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Personenwagen 2 (Seatbelt Law)

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Thu, 22 Nov 2007 05:54:54 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/22/t1195735652607hbfkni0txnbv.htm/, Retrieved Thu, 22 Nov 2007 13:47:42 +0100
 
User-defined keywords:
Klaas Van Pelt Effect 2 maanden
 
Dataseries X:
» Textbox « » Textfile « » CSV «
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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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 16229.9336419753 + 2895.57142857152x[t] + 20108.9947909600M1[t] + 16289.7097521819M2[t] + 20987.5346035138M3[t] + 17522.8649493510M4[t] + 13797.7337567268M5[t] + 13960.6025641026M6[t] + 9499.39444840138M7[t] + 6171.26325577715M8[t] + 8077.59360161443M9[t] + 12002.2316397594M10[t] + 6755.04785929092M11[t] -36.8688073757519t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)16229.9336419753905.69126917.919900
x2895.571428571521108.0575472.61320.009950.004975
M120108.99479096001238.37682116.238200
M216289.70975218191238.28175713.155100
M320987.53460351381127.66005518.611600
M417522.86494935101127.60205715.539900
M513797.73375672681127.56725712.236700
M613960.60256410261127.55565612.381300
M79499.394448401381127.5672578.424700
M86171.263255777151127.6020575.472900
M98077.593601614431127.6600557.163100
M1012002.23163975941127.74124710.642700
M116755.047859290921149.8970345.874500
t-36.86880737575195.114696-7.208400


Multiple Linear Regression - Regression Statistics
Multiple R0.923656256535195
R-squared0.85314088023661
Adjusted R-squared0.839503961972867
F-TEST (value)62.5611200226129
F-TEST (DF numerator)13
F-TEST (DF denominator)140
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2816.63312697278
Sum Squared Residuals1110679104.07446


