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Zoogdier Regressie PS

*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: Wed, 08 Dec 2010 17:50:41 +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/08/t1291830570td2smy4trj1cqmg.htm/, Retrieved Wed, 08 Dec 2010 18:49:40 +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/08/t1291830570td2smy4trj1cqmg.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 «
0,301029996 1,62324929 3 -0,301029996 2,301029996 3 -0,045757491 2,230448921 4 0,278753601 2,426511261 1 0,176091259 2,491361694 1 0 2,593286067 4 0,278753601 2,06069784 4 -0,15490196 2,44870632 5 -0,096910013 2,526339277 5 0,255272505 2,79518459 4 0,301029996 1,698970004 1 0,113943352 1,278753601 3 0,591064607 1,544068044 1 0,322219295 1,62324929 1 0,531478917 1,447158031 3 0,414973348 1,662757832 2 0,531478917 1,204119983 2 0,079181246 2,079181246 2 0,414973348 1,322219295 3 0,176091259 2,049218023 4 0,255272505 2,146128036 2 -0,045757491 2,352182518 2 0,612783857 1,62324929 2 0,361727836 1,77815125 2 -0,096910013 1,832508913 4 0,255272505 1,230448921 2 0,748188027 1,079181246 1 -0,15490196 2,255272505 4 -0,045757491 1,491361694 5 -0,301029996 2,170261715 5 0,556302501 1,799340549 1 0,491361694 2,079181246 1 0,819543936 1,146128036 1 -0,301029996 2,352182518 3 -0,22184875 2,322219295 4 0,380211242 1,716003344 1 0,146128036 2,361727836 1 -0,22184875 2,178976947 5 0,07918 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 time9 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
SWS[t] = + 1.07450734071795 -0.303538868542365GT[t] -0.110510499899245D[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.074507340717950.1287518.345600
GT-0.3035388685423650.068904-4.40539.1e-054.5e-05
D-0.1105104998992450.022191-4.981.6e-058e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.809091683127883
R-squared0.654629351706711
Adjusted R-squared0.635442093468194
F-TEST (value)34.1179205266869
F-TEST (DF numerator)2
F-TEST (DF denominator)36
p-value4.88807283538506e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.181764010742274
Sum Squared Residuals1.18937360164024


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
10.3010299960.2502565881714210.0507734078285795
2-0.3010299960.0445237995523333-0.345553795552333
3-0.045757491-0.0445626007009073-0.00119489029909274
40.2787536010.2274563581494580.051297242850542
50.1760912590.207771731092156-0.0316804720921556
60-0.1546977774628890.154697777462889
70.2787536010.006963450359675880.271790150640324
8-0.15490196-0.2213227045436120.0664207445436118
9-0.096910013-0.244887324472990.14797731147299
100.255272505-0.2159818266946830.471254331694683
110.3010299960.448293408117128-0.147263412117128
120.1139433520.354824419828202-0.240881067828202
130.5910646070.4953121737905230.0957524332094769
140.3222192950.471277587969908-0.149058292969908
150.5314789170.3037071296884800.227771787311520
160.4149733480.3487747099342250.0661986380657748
170.5314789170.4879891236903890.0434897933096106
180.0791812460.222374018014116-0.143192772014116
190.4149733480.3416308922510330.073342455748967
200.1760912590.01044802102292930.165643237977071
210.2552725050.2020530651249730.0532194398750272
22-0.0457574910.139507520800610-0.185265011800610
230.6127838570.3607670880706640.252016768929336
240.3617278360.3137483223972690.0479795136027311
25-0.0969100130.0762276590751523-0.173137672075152
260.2552725050.479997267639947-0.224724762639947
270.7481880270.6364233864557260.111764640544274
28-0.15490196-0.052097523301434-0.102804436698566
29-0.0457574910.0692686000375422-0.115026091037542
30-0.301029996-0.136803944190186-0.164226051809814
310.5563025010.4178270464528480.138475454547152
320.4913616940.3328845179133610.158477176086639
330.8195439360.6161024335665830.203441502433417
34-0.3010299960.0289970209013647-0.330027016901365
35-0.22184875-0.0724184761905773-0.149430273809423
360.3802112420.443123127366031-0.062911885366031
370.1461280360.247120645674257-0.100992609674257
38-0.22184875-0.139449355850550-0.0823993941494498
390.0791812460.181195145299523-0.102013899299523


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.7402403846399930.5195192307200150.259759615360007
70.7831189953552520.4337620092894950.216881004644748
80.6660096477932660.6679807044134670.333990352206734
90.5677465381954350.864506923609130.432253461804565
100.9204904653960220.1590190692079570.0795095346039783
110.8881886685662580.2236226628674830.111811331433742
120.897046926526910.205906146946180.10295307347309
130.9121148232200710.1757703535598570.0878851767799286
140.8990056513908670.2019886972182660.100994348609133
150.9426528821681130.1146942356637730.0573471178318867
160.9154374547244180.1691250905511630.0845625452755816
170.8786394807426230.2427210385147540.121360519257377
180.8574878669403810.2850242661192370.142512133059619
190.8008441836119750.3983116327760500.199155816388025
200.859304908204910.281390183590180.14069509179509
210.8175907147931370.3648185704137250.182409285206863
220.8073850415823020.3852299168353960.192614958417698
230.905745314775650.1885093704486990.0942546852243495
240.8640322529442850.271935494111430.135967747055715
250.8505749003008170.2988501993983650.149425099699183
260.9563828450670940.08723430986581260.0436171549329063
270.9373273527563610.1253452944872790.0626726472436394
280.9073584037275050.1852831925449900.0926415962724952
290.8754275421757460.2491449156485080.124572457824254
300.8101693317833140.3796613364333720.189830668216686
310.7435166598450540.5129666803098930.256483340154946
320.8757543180716860.2484913638566280.124245681928314
330.7826304785483390.4347390429033230.217369521451661


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level10.0357142857142857OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/10897z1291830631.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/10897z1291830631.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/1ry7t1291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/1ry7t1291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/227ow1291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/227ow1291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/327ow1291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/327ow1291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/427ow1291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/427ow1291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/5uynh1291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/5uynh1291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/6uynh1291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/6uynh1291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/7n8521291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/7n8521291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/8n8521291830630.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/8n8521291830630.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/9897z1291830631.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291830570td2smy4trj1cqmg/9897z1291830631.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; 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')
}
 





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