Home » date » 2009 » Dec » 20 »

Paper: Regressie analyse (seasonal dummies, linear trend en gegevens van vorige jaren)

*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: Sat, 19 Dec 2009 23:08:45 -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/Dec/20/t126128965073gdx3s0vm9kmei.htm/, Retrieved Sun, 20 Dec 2009 07:14:22 +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/Dec/20/t126128965073gdx3s0vm9kmei.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 «
79 75 74 78 84 79 79 75 74 78 82 79 79 75 74 88 82 79 79 75 81 88 82 79 79 69 81 88 82 79 62 69 81 88 82 62 62 69 81 88 68 62 62 69 81 57 68 62 62 69 67 57 68 62 62 72 67 57 68 62 75 72 67 57 68 81 75 72 67 57 80 81 75 72 67 79 80 81 75 72 81 79 80 81 75 83 81 79 80 81 84 83 81 79 80 90 84 83 81 79 84 90 84 83 81 90 84 90 84 83 92 90 84 90 84 93 92 90 84 90 85 93 92 90 84 93 85 93 92 90 94 93 85 93 92 94 94 93 85 93 102 94 94 93 85 96 102 94 94 93 96 96 102 94 94 92 96 96 102 94 90 92 96 96 102 84 90 92 96 96 86 84 90 92 96 70 86 84 90 92 67 70 86 84 90 60 67 70 86 84 62 60 67 70 86 61 62 60 67 70 54 61 62 60 67 50 54 61 62 60 45 50 54 61 62 34 45 50 54 61 37 34 45 50 54 44 37 34 45 50 34 44 37 34 45 37 34 44 37 34 31 37 34 44 37 31 31 37 34 44 28 31 31 37 34 31 28 31 31 37 33 31 28 31 31 36 33 31 28 31 39 36 33 31 28 42 39 36 33 31
 
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 time8 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
Y(t)[t] = + 6.64321270528053 + 0.872702527227202`Y(t-1)`[t] + 0.258918872405125`Y(t-2)`[t] -0.0448813312088279`Y(t-3)`[t] -0.167125823727214`Y(t-4) `[t] -0.64550965373359M1[t] + 2.56198536203161M2[t] + 2.28982093315230M3[t] + 2.77357881188303M4[t] + 0.862448902919936M5[t] -2.21338885997563M6[t] -0.527309563378737M7[t] + 0.85100122897588M8[t] + 2.81894668946818M9[t] + 1.30992470299167M10[t] + 2.642957463527M11[t] -0.0856389618791044t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)6.643212705280535.9573661.11510.2716210.135811
`Y(t-1)`0.8727025272272020.1588145.49513e-061e-06
`Y(t-2)`0.2589188724051250.209611.23520.224130.112065
`Y(t-3)`-0.04488133120882790.20937-0.21440.831380.41569
`Y(t-4) `-0.1671258237272140.161755-1.03320.3078750.153937
M1-0.645509653733594.208103-0.15340.8788760.439438
M22.561985362031614.2076230.60890.5461270.273064
M32.289820933152304.1842550.54720.5873270.293664
M42.773578811883034.1969650.66090.5125910.256296
M50.8624489029199364.1783640.20640.8375460.418773
M6-2.213388859975634.188079-0.52850.6001490.300074
M7-0.5273095633787374.230848-0.12460.9014530.450727
M80.851001228975884.2057540.20230.8407010.420351
M92.818946689468184.518710.62380.5363660.268183
M101.309924702991674.4299820.29570.7690320.384516
M112.6429574635274.4200520.59790.5533320.276666
t-0.08563896187910440.066964-1.27890.2084940.104247


Multiple Linear Regression - Regression Statistics
Multiple R0.971615849687214
R-squared0.944037359363406
Adjusted R-squared0.921078327307367
F-TEST (value)41.118343188824
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.21182366115827
Sum Squared Residuals1504.88337469570


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
17972.98543716231266.01456283768739
27981.0393024647114-2.03930246471138
38282.3407965272735-0.340796527273466
48885.01037187724422.98962812275582
58188.3580714920717-7.35807149207171
66980.5065463175109-11.5065463175109
76269.0514587602318-7.05145876023176
86260.43960080735391.56039919264613
96862.21793193972765.78206806027238
105768.1791653579236-11.1791653579236
116762.55022535760184.44977464239818
127265.43125862075846.56874137924159
137571.14375106626683.85624893373321
148179.56787981277121.4321201872288
158083.3273833092751-3.32738330927510
167983.4360398210677-4.43603982106772
178179.53698409215861.46301590784141
188376.90411993827876.09588006172126
198480.97981022719723.02018977280278
209083.74038549101986.25961450898025
218490.6938117155292-6.6938117155292
229085.03731585957794.96268414042212
239289.53099777618642.46900222381363
249389.36785268455513.63214731544489
258590.7607112960902-5.76071129609018
269386.06734839978296.93265160021715
279490.24068126893783.75931873106221
289493.7747785182010.225221481798963
2910293.0148844599118.98511554008894
309695.45314003192750.546859968072538
319693.72159035879582.27840964120418
329293.10169830517-1.10169830516997
339090.4254760923096-0.425476092309607
348487.0524895422424-3.05248954224237
358682.72535575756043.27464424243956
367080.9469171095045-10.9469171095045
376767.3739054377742-0.373905437774209
386064.6479442314423-4.64794423144232
396257.78831618476494.21168381523508
406160.9280652224970.0719347775030117
415459.3919783588813-5.39197835888127
425050.9427831747839-0.942783174783904
434546.9506109775114-1.9506109775114
443443.3253898244194-9.32538982441942
453735.66278025243361.33721974756643
464434.73102924025629.26897075974382
473444.1934211086514-10.1934211086514
483736.2539715851820.746028414818011
493134.7361950375562-3.7361950375562
503132.6775250912922-1.67752509129224
512832.3028227097487-4.30282270974872
523129.85074456099011.14925543900993
533330.69808159697742.30191840302261
543630.1934105374995.80658946250101
553935.29652967626383.70347032373621
564239.3929255720372.60707442796301


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.6783014152481940.6433971695036130.321698584751806
210.7459480321590530.5081039356818950.254051967840947
220.8693060115166040.2613879769667920.130693988483396
230.8365065503419690.3269868993160620.163493449658031
240.8379787972901950.3240424054196090.162021202709805
250.8656822671100320.2686354657799360.134317732889968
260.8031306806048410.3937386387903170.196869319395159
270.7323832238937820.5352335522124370.267616776106218
280.6414466535847630.7171066928304740.358553346415237
290.6863163314984070.6273673370031870.313683668501593
300.5970398160841480.8059203678317050.402960183915852
310.5047634208891320.9904731582217370.495236579110868
320.5670060830681840.8659878338636330.432993916931816
330.5051869967891490.9896260064217020.494813003210851
340.5766881717974990.8466236564050020.423311828202501
350.5165524957150540.9668950085698930.483447504284946
360.895410266304720.2091794673905600.104589733695280


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 level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/1059u01261289316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/1enz11261289316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/1enz11261289316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/267801261289316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/267801261289316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/3ib0b1261289316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/3ib0b1261289316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/4eycy1261289316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/68sye1261289316.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/7g5ve1261289316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/7g5ve1261289316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/80e0i1261289316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/80e0i1261289316.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/96u6f1261289316.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/20/t126128965073gdx3s0vm9kmei/96u6f1261289316.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')
}
 





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Software written by Ed van Stee & Patrick Wessa


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