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regressiemodel

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 07 May 2008 09:01:33 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/07/t1210172647k1xc3wbfj8rxtfd.htm/, Retrieved Wed, 07 May 2008 17:04:19 +0200
 
User-defined keywords:
poging1
 
Dataseries X:
» Textbox « » Textfile « » CSV «
56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577
 
Text written by user:
 
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


Multiple Linear Regression - Estimated Regression Equation
registraties[t] = + 18935.8222222222 + 31487.6691358025M1[t] + 27454.1419753086M2[t] + 34760.1148148148M3[t] + 27482.587654321M4[t] + 20811.5604938272M5[t] + 22451.5333333334M6[t] + 12611.3395061728M7[t] + 8403.14567901236M8[t] + 11943.6185185185M9[t] + 17990.7580246914M10[t] + 10203.7308641976M11[t] + 96.8604938271604t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)18935.82222222221714.88938311.04200
M131487.66913580252102.75600314.974500
M227454.14197530862101.87288413.061800
M334760.11481481482101.18575716.543100
M427482.5876543212100.69481413.082600
M520811.56049382722100.4001939.908400
M622451.53333333342100.30197710.689700
M712611.33950617282100.4001936.004300
M88403.145679012362100.6948144.00020.0001829.1e-05
M911943.61851851852101.1857575.684200
M1017990.75802469142101.8728848.559400
M1110203.73086419762102.7560034.85261e-055e-06
t96.860493827160420.311984.76861.3e-056e-06


Multiple Linear Regression - Regression Statistics
Multiple R0.952646944818744
R-squared0.907536201472488
Adjusted R-squared0.88840576039783
F-TEST (value)47.4393767467658
F-TEST (DF numerator)12
F-TEST (DF denominator)58
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3468.53455910986
Sum Squared Residuals697782455.288888


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
15642150520.35185185185900.6481481482
25315246583.68518518536568.3148148147
35353653986.5185185185-450.518518518497
45240846805.85185185185602.14814814817
54145440231.68518518521222.31481481484
63827141968.5185185185-3697.51851851849
73530632225.18518518523080.81481481477
82641428113.8518518518-1699.85185185184
93191731751.1851851852165.814814814821
103803037895.1851851852134.814814814837
112753430205.0185185185-2671.01851851852
121838720098.1481481481-1711.14814814815
135055651682.6777777778-1126.67777777779
144390147746.0111111111-3845.01111111109
154857255148.8444444444-6576.84444444445
164389947968.1777777778-4069.17777777778
173753241394.0111111111-3862.01111111112
184035743130.8444444445-2773.84444444445
193548933387.51111111112101.48888888889
202902729276.1777777778-249.177777777783
213448532913.51111111111571.48888888889
224259839057.51111111113540.48888888888
233030631367.3444444444-1061.34444444445
242645121260.47407407415190.52592592594
254746052845.0037037037-5385.00370370372
265010448908.3370370371195.66296296298
276146556311.17037037045153.82962962962
285372649130.50370370374595.49629629629
293947742556.337037037-3079.33703703704
304389544293.1703703704-398.170370370378
313148134549.8370370370-3068.83703703703
322989630438.5037037037-542.503703703708
333384234075.8370370370-233.837037037040
343912040219.837037037-1099.83703703704
353370232529.67037037041172.32962962963
362509422422.82671.20000000001
375144254007.3296296296-2565.32962962964
384559450070.662962963-4476.66296296294
395251857473.4962962963-4955.4962962963
404856450292.8296296296-1728.82962962963
414174543718.662962963-1973.66296296297
424958545455.49629629634129.5037037037
433274735712.1629629630-2965.16296296296
443337931600.82962962961778.17037037037
453564535238.1629629630406.837037037037
463703441382.162962963-4348.16296296297
473568133691.99629629631989.00370370371
482097223585.1259259259-2613.12592592592
495855255169.65555555563382.34444444443
505495551232.98888888893722.01111111113
516554058635.82222222226904.17777777777
525157051455.1555555556114.844444444442
535114544880.98888888896264.01111111111
544664146617.822222222223.1777777777726
553570436874.4888888889-1170.48888888888
563325332763.1555555556489.844444444443
573519336400.4888888889-1207.48888888889
584166842544.4888888889-876.488888888891
593486534854.322222222210.6777777777801
602121024747.4518518518-3537.45185185184
615612656331.9814814815-205.981481481489
624923152395.3148148148-3164.31481481479
635972359798.1481481482-75.148148148152
644810352617.4814814815-4514.48148148148
654747246043.31481481481428.68518518518
665049747780.14814814822716.85185185185
674005938036.81481481482022.18518518519
683414933925.4814814815223.518518518516
693686037562.8148148148-702.814814814815
704635643706.81481481482649.18518518518
713657736016.6481481481560.351851851855


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1036778206025560.2073556412051120.896322179397444
170.09219828344044020.1843965668808800.90780171655956
180.4420584423109980.8841168846219960.557941557689002
190.4609251785653300.9218503571306590.53907482143467
200.5493513952148220.9012972095703560.450648604785178
210.5740991666296470.8518016667407050.425900833370353
220.6693162288680490.6613675422639030.330683771131951
230.6410205867149810.7179588265700380.358979413285019
240.8182900234819460.3634199530361090.181709976518054
250.8299608691354430.3400782617291140.170039130864557
260.8028773781066390.3942452437867220.197122621893361
270.9427896177802220.1144207644395570.0572103822197784
280.9677829714379180.06443405712416330.0322170285620817
290.9590835832657480.08183283346850470.0409164167342523
300.9470854011090730.1058291977818550.0529145988909275
310.9381028845536350.1237942308927290.0618971154463646
320.9095327593284140.1809344813431720.0904672406715862
330.8702713144346970.2594573711306060.129728685565303
340.8242563330415980.3514873339168030.175743666958402
350.7887908303207340.4224183393585320.211209169679266
360.8138291249876390.3723417500247230.186170875012361
370.7771845056317360.4456309887365270.222815494368264
380.7808329698075310.4383340603849380.219167030192469
390.880473847765660.2390523044686790.119526152234340
400.8344943243555820.3310113512888360.165505675644418
410.8803117753912130.2393764492175750.119688224608787
420.8968242670909810.2063514658180380.103175732909019
430.8949554745227440.2100890509545130.105044525477256
440.8580377349963960.2839245300072080.141962265003604
450.7977615425629430.4044769148741140.202238457437057
460.8932203114606250.2135593770787510.106779688539376
470.8499120238684110.3001759522631770.150087976131589
480.7898516209035450.4202967581929090.210148379096455
490.7491008752890160.5017982494219670.250899124710984
500.8039403469373440.3921193061253120.196059653062656
510.9174675319107880.1650649361784240.0825324680892118
520.9391264048075280.1217471903849440.060873595192472
530.9941050338091230.01178993238175390.00589496619087696
540.9819059216178860.03618815676422880.0180940783821144
550.9621220034449330.07575599311013330.0378779965550666


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.05NOK
10% type I error level50.125NOK
 
Charts produced by software:
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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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