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WS 7

*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 08:43:04 -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/t1258731810utzgisur5yycwbv.htm/, Retrieved Fri, 20 Nov 2009 16:43:42 +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/t1258731810utzgisur5yycwbv.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
100 100 96,21064363 97,82226485 96,31280765 94,04971502 107,1793443 91,12460521 114,9066592 93,13202153 92,56060184 93,88342812 114,9995356 92,55349954 107,1236185 94,43494835 117,7765394 96,25017563 107,3650971 100,4355715 106,2970187 101,5036685 114,5072908 99,39789728 98,0031578 99,68990733 103,0649206 101,6895041 100,2879168 103,6652759 104,6066685 103,0532766 111,1544534 100,9500712 104,9874617 102,345366 109,9284852 101,6472299 111,5352466 99,56809393 132,4974459 95,67727392 100,3436426 96,58494865 123,0983561 96,32604937 114,2379493 95,37109101 104,569518 96,00056203 109,0833101 96,88367859 106,9843039 94,85280372 133,6769759 92,46943974 124,8537197 93,99180173 122,5132349 93,45262168 116,8013374 92,26698759 116,0118882 90,39653498 129,7575926 90,43001228 125,1973623 91,04995327 143,7912139 89,07845784 127,9465032 89,69314509 130,2962757 87,92459054 108,4424631 85,8789319 129,3675118 83,20612366 143,6797622 83,85722053 131,8844618 83,01393462 117,6186496 82,8450 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Import[t] = + 222.724184604475 -1.08884531590375Wisselkoers[t] -3.43675003487935M1[t] -10.6811622089806M2[t] -2.69348059950483M3[t] + 2.95796464459367M4[t] + 1.09917038098968M5[t] -4.38448659729871M6[t] -9.19465016228743M7[t] -13.1031916205358M8[t] + 3.13537411617422M9[t] -8.82688454470125M10[t] -1.81513701099472M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)222.72418460447525.9253998.59100
Wisselkoers-1.088845315903750.277986-3.91690.0002890.000145
M1-3.436750034879359.158767-0.37520.7091690.354584
M2-10.68116220898069.194129-1.16170.2512080.125604
M3-2.693480599504839.178091-0.29350.7704560.385228
M42.957964644593679.1259660.32410.7472810.37364
M51.099170380989689.1332860.12030.9047210.45236
M6-4.384486597298719.155683-0.47890.6342430.317122
M7-9.194650162287439.118665-1.00830.3184580.159229
M8-13.10319162053589.111566-1.43810.1570360.078518
M93.135374116174229.1104010.34420.7322660.366133
M10-8.826884544701259.110883-0.96880.337590.168795
M11-1.815137010994729.110179-0.19920.8429320.421466


Multiple Linear Regression - Regression Statistics
Multiple R0.589301759016927
R-squared0.347276563180444
Adjusted R-squared0.180623770800983
F-TEST (value)2.0838328492553
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.0368566998434336
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation14.4043696553305
Sum Squared Residuals9751.83566286806


