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dummie seizoenale effecten belgie

*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, 19 Dec 2008 03:38:56 -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/19/t1229683193380u8b5jeuks4ee.htm/, Retrieved Fri, 19 Dec 2008 11:40:28 +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/2008/Dec/19/t1229683193380u8b5jeuks4ee.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},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 0 610763 0 612613 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1
 
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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 610130.509090909 -65144.7727272727X[t] -16381.5545454547M1[t] -34600.9545454545M2[t] -33318.5545454545M3[t] -19253.4000000001M4[t] -24728.6000000001M5[t] -35301.8M6[t] -42659.4M7[t] -52615.0000000001M8[t] -51885.8M9[t] -558.000000000017M10[t] + 8654.79999999998M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)610130.5090909098594.14216570.993800
X-65144.77272727275135.982294-12.68400
M1-16381.554545454711846.207458-1.38290.1732450.086623
M2-34600.954545454511846.207458-2.92080.0053480.002674
M3-33318.554545454511846.207458-2.81260.007150.003575
M4-19253.400000000111801.588816-1.63140.1094840.054742
M5-24728.600000000111801.588816-2.09540.0415530.020776
M6-35301.811801.588816-2.99130.0044140.002207
M7-42659.411801.588816-3.61470.0007310.000365
M8-52615.000000000111801.588816-4.45835.1e-052.6e-05
M9-51885.811801.588816-4.39656.3e-053.1e-05
M10-558.00000000001711801.588816-0.04730.9624890.481244
M118654.7999999999811801.5888160.73340.4669820.233491


Multiple Linear Regression - Regression Statistics
Multiple R0.910591205177868
R-squared0.829176342947282
Adjusted R-squared0.785561792210418
F-TEST (value)19.0114612884557
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value4.08562073062058e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation18659.950333175
Sum Squared Residuals16365106082.5182


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1565464593748.954545455-28284.9545454549
2547344575529.554545454-28185.5545454545
3554788576811.954545454-22023.9545454545
4562325590877.109090909-28552.1090909091
5560854585401.909090909-24547.9090909092
6555332574828.709090909-19496.7090909091
7543599567471.109090909-23872.1090909090
8536662557515.509090909-20853.5090909091
9542722558244.709090909-15522.7090909091
10593530609572.509090909-16042.5090909091
11610763618785.309090909-8022.3090909091
12612613610130.5090909092482.49090909090
13611324593748.95454545417575.0454545455
14594167575529.55454545518637.4454545455
15595454576811.95454545518642.0454545454
16590865590877.109090909-12.1090909090858
17589379585401.9090909093977.09090909092
18584428574828.7090909099599.2909090909
19573100567471.1090909095628.89090909091
20567456557515.5090909099940.4909090909
21569028558244.70909090910783.2909090909
22620735609572.50909090911162.4909090909
23628884618785.30909090910098.6909090909
24628232610130.50909090918101.4909090909
25612117593748.95454545418368.0454545456
26595404575529.55454545519874.4454545455
27597141576811.95454545520329.0454545454
28593408590877.1090909092530.89090909092
29590072585401.9090909094670.09090909092
30579799574828.7090909094970.29090909091
31574205567471.1090909096733.89090909091
32572775557515.50909090915259.4909090909
33572942558244.70909090914697.2909090909
34619567609572.5090909099994.49090909092
35625809618785.3090909097023.69090909091
36619916610130.5090909099785.4909090909
37587625593748.954545454-6123.95454545446
38565742575529.554545455-9787.55454545456
39557274576811.954545455-19537.9545454546
40560576525732.33636363634843.6636363636
41548854520257.13636363628596.8636363636
42531673509683.93636363621989.0636363636
43525919502326.33636363623592.6636363636
44511038492370.73636363618667.2636363636
45498662493099.9363636365562.06363636363
46555362544427.73636363610934.2636363636
47564591553640.53636363610950.4636363636
48541657544985.736363636-3328.73636363639
49527070528604.181818182-1534.18181818173
50509846510384.781818182-538.781818181832
51514258511667.1818181822590.81818181817
52516922525732.336363636-8810.33636363637
53507561520257.136363636-12696.1363636364
54492622509683.936363636-17061.9363636364
55490243502326.336363636-12083.3363636364
56469357492370.736363636-23013.7363636364
57477580493099.936363636-15519.9363636364
58528379544427.736363636-16048.7363636364
59533590553640.536363636-20050.5363636364
60517945544985.736363636-27040.7363636364


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.9877431918115890.02451361637682260.0122568081884113
170.9815783838503570.03684323229928690.0184216161496434
180.9738427697330710.05231446053385720.0261572302669286
190.9652033309174450.06959333816510890.0347966690825544
200.955448992887460.08910201422508210.0445510071125411
210.938536694125260.1229266117494820.061463305874741
220.9187621007688760.1624757984622480.0812378992311238
230.8825289528694280.2349420942611440.117471047130572
240.8503393782018540.2993212435962920.149660621798146
250.8314600505708760.3370798988582470.168539949429124
260.820157433403410.359685133193180.17984256659659
270.8136482600024110.3727034799951780.186351739997589
280.7712267556865730.4575464886268540.228773244313427
290.7099403518551960.5801192962896080.290059648144804
300.6278995432088660.7442009135822680.372100456791134
310.5520588471135610.8958823057728780.447941152886439
320.4899327816772330.9798655633544670.510067218322767
330.4261458988286480.8522917976572960.573854101171352
340.3459046784700730.6918093569401450.654095321529927
350.2668743192264260.5337486384528530.733125680773574
360.2520434602316830.5040869204633670.747956539768317
370.1826965859170480.3653931718340960.817303414082952
380.1290761085881140.2581522171762290.870923891411886
390.09594183003780870.1918836600756170.904058169962191
400.1087980093565440.2175960187130880.891201990643456
410.1246682622517430.2493365245034870.875331737748257
420.1451357215402370.2902714430804740.854864278459763
430.1550464982466920.3100929964933830.844953501753308
440.2375647272735980.4751294545471960.762435272726402


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0689655172413793NOK
10% type I error level50.172413793103448NOK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229683193380u8b5jeuks4ee/1qylw1229683131.ps (open in new window)


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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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