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Paper - Regression Analyse - Zonder trend en met seizonaliteit

*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, 05 Dec 2008 08:23:42 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228490703jv7j5b4rr1elcx2.htm/, Retrieved Fri, 05 Dec 2008 15:25:03 +0000
 
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/2008/Dec/05/t1228490703jv7j5b4rr1elcx2.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
Feedback Forum:
2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply
test

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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
95.2 0 95.00 0 94.00 0 92.2 0 91.00 0 91.2 0 103.4 1 105.00 0 104.6 0 103.8 0 101.8 0 102.4 0 103.8 0 103.4 0 102.00 0 101.8 0 100.2 0 101.4 0 113.8 0 116.00 0 115.6 0 113.00 0 109.4 0 111.00 0 112.4 0 112.2 0 111.00 0 108.8 0 107.4 0 108.6 0 118.8 0 122.2 1 122.6 0 122.2 0 118.8 0 119.00 0 118.2 0 117.8 0 116.8 0 114.6 0 113.4 0 113.8 0 124.2 0 125.8 0 125.6 0 122.4 0 119.00 0 119.4 0 118.6 0 118.00 0 116.00 0 114.8 0 114.6 0 114.6 0 124.00 0 125.2 0 124.00 0 117.6 1 113.2 0 111.4 0 112.2 0 109.8 0 106.4 0 105.2 0 102.2 0 99.8 0 111.00 0 113.00 0 108.4 0 105.4 0 102.00 0 102.8 0
 
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 time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Werkloosheid[t] = + 111 -1.84000000000000Dumivariabele[t] -0.933333333333302M1[t] -1.63333333333334M2[t] -3.30000000000001M3[t] -4.76666666666668M4[t] -6.20000000000001M5[t] -6.10000000000001M6[t] + 5.17333333333332M7[t] + 7.17333333333332M8[t] + 5.79999999999999M9[t] + 3.37333333333332M10[t] -0.300000000000011M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1113.48497831.85100
Dumivariabele-1.840000000000005.398905-0.34080.7344570.367229
M1-0.9333333333333024.928504-0.18940.8504490.425225
M2-1.633333333333344.928504-0.33140.7415120.370756
M3-3.300000000000014.928504-0.66960.5057410.252871
M4-4.766666666666684.928504-0.96720.337410.168705
M5-6.200000000000014.928504-1.2580.2133520.106676
M6-6.100000000000014.928504-1.23770.2207310.110365
M75.173333333333325.0099721.03260.3060020.153001
M87.173333333333325.0099721.43180.1574740.078737
M95.799999999999994.9285041.17680.243990.121995
M103.373333333333325.0099720.67330.503370.251685
M11-0.3000000000000114.928504-0.06090.9516680.475834


Multiple Linear Regression - Regression Statistics
Multiple R0.490981929489039
R-squared0.24106325508478
Adjusted R-squared0.08670323916982
F-TEST (value)1.56169493541376
F-TEST (DF numerator)12
F-TEST (DF denominator)59
p-value0.128496057516813
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation8.53641849243381
Sum Squared Residuals4299.35599999999


