6 7.9 8 8.4 89.9 8.3 7.6 7.6 7.9 8.4 109.8 8.4 8.3 7.6 7.6 8.4 111.7 8.4 8.4 8.3 7.6 8.4 98.6 8.4 8.4 8.4 8.3 8.6 96.9 8.4 8.4 8.4 8.4 8.9 95.1 8.6 8.4 8.4 8.4 8.8 97 8.9 8.6 8.4 8.4 8.3 112.7 8.8 8.9 8.6 8.4 7.5 102.9 8.3 8.8 8.9 8.6 7.2 97.4 7.5 8.3 8.8 8.9 7.4 111.4 7.2 7.5 8.3 8.8 8.8 87.4 7.4 7.2 7.5 8.3 9.3 96.8 8.8 7.4 7.2 7.5 9.3 114.1 9.3 8. 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 2.80871688717935 + 0.00219088351317846X[t] + 0.68729913105026Y1[t] -0.239085441528047Y2[t] -0.0409734428967782Y3[t] + 0.21095965078892Y4[t] + 0.141196595109811M1[t] -0.242648801192167M2[t] + 0.681888267994503M3[t] + 0.334352165097872M4[t] + 0.298794143047685M5[t] + 0.308872252168863M6[t] + 0.129614560491464M7[t] + 0.324046218241749M8[t] + 0.42947025602853M9[t] + 0.248535643118973M10[t] + 0.138288439029698M11[t] -0.00505416953979656t + 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)	2.80871688717935	1.173255	2.394	0.019168	0.009584
X	0.00219088351317846	0.010836	0.2022	0.840319	0.42016
Y1	0.68729913105026	0.104841	6.5557	0	0
Y2	-0.239085441528047	0.131833	-1.8135	0.073748	0.036874
Y3	-0.0409734428967782	0.131618	-0.3113	0.756432	0.378216
Y4	0.21095965078892	0.085342	2.4719	0.015706	0.007853
M1	0.141196595109811	0.215567	0.655	0.514472	0.257236
M2	-0.242648801192167	0.22589	-1.0742	0.286182	0.143091
M3	0.681888267994503	0.288252	2.3656	0.020587	0.010293
M4	0.334352165097872	0.243105	1.3753	0.17312	0.08656
M5	0.298794143047685	0.229515	1.3018	0.196953	0.098476
M6	0.308872252168863	0.228625	1.351	0.180758	0.090379
M7	0.129614560491464	0.208424	0.6219	0.535906	0.267953
M8	0.324046218241749	0.225254	1.4386	0.154428	0.077214
M9	0.42947025602853	0.222787	1.9277	0.057677	0.028839
M10	0.248535643118973	0.222361	1.1177	0.267258	0.133629
M11	0.138288439029698	0.22411	0.6171	0.539066	0.269533
t	-0.00505416953979656	0.002206	-2.2915	0.024744	0.012372

Multiple Linear Regression - Regression Statistics
Multiple R	0.871851262816224
R-squared	0.760124624474244
Adjusted R-squared	0.705752872688407
F-TEST (value)	13.9801385739466
F-TEST (DF numerator)	17
F-TEST (DF denominator)	75
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.402113921449158
Sum Squared Residuals	12.1271704367415

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	6.3	4.34360880362798	1.95639119637202
2	6	6.92434898907602	-0.924348989076022
3	6.2	6.41176551366118	-0.21176551366118
4	6.4	6.25756972225082	0.142430277749177
5	6.8	7.30310926119637	-0.503109261196373
6	7.5	7.48215660258692	0.0178433974130835
7	7.5	7.70176192512855	-0.201761925128545
8	7.6	7.7241679085156	-0.124167908515603
9	7.6	7.96101999947792	-0.361019999477918
10	7.4	7.89857534007669	-0.498575340076686
11	7.3	7.66340654272835	-0.363406542728353
12	7.1	7.51389351225011	-0.413893512250115
13	6.9	7.54226937247774	-0.642269372477741
14	6.8	7.031547868349	-0.231547868349001
15	7.5	7.87624714500048	-0.376247145000484
16	7.6	8.008041956304	-0.408041956304002
17	7.8	7.86313035887635	-0.0631303588763472
18	8	7.94441624143346	0.0555837585665431
19	8.1	7.96944089908962	0.130559100910375
20	8.2	8.17138091852124	0.0286190814787650
21	8.3	8.36240016827003	-0.0624001682700315
22	8.2	8.25845098723574	-0.0584509872357365
23	8	8.08591319864875	-0.0859131986487455
24	7.9	7.84010254332564	0.0598974566743637
25	7.6	7.97044738930418	-0.370447389304184
26	7.6	7.40038700628494	0.199612993715058
27	8.3	8.31603684444677	-0.0160368444467706
28	8.4	8.44122924031861	-0.041229240318613
29	8.4	8.2822978394396	0.117702160560403
30	8.4	8.23889450351547	0.161105496484531
31	8.4	8.1694564795382	0.230543520461798
32	8.6	8.37620543085518	0.223794569144820
33	8.9	8.61009153498849	0.289908465011507
