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Personenwagens (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 05:43:33 -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/t11957350004r2ctbskj5dibxl.htm/, Retrieved Thu, 22 Nov 2007 13:36:41 +0100
 
User-defined keywords:
Klaas Van pelt
 
Dataseries X:
» Textbox « » Textfile « » CSV «
35466 0 25954 0 33504 0 28115 0 28501 0 28618 0 21434 0 20177 0 21484 0 25642 0 23515 0 12941 0 36190 1 37785 1 38407 1 33326 0 30304 0 27576 0 27048 0 17291 0 21018 0 26792 0 19426 0 13927 0 35647 0 31746 0 31277 0 31583 0 25607 0 28151 0 24947 0 18077 0 23429 0 26313 0 18862 0 14753 0 36409 1 33163 1 34122 1 35225 0 28249 0 30374 0 26311 0 22069 0 23651 0 28628 0 23187 0 14727 0 43080 0 32519 0 39657 0 33614 0 28671 0 34243 0 27336 0 22916 0 24537 0 26128 0 22602 0 15744 0 41086 1 39690 1 43129 1 37863 0 35953 0 29133 0 24693 0 22205 0 21725 0 27192 0 21790 0 13253 0 37702 0 30364 0 32609 0 30212 0 29965 0 28352 0 25814 0 22414 0 20506 0 28806 0 22228 0 13971 0 36845 1 35338 1 35022 1 34777 0 26887 0 23970 0 22780 0 17351 0 21382 0 24561 0 17409 0 11514 0 31514 0 27071 0 29462 0 26105 0 22397 0 23843 0 21705 0 18089 0 20764 0 25316 0 17704 0 15548 0 28029 1 29383 1 36438 1 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 1 29506 1 34506 1 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0
 
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 time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 16229.9336419753 + 3468.73015873016x[t] + 19844.4599924253M1[t] + 16025.1749536472M2[t] + 19386.5822225614M3[t] + 17522.8649493511M4[t] + 13797.7337567268M5[t] + 13960.6025641026M6[t] + 9499.3944484014M7[t] + 6171.26325577715M8[t] + 8077.59360161444M9[t] + 12002.2316397594M10[t] + 6755.04785929092M11[t] -36.8688073757518t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)16229.9336419753879.8637718.44600
x3468.73015873016878.9252483.94660.0001256.2e-05
M119844.45999242531168.36614216.984800
M216025.17495364721168.27104613.71700
M319386.58222256141168.19707816.595300
M417522.86494935111095.44635215.996100
M513797.73375672681095.41254412.595900
M613960.60256410261095.40127412.744700
M79499.39444840141095.4125448.67200
M86171.263255777151095.4463525.633600
M98077.593601614441095.5026967.373400
M1012002.23163975941095.58157210.955100
M116755.047859290921117.1055456.046900
t-36.86880737575184.968841-7.4200


Multiple Linear Regression - Regression Statistics
Multiple R0.928114962499126
R-squared0.861397383614755
Adjusted R-squared0.848527140664696
F-TEST (value)66.9293801956427
F-TEST (DF numerator)13
F-TEST (DF denominator)140
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2736.31150599019
Sum Squared Residuals1048236092.094


