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Multiple regression Totaal

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Sun, 16 Dec 2007 16:41:47 -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/Dec/17/t1197847681k0p484pz2tu4510.htm/, Retrieved Mon, 17 Dec 2007 00:28:11 +0100
 
User-defined keywords:
Multiple regression Totaal
 
Dataseries X:
» Textbox « » Textfile « » CSV «
174.1 0 180.4 0 182.6 0 207.1 0 213.7 0 186.5 0 179.1 0 168.3 0 156.5 0 144.3 0 138.9 0 137.8 0 136.3 0 140.3 0 149.1 0 149.2 0 140.4 0 129 0 124.7 0 130.8 0 130.1 0 133.2 0 130.1 0 126.6 0 124.8 0 125.3 0 126.9 0 120.1 0 118.7 0 117.7 0 113.4 0 107.5 0 107.6 0 114.3 0 114.9 0 111.2 0 109.9 0 108.6 0 109.2 0 106.4 0 103.7 0 103 0 96.9 0 104.7 0 102.2 0 99 0 95.8 0 94.5 0 102.7 0 103.2 0 105.6 0 103.9 0 107.2 0 100.7 0 92.1 0 90.3 0 93.4 0 98.5 0 100.8 0 102.3 0 104.7 0 101.1 0 101.4 0 99.5 0 98.4 0 96.3 0 100.7 0 101.2 0 100.3 0 97.8 0 97.4 1 98.6 1 99.7 1 99 1 98.1 1 97 1 98.5 1 103.8 1 114.4 1 124.5 1 134.2 1 131.8 1 125.6 1 119.9 1 114.9 1 115.5 1 112.5 1 111.4 1 115.3 1 110.8 1 103.7 1 111.1 1 113 1 111.2 1 117.6 1 121.7 1 127.3 1 129.8 1 137.1 1 141.4 1 137.4 1 130.7 1 117.2 1 110.8 1 111.4 1 108.2 1 108.8 1 110.2 1 109.5 1 109.5 1 116 1 111.2 1 112.1 1 114 1 119.1 1 114.1 1 115.1 1 115.4 1 110.8 1 116 1 119.2 1 126.5 1 127.8 1 131.3 1 140.3 1 137.3 1 143 1 134.5 1 139.9 1 159.3 1 170.4 1 175 1 175.8 1 180.9 1 180.3 1 169.6 1 172.3 1 184.8 1 177.7 1 184.6 1 211.4 1
 
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Totaal[t] = + 119.776923076923 + 13.8396794871795`9/11`[t] + 5.55316579254073M1[t] + 7.42940850815842M2[t] + 9.74731789044272M3[t] + 9.98189393939383M4[t] + 10.9164699883448M5[t] + 7.40937937062927M6[t] + 4.80228875291364M7[t] + 4.94519813519803M8[t] + 7.77977418414907M9[t] + 0.966273310023195M10[t] -0.355030594405694M11[t] -0.109576048951049t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)119.7769230769239.75216912.282100
`9/11`13.83967948717959.5987841.44180.1518160.075908
M15.5531657925407311.8103950.47020.6390240.319512
M27.4294085081584211.8088730.62910.5303890.265194
M39.7473178904427211.8085310.82540.4106660.205333
M49.9818939393938311.8093670.84530.399560.19978
M510.916469988344811.8113820.92420.3571180.178559
M67.4093793706292711.8145740.62710.5316940.265847
M74.8022887529136411.8189440.40630.685190.342595
M84.9451981351980311.824490.41820.6764950.338248
M97.7797741841490711.831210.65760.5120090.256004
M100.96627331002319512.0794920.080.9363690.468184
M11-0.35503059440569412.061025-0.02940.9765630.488281
t-0.1095760489510490.117988-0.92870.3548050.177403


Multiple Linear Regression - Regression Statistics
Multiple R0.190736931444518
R-squared0.0363805770168706
Adjusted R-squared-0.0622576316349459
F-TEST (value)0.368828444008859
F-TEST (DF numerator)13
F-TEST (DF denominator)127
p-value0.977168178571238
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation28.2842573680236
Sum Squared Residuals101599.900287296


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1174.1125.22051282051248.8794871794878
2180.4126.98717948717953.4128205128206
3182.6129.19551282051353.4044871794872
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5213.7130.14551282051383.5544871794874
6186.5126.52884615384659.9711538461538
7179.1123.81217948717955.2878205128205
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10144.3119.64743589743624.6525641025641
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21130.1125.2556002331004.84439976689975
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23130.1116.90164335664313.1983566433566
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29118.7127.515687645688-8.8156876456876
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31113.4121.182354312354-7.78235431235431
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61104.7118.64594988345-13.9459498834500
62101.1120.412616550117-19.3126165501166
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79114.4129.762383449883-15.3623834498834
80124.5129.795716783217-5.29571678321678
81134.2132.5207167832171.67928321678322
82131.8125.5976398601406.20236013986016
83125.6124.1667599067601.43324009324009
84119.9124.412214452215-4.51221445221455
85114.9129.855804195804-14.9558041958042
86115.5131.622470862471-16.1224708624708
87112.5133.830804195804-21.3308041958042
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89115.3134.780804195804-19.4808041958041
90110.8131.164137529138-20.3641375291375
91103.7128.447470862471-24.7474708624708
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93113131.205804195804-18.2058041958042
94111.2124.282727272727-13.0827272727273
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96121.7123.097301864802-1.39730186480197
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99137.1132.5158916083924.58410839160841
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101137.4133.4658916083923.93410839160845
102130.7129.8492249417250.850775058275053
103117.2127.132558275058-9.93255827505826
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105111.4129.890891608392-18.4908916083916
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114114128.534312354312-14.5343123543123
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116114.1125.850979020979-11.7509790209790
117115.1128.575979020979-13.4759790209790
118115.4121.652902097902-6.25290209790208
119110.8120.222022144522-9.42202214452215
120116120.467476689977-4.4674766899768
121119.2125.911066433566-6.71106643356648
122126.5127.677733100233-1.17773310023309
123127.8129.886066433566-2.08606643356642
124131.3130.0110664335661.28893356643359
125140.3130.8360664335669.46393356643363
126137.3127.21939976690010.0806002331002
127143124.50273310023318.4972668997669
128134.5124.5360664335669.96393356643357
129139.9127.26106643356612.6389335664336
130159.3120.33798951049038.9620104895105
131170.4118.90710955711051.4928904428904
132175119.15256410256455.8474358974358
133175.8124.59615384615451.2038461538461
134180.9126.36282051282054.5371794871795
135180.3128.57115384615451.7288461538462
136169.6128.69615384615440.9038461538462
137172.3129.52115384615442.7788461538462
138184.8125.90448717948758.8955128205128
139177.7123.18782051282054.5121794871795
140184.6123.22115384615461.3788461538462
141211.4125.94615384615485.4538461538462
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/1s0if1197848502.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/4yh901197848502.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/5hebs1197848502.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/65t2o1197848502.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/65t2o1197848502.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/7yx4g1197848502.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/7yx4g1197848502.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/8ytg51197848502.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/8ytg51197848502.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/929hw1197848502.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197847681k0p484pz2tu4510/929hw1197848502.ps (open in new window)


 
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)
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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