34	8.8	8.58663808222365	0.213361917776352
35	8.3	8.35708334560868	-0.0570833456086827
36	7.5	7.90242895452646	-0.402428954526465
37	7.2	7.66361017622417	-0.463610176224167
38	7.4	7.28985234984375	0.110147650156252
39	8.8	8.29323843276577	0.506761567234233
40	9.3	8.71916847275587	0.580831527244132
41	9.3	8.6539059295137	0.646094070486296
42	8.7	8.51589090108328	0.184109098916720
43	8.2	8.18003469640768	0.0199653035923150
44	8.3	8.26965467732402	0.03034532267598
45	8.5	8.56754506058587	-0.067545060585873
46	8.6	8.39186663973594	0.208133360264065
47	8.5	8.20718069613811	0.292819303861888
48	8.2	7.97993822813528	0.220061771864714
49	8.1	7.9615968918992	0.138403108100807
50	7.9	7.6355023142876	0.264497685712404
51	8.6	8.36033084373248	0.239669156267524
52	8.7	8.50990157638488	0.190098423615119
53	8.7	8.39609867381138	0.303901326188622
54	8.5	8.29034727940822	0.209652720591777
55	8.4	8.11850356543176	0.281496434568241
56	8.5	8.29382345108606	0.206176548913937
57	8.7	8.48779654957674	0.212203450423255
58	8.7	8.38098896528894	0.319011034711064
59	8.6	8.22510226998073	0.374897730019273
60	8.5	7.9935059488107	0.506494051189299
61	8.3	8.14717506390752	0.152824936092481
62	8	7.65911871281012	0.340881287189885
63	8.2	8.3392565420735	-0.139256542073495
64	8.1	8.21603279285499	-0.116032792854991
65	8.1	8.06030333680407	0.039696663195926
66	8	8.02147773869463	-0.0214777386946323
67	7.9	7.80683805817243	0.0931619418275705
68	7.9	7.90641758205816	-0.00641758205815926
69	8	8.04355687280034	-0.0435568728003401
70	8	7.90776576420757	0.0922342357924267
71	7.9	7.77703680877471	0.122963191225286
72	8	7.53304272219315	0.46695727780685
73	7.7	7.78993039734206	-0.0899303973420581
74	7.2	7.19233787207619	0.00766212792381141
75	7.5	7.76058870651227	-0.260588706512269
76	7.3	7.79275222920706	-0.492752229207055
77	7	7.5183377383197	-0.518337738319700
78	7	7.26890691540859	-0.268906915408587
79	7	7.20786623049591	-0.207866230495913
80	7.2	7.33820507069238	-0.138205070692377
81	7.3	7.53618932350375	-0.236189323503747
82	7.1	7.37571422123149	-0.275714221231485
83	6.8	7.08427713812067	-0.284277138120665
84	6.4	6.83708809075865	-0.437088090758647
85	6.1	6.78136190521716	-0.681361905217156
86	6.5	6.26690488727238	0.233095112727615
87	7.7	7.44253597180756	0.257464028192440
88	7.9	7.75530400992377	0.144695990076231
89	7.5	7.52281686203883	-0.0228168620388276
90	6.9	7.23790981786943	-0.337909817869434
91	6.6	6.94609814573584	-0.346098145735842
92	6.9	7.12014496094736	-0.220144960947364
93	7.7	7.43140049079685	0.268599509203149

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.183778709681325	0.367557419362651	0.816221290318675
22	0.276495184312843	0.552990368625687	0.723504815687157
23	0.231282555413019	0.462565110826038	0.768717444586981
24	0.228276548967333	0.456553097934666	0.771723451032667
25	0.212186949180747	0.424373898361495	0.787813050819253
26	0.153244039289497	0.306488078578995	0.846755960710503
27	0.107175702352426	0.214351404704852	0.892824297647574
28	0.0814197107573912	0.162839421514782	0.918580289242609
29	0.0509079167856032	0.101815833571206	0.949092083214397
30	0.227898635774185	0.45579727154837	0.772101364225815
31	0.321025832978041	0.642051665956082	0.678974167021959
32	0.591461579510419	0.817076840979162	0.408538420489581
33	0.510738831541325	0.97852233691735	0.489261168458675
34	0.451581218903728	0.903162437807456	0.548418781096272
35	0.535154965919696	0.929690068160607	0.464845034080304
36	0.968923481342472	0.0621530373150566	0.0310765186575283
37	0.99629234185043	0.00741531629913951	0.00370765814956976
38	0.99881409600829	0.00237180798341828	0.00118590399170914