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
13546636037.5248270248-571.524827024835
22595432181.370980871-6227.37098087098
33350435505.9094424095-2001.90944240946
42811533605.3233618234-5490.32336182337
52850129843.3233618234-1342.32336182338
62861829969.3233618234-1351.32336182337
72143425471.2464387464-4037.24643874643
82017722106.2464387464-1929.24643874643
92148423975.7079772080-2491.70797720797
102564227863.4772079772-2221.47720797721
112351522579.4246201330935.575379867049
121294115787.5079534663-2846.50795346629
133619039063.8292972460-2873.82929724596
143778535207.67545109212577.32454890788
153840738532.2139126306-125.213912630577
163332633162.8976733143163.102326685662
173030429400.8976733143903.10232668566
182757629526.8976733143-1950.89767331434
192704825028.82075023742019.17924976258
201729121663.8207502374-4372.82075023742
212101823533.2822886990-2515.28228869895
222679227421.0515194682-629.051519468185
231942622136.9989316239-2710.99893162393
241392715345.0822649573-1418.08226495726
253564735152.6734500068494.326549993218
263174631296.5196038529449.480396147065
273127734621.0580653914-3344.05806539140
283158332720.4719848053-1137.47198480532
292560728958.4719848053-3351.47198480532
302815129084.4719848053-933.471984805316
312494724586.3950617284360.604938271605
321807721221.3950617284-3144.39506172840
332342923090.8566001899338.143399810066
342631326978.6258309592-665.625830959164
351886221694.5732431149-2832.57324311491
361475314902.6565764482-149.656576448243
373640938178.9779202279-1769.97792022792
383316334322.8240740741-1159.82407407407
393412237647.3625356125-3525.36253561253
403522532278.04629629632946.95370370371
412824928516.0462962963-267.046296296295
423037428642.04629629631731.95370370370
432631124143.96937321942167.03062678063
442206920778.96937321941290.03062678063
452365122648.43091168091002.56908831909
462862826536.20014245012091.79985754986
472318721252.14755460591934.85244539411
481472714460.2308879392266.769112060779
494308034267.82207298878812.17792701127
503251930411.66822683492107.33177316511
513965733736.20668837335920.79331162665
523361431835.62060778731778.37939221273
532867128073.6206077873597.379392212727
543424328199.62060778736043.37939221273
552733623701.54368471043634.45631528965
562291620336.54368471032579.45631528965
572453722206.00522317192330.99477682811
582612826093.774453941134.22554605888
592260220809.72186609691792.27813390313
601574414017.80519943021726.1948005698
614108637294.12654320993791.87345679012
623969033437.9726970566252.02730294397
634312936762.51115859456366.48884140551
643786331393.19491927836469.80508072175
653595327631.19491927838321.80508072175
662913327757.19491927831375.80508072175
672469323259.11799620131433.88200379867
682220519894.11799620132310.88200379867
692172521763.5795346629-38.5795346628669
702719225651.34876543211540.6512345679
712179020367.29617758781422.70382241216
721325313575.3795109212-322.379510921178
733770233382.97069597074319.02930402930
743036429526.8168498168837.183150183151
753260932851.3553113553-242.355311355309
763021230950.7692307692-738.769230769232
772996527188.76923076922776.23076923077
782835227314.76923076921037.23076923077
792581422816.69230769232997.30769230769
802241419451.69230769232962.30769230769
812050621321.1538461538-815.153846153846
822880625208.92307692313597.07692307693
832222819924.87048907882303.12951092118
841397113132.9538224122838.046177587844
853684536409.2751661918435.724833808166
863533832553.1213200382784.87867996201
873502235877.6597815764-855.65978157645
883477730508.34354226024268.65645773979
892688726746.3435422602140.656457739792
902397026872.3435422602-2902.34354226021
912278022374.2666191833405.733380816714
921735119009.2666191833-1658.26661918329
932138220878.7281576448503.271842355176
942456124766.4973884141-205.497388414055
951740919482.4448005698-2073.44480056980
961151412690.5281339031-1176.52813390313
973151432498.1193189526-984.11931895265
982707128641.9654727988-1570.96547279880
992946231966.5039343373-2504.50393433727
1002610530065.9178537512-3960.91785375119
1012239726303.9178537512-3906.91785375118
1022384326429.9178537512-2586.91785375119
1032170521931.8409306743-226.840930674265
1041808918566.8409306743-477.840930674266
1052076420436.3024691358327.697530864196
1062531624324.0716999050991.928300094967
1071770419040.0191120608-1336.01911206078
1081554812248.10244539413299.89755460589
1092802935524.4237891738-7495.42378917379
1102938331668.2699430199-2285.26994301995
1113643834992.80840455841445.19159544159
1123203429623.49216524222410.50783475784
1132267925861.4921652422-3182.49216524216
1142431925987.4921652422-1668.49216524216
1151800421489.4152421652-3485.41524216524
1161753718124.4152421652-587.415242165244
1172036619993.8767806268372.123219373218
1182278223881.646011396-1099.64601139601
1191916918597.5934235518571.406576448242
1201380711805.67675688512001.32324311491
1212974331613.2679419346-1870.26794193461
1222559127757.1140957808-2166.11409578076
1232909631081.6525573192-1985.65255731922
1242648229181.0664767331-2699.06647673314
1252240525419.0664767331-3014.06647673314
1262704425545.06647673311498.93352326686
1271797021046.9895536562-3076.98955365622
1281873017681.98955365621048.01044634378
1291968419551.4510921178132.548907882240
1301978523439.220322887-3654.22032288699
1311847918155.1677350427323.832264957263
1321069811363.2510683761-665.25106837607
1333195634639.5724121557-2683.57241215575
1342950630783.4185660019-1277.41856600190
1353450634107.9570275404398.042972459639
1362716528738.6407882241-1573.64078822412
1372673624976.64078822411759.35921177588
1382369125102.6407882241-1411.64078822412
1391815720604.5638651472-2447.5638651472
1401732817239.563865147288.4361348527991
1411820519109.0254036087-904.02540360874
1422099522996.7946343780-2001.79463437797
1431738217712.7420465337-330.742046533715
144936710920.8253798670-1553.82537986705
1453112430728.4165649166395.583435083436
1462655126872.2627187627-321.262718762718
1473065130196.8011803012454.198819698821
1482585928296.2150997151-2437.2150997151
1492510024534.2150997151565.7849002849
1502577824660.21509971511117.7849002849
1512041820162.1381766382255.861823361822
1521868816797.13817663821890.86182336182
1532042418666.59971509971757.40028490028
1542477622554.36894586892221.63105413105
 
Charts produced by software:
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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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