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1100110.402902979220-10.4029029792204
296.21064363105.529707522475-9.31906389247546
396.31280765117.625112343360-21.3123046933602
4107.1793443126.461549702581-19.2822054025813
5114.9066592122.416989581877-7.51033038187651
692.56060184116.115167057727-23.5545652177274
7114.9995356112.7530899975582.24644560244179
8107.1236185106.7959418154290.327676684571365
9117.7765394121.05800583101-3.28146643100999
10107.3650971104.5384984818822.82659861811785
11106.2970187110.387253600208-4.0902349002078
12114.5072908114.4952497404640.0120410595355431
1398.0031578110.740545930446-12.7373881304458
14103.0649206101.3188821796341.74603842036619
15100.2879168107.155253919385-6.86733711938481
16104.6066685113.473071734625-8.86640323462469
17111.1544534113.904342819194-2.74988941919418
18104.9874617106.901425633621-1.91396393362092
19109.9284852102.8514242909817.07706090901949
20111.5352466101.20674029479410.3285063052064
21132.4974459121.68180717441710.8156387255833
22100.3436426108.731231135417-8.38758853541656
23123.0983561116.0248799374427.07347616255807
24114.2379493118.879818885606-4.6418695856058
25104.569518114.757672279102-10.1881542791023
26109.0833101106.5516827752482.53162732475197
27106.9843039116.75067297411-9.76636907410992
28133.6769759124.9972329239258.67974297607486
29124.8537197121.4808219384003.37289776160027
30122.5132349116.5842486319835.9289862680174
31116.8013374113.0650571922663.73628020773383
32116.0118882111.1931492970364.81873890296378
33129.7575926127.3952634324522.36232916754785
34125.1973623114.75798492847810.4393773715215
35143.7912139123.91638602646619.8748278735339
36127.9465032125.0622237045532.88427949544739
37130.2962757123.5511560073616.74511969263898
38108.4424631118.534149661362-10.0916865613618
39129.3675118129.432106003271-0.0645942032705193
40143.6797622134.374607470279.30515472973008
41131.8844618133.434021119737-1.54955931973706
42117.6186496128.134218580256-10.5155689802560
43118.9560695127.849774358138-8.89370485813757
44104.8202842125.159700906158-20.3394167061585
45134.624315140.345028158509-5.72071315850896
46140.401226128.36068568937512.0405403106253
47143.8005015136.5495273285917.2509741714094
48153.4317823133.88603940766519.5457428923351
49153.2924677126.70914200387126.5833256961295
50127.3149438112.18185909128115.1330847087191
51153.5525216115.54191650987538.0106050901254
52136.9276493126.76393836859910.163710931401
53131.7730101123.3361287407938.43688135920747
54144.3391845114.28407263641330.0551118635870
55107.4208229111.586904761058-4.16608186105755
56113.6249652108.7604703865834.86449481341694
57124.2221603128.397948603612-4.17578830361216
58102.0618557118.980783464848-16.9189277648482
5996.36853348126.477576787294-30.1090433072935
60111.6838488129.484042661712-17.8001938617122


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.01646020112319790.03292040224639580.983539798876802
170.004904235340485090.009808470680970180.995095764659515
180.007730788164369190.01546157632873840.992269211835631
190.003607678504847750.00721535700969550.996392321495152
200.001147203002228620.002294406004457250.998852796997771
210.002554637598549570.005109275197099140.99744536240145
220.001211869828930580.002423739657861160.99878813017107
230.002588970990713040.005177941981426080.997411029009287
240.000997195808184890.001994391616369780.999002804191815
250.0008201781053166530.001640356210633310.999179821894683
260.000568572758312950.00113714551662590.999431427241687
270.0007524917064424050.001504983412884810.999247508293558
280.008323268193902650.01664653638780530.991676731806097
290.00583852602512150.0116770520502430.994161473974879
300.0102390448396180.0204780896792360.989760955160382
310.005143454293420530.01028690858684110.99485654570658
320.002556885632309790.005113771264619590.99744311436769
330.001136932559275810.002273865118551610.998863067440724
340.0009980550772391020.001996110154478200.99900194492276
350.002160475314135580.004320950628271160.997839524685864
360.000997215373567090.001994430747134180.999002784626433
370.001217488480520880.002434976961041760.998782511519479
380.001077136964504530.002154273929009060.998922863035495
390.001532466008271860.003064932016543710.998467533991728
400.0008504710208638270.001700942041727650.999149528979136
410.0003502076984589270.0007004153969178540.999649792301541
420.001438051369951810.002876102739903630.998561948630048
430.001101316708924020.002202633417848030.998898683291076
440.03869424399823450.0773884879964690.961305756001765


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level220.758620689655172NOK
5% type I error level280.96551724137931NOK
10% type I error level291NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/10jp1r1258731778.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/10jp1r1258731778.ps (open in new window)


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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/2iine1258731778.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/3qojl1258731778.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/4lqux1258731778.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/8ssr61258731778.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/90oex1258731778.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258731810utzgisur5yycwbv/90oex1258731778.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')
}
 





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Software written by Ed van Stee & Patrick Wessa


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