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
13546636302.0596255595-836.059625559482
22595432445.9057794059-6491.90577940594
33350437106.8618233618-3602.86182336177
42811533605.3233618232-5490.32336182322
52850129843.3233618233-1342.32336182333
62861829969.3233618233-1351.32336182325
72143425471.2464387465-4037.2464387465
82017722106.2464387464-1929.24643874639
92148423975.707977208-2491.70797720798
102564227863.4772079772-2221.47720797723
112351522579.4246201329935.575379867069
121294115787.5079534663-2846.50795346630
133619038755.2053656220-2565.20536562205
143778534899.05151946822885.94848053182
153840736664.43613485281742.56386514719
163332633162.8976733144163.102326685642
173030429400.8976733143903.102326685653
182757629526.8976733144-1950.89767331436
192704825028.82075023742019.17924976258
201729121663.8207502374-4372.82075023743
212101823533.2822886990-2515.28228869896
222679227421.0515194682-629.05151946819
231942622136.9989316239-2710.99893162394
241392715345.0822649573-1418.08226495727
253564735417.2082485416229.791751458402
263174631561.0544023877184.945597612269
273127736222.0104463438-4945.01044634379
283158332720.4719848053-1137.47198480534
292560728958.4719848053-3351.47198480532
302815129084.4719848053-933.471984805333
312494724586.3950617284360.604938271606
321807721221.3950617284-3144.39506172840
332342923090.8566001899338.143399810061
342631326978.6258309592-665.625830959168
351886221694.5732431149-2832.57324311492
361475314902.6565764482-149.656576448247
373640937870.353988604-1461.35398860400
383316334014.2001424501-851.200142450132
393412235779.5847578348-1657.58475783477
403522532278.04629629632946.95370370368
412824928516.0462962963-267.046296296302
423037428642.04629629631731.95370370369
432631124143.96937321942167.03062678063
442206920778.96937321941290.03062678062
452365122648.43091168091002.56908831908
462862826536.20014245012091.79985754986
472318721252.14755460591934.85244539411
481472714460.2308879392266.769112060776
494308034532.35687152368547.64312847644
503251930676.20302536971842.79697463032
513965735337.15906932574319.84093067426
523361431835.62060778731778.37939221271
532867128073.6206077873597.379392212721
543424328199.62060778736043.37939221271
552733623701.54368471033634.45631528965
562291620336.54368471042579.45631528964
572453722206.00522317192330.99477682811
582612826093.774453941134.2255460588785
592260220809.72186609691792.27813390313
601574414017.80519943021726.1948005698
614108636985.50261158604100.49738841405
623969033129.34876543216560.65123456791
634312934894.73338081678234.26661918328
643786331393.19491927836469.80508072173
653595327631.19491927838321.80508072174
662913327757.19491927831375.80508072174
672469323259.11799620131433.88200379867
682220519894.11799620132310.88200379866
692172521763.5795346629-38.5795346628696
702719225651.34876543211540.6512345679
712179020367.29617758781422.70382241215
721325313575.3795109212-322.379510921178
733770233647.50549450554054.49450549449
743036429791.3516483516572.648351648362
753260934452.3076923077-1843.30769230770
763021230950.7692307692-738.769230769245
772996527188.76923076922776.23076923077
782835227314.76923076921037.23076923076
792581422816.69230769232997.3076923077
802241419451.69230769232962.30769230769
812050621321.1538461538-815.153846153847
822880625208.92307692313597.07692307692
832222819924.87048907882303.12951092118
841397113132.9538224122838.046177587845
853684536100.6512345679744.348765432093
863533832244.49738841403093.50261158596
873502234009.88200379871012.11799620132
883477730508.34354226024268.65645773978
892688726746.3435422602140.656457739790
902397026872.3435422602-2902.34354226022
912278022374.2666191833405.733380816721
921735119009.2666191833-1658.26661918329
932138220878.7281576448503.271842355176
942456124766.4973884141-205.497388414053
951740919482.4448005698-2073.44480056980
961151412690.5281339031-1176.52813390313
973151432762.6541174875-1248.65411748746
982707128906.5002713336-1835.50027133359
992946233567.4563152897-4105.45631528965
1002610530065.9178537512-3960.9178537512
1012239726303.9178537512-3906.91785375119
1022384326429.9178537512-2586.91785375119
1032170521931.8409306743-226.840930674255
1041808918566.8409306743-477.840930674266
1052076420436.3024691358327.697530864199
1062531624324.0716999050991.92830009497
1071770419040.0191120608-1336.01911206078
1081554812248.10244539413299.89755460589
1092802935215.7998575499-7186.79985754986
1102938331359.646011396-1976.64601139599
1113643833125.03062678063312.96937321937
1123203429623.49216524222410.50783475782
1132267925861.4921652422-3182.49216524216
1142431925987.4921652422-1668.49216524217
1151800421489.4152421652-3485.41524216523
1161753718124.4152421652-587.415242165244
1172036619993.8767806268372.123219373222
1182278223881.646011396-1099.64601139601
1191916918597.5934235518571.406576448245
1201380711805.67675688512001.32324311491
1212974331877.8027404694-2134.80274046941
1222559128021.6488943155-2430.64889431555
1232909632682.6049382716-3586.6049382716
1242648229181.0664767332-2699.06647673315
1252240525419.0664767331-3014.06647673314
1262704425545.06647673321498.93352326685
1271797021046.9895536562-3076.98955365621
1281873017681.98955365621048.01044634378
1291968419551.4510921178132.548907882246
1301978523439.220322887-3654.22032288698
1311847918155.1677350427323.832264957268
1321069811363.2510683761-665.251068376061
1333195634330.9484805318-2374.94848053181
1342950630474.7946343779-968.794634377949
1353450632240.17924976262265.82075023742
1362716528738.6407882241-1573.64078822413
1372673624976.64078822411759.35921177588
1382369125102.6407882241-1411.64078822413
1391815720604.5638651472-2447.56386514719
1401732817239.563865147288.4361348528018
1411820519109.0254036087-904.025403608731
1422099522996.7946343780-2001.79463437796
1431738217712.7420465337-330.74204653371
144936710920.8253798670-1553.82537986704
1453112430992.9513634514131.048636548631
1462655127136.7975172975-585.7975172975
1473065131797.7535612536-1146.75356125356
1482585928296.2150997151-2437.21509971511
1492510024534.2150997151565.784900284904
1502577824660.21509971511117.78490028490
1512041820162.1381766382255.861823361837
1521868816797.13817663821890.86182336183
1532042418666.59971509971757.40028490029
1542477622554.36894586892221.63105413106
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195735652607hbfkni0txnbv/2mx4s1195736088.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195735652607hbfkni0txnbv/7adlj1195736088.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195735652607hbfkni0txnbv/80ph61195736088.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195735652607hbfkni0txnbv/9uoa01195736089.ps (open in new window)


 
Parameters:
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')
 




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