39	0.998621889519757	0.00275622096048499	0.00137811048024250
40	0.998666271482323	0.00266745703535437	0.00133372851767718
41	0.9990670726631	0.00186585467379976	0.000932927336899878
42	0.998451123278567	0.00309775344286637	0.00154887672143319
43	0.999395918413688	0.00120816317262407	0.000604081586312037
44	0.999900635595037	0.000198728809925387	9.93644049626935e-05
45	0.999971574436866	5.6851126267352e-05	2.8425563133676e-05
46	0.999949756926287	0.000100486147425625	5.02430737128124e-05
47	0.999912375544895	0.000175248910209541	8.76244551047705e-05
48	0.999885161773606	0.000229676452787863	0.000114838226393932
49	0.999815717451542	0.000368565096916685	0.000184282548458343
50	0.999846692378002	0.000306615243996369	0.000153307621998184
51	0.999688600005488	0.000622799989024539	0.000311399994512269
52	0.99955515381183	0.000889692376338397	0.000444846188169198
53	0.999417266435143	0.00116546712971336	0.000582733564856679
54	0.999389047680862	0.00122190463827560	0.000610952319137801
55	0.9993633594654	0.00127328106920168	0.00063664053460084
56	0.999062767443788	0.00187446511242428	0.000937232556212142
57	0.998336304856334	0.00332739028733236	0.00166369514366618
58	0.996864391592666	0.00627121681466741	0.00313560840733371
59	0.995170389772602	0.00965922045479562	0.00482961022739781
60	0.99133849647975	0.0173230070404990	0.00866150352024951
61	0.990450423964765	0.0190991520704691	0.00954957603523454
62	0.985194891643382	0.0296102167132352	0.0148051083566176
63	0.990136461558484	0.0197270768830318	0.00986353844151592
64	0.992569174185603	0.0148616516287943	0.00743082581439714
65	0.989830157771247	0.0203396844575067	0.0101698422287534
66	0.990789257697462	0.0184214846050769	0.00921074230253845
67	0.987989018002623	0.0240219639947537	0.0120109819973769
68	0.975709542234312	0.048580915531375	0.0242904577656875
69	0.953438030371067	0.0931239392578663	0.0465619696289332
70	0.905544253699654	0.188911492600693	0.0944557463003464
71	0.930615160850735	0.138769678298530	0.0693848391492648
72	0.902736898692558	0.194526202614883	0.0972631013074415

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	23	0.442307692307692	NOK
5% type I error level	32	0.615384615384615	NOK
10% type I error level	34	0.653846153846154	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/10czb01258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/10czb01258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/1zloc1258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/1zloc1258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/2klq71258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/2klq71258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/31ce51258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/31ce51258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/4q43b1258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/4q43b1258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/5lf7p1258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/5lf7p1258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/6lgf31258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/6lgf31258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/7iyyt1258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/7iyyt1258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/8k37o1258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/8k37o1258718185.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/9e8i51258718185.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258718344qd2wt1onp84z0mt/9e8i51258718185.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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