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
195.2110.066666666666-14.8666666666665
295109.366666666667-14.3666666666667
394107.7-13.7
492.2106.233333333333-14.0333333333333
591104.8-13.8
691.2104.9-13.7
7103.4114.333333333333-10.9333333333333
8105118.173333333333-13.1733333333333
9104.6116.8-12.2
10103.8114.373333333333-10.5733333333333
11101.8110.7-8.9
12102.4111-8.6
13103.8110.066666666667-6.26666666666671
14103.4109.366666666667-5.96666666666666
15102107.7-5.7
16101.8106.233333333333-4.43333333333334
17100.2104.8-4.6
18101.4104.9-3.49999999999999
19113.8116.173333333333-2.37333333333334
20116118.173333333333-2.17333333333333
21115.6116.8-1.2
22113114.373333333333-1.37333333333334
23109.4110.7-1.29999999999999
24111111-8.40137421437293e-15
25112.4110.0666666666672.3333333333333
26112.2109.3666666666672.83333333333334
27111107.73.3
28108.8106.2333333333332.56666666666667
29107.4104.82.60000000000000
30108.6104.93.69999999999999
31118.8116.1733333333332.62666666666666
32122.2116.3333333333335.86666666666667
33122.6116.85.8
34122.2114.3733333333337.82666666666667
35118.8110.78.1
361191117.99999999999999
37118.2110.0666666666678.1333333333333
38117.8109.3666666666678.43333333333333
39116.8107.79.1
40114.6106.2333333333338.36666666666666
41113.4104.88.6
42113.8104.98.9
43124.2116.1733333333338.02666666666667
44125.8118.1733333333337.62666666666667
45125.6116.88.8
46122.4114.3733333333338.02666666666667
47119110.78.3
48119.41118.4
49118.6110.0666666666678.53333333333329
50118109.3666666666678.63333333333333
51116107.78.3
52114.8106.2333333333338.56666666666666
53114.6104.89.8
54114.6104.99.7
55124116.1733333333337.82666666666667
56125.2118.1733333333337.02666666666667
57124116.87.2
58117.6112.5333333333335.06666666666666
59113.2110.72.5
60111.41110.399999999999996
61112.2110.0666666666672.13333333333330
62109.8109.3666666666670.433333333333331
63106.4107.7-1.29999999999999
64105.2106.233333333333-1.03333333333333
65102.2104.8-2.6
6699.8104.9-5.1
67111116.173333333333-5.17333333333333
68113118.173333333333-5.17333333333333
69108.4116.8-8.39999999999999
70105.4114.373333333333-8.97333333333333
71102110.7-8.7
72102.8111-8.20000000000001


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.717803260120280.5643934797594410.282196739879721
170.7093842639580430.5812314720839140.290615736041957
180.7240072687327190.5519854625345620.275992731267281
190.6145471814620970.7709056370758060.385452818537903
200.6476626157348570.7046747685302860.352337384265143
210.6691781619850720.6616436760298560.330821838014928
220.6500136409797070.6999727180405870.349986359020293
230.6074500582531010.7850998834937990.392549941746899
240.5742790075366970.8514419849266060.425720992463303
250.654469030275460.691061939449080.34553096972454
260.7095735536097290.5808528927805420.290426446390271
270.745305366582120.5093892668357590.254694633417880
280.7546279634245560.4907440731508890.245372036575444
290.7583053249879990.4833893500240020.241694675012001
300.7601627769045930.4796744461908140.239837223095407
310.6975392752520670.6049214494958650.302460724747933
320.7566125637300850.486774872539830.243387436269915
330.7505258630422470.4989482739155060.249474136957753
340.7722725884474020.4554548231051960.227727411552598
350.7820602562751320.4358794874497360.217939743724868
360.7852230545255790.4295538909488430.214776945474421
370.783951233847780.4320975323044390.216048766152220
380.7791996215263920.4416007569472150.220800378473608
390.7771440341221770.4457119317556470.222855965877823
400.7617277688257380.4765444623485240.238272231174262
410.7447889806849490.5104220386301020.255211019315051
420.728559263351670.5428814732966590.271440736648329
430.6999792561706120.6000414876587760.300020743829388
440.6610293639140650.677941272171870.338970636085935
450.6451024249003920.7097951501992150.354897575099608
460.6882081680583620.6235836638832760.311791831941638
470.6878637832396290.6242724335207430.312136216760371
480.7015078822138380.5969842355723250.298492117786162
490.6484537565982480.7030924868035030.351546243401752
500.6002765492853680.7994469014292640.399723450714632
510.556382667516580.887234664966840.44361733248342
520.5081062892420790.9837874215158420.491893710757921
530.4949412187503580.9898824375007160.505058781249642
540.5223269545823210.9553460908353580.477673045417679
550.5099827307578410.9800345384843180.490017269242159
560.4760299813871310.9520599627742630.523970018612869


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:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490703jv7j5b4rr1elcx2/9jdvw1228490611.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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