Home » date » 2007 » Nov » 21 » attachments

broodprijzen

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 21 Nov 2007 06:56:14 -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/21/t1195652918jhygpn9emb95gue.htm/, Retrieved Wed, 21 Nov 2007 14:48:48 +0100
 
User-defined keywords:
s0650531
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,44 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,57 0 1,58 0 1,58 0 1,58 0 1,58 0 1,59 1 1,6 1 1,6 1 1,61 1 1,61 1 1,61 1 1,62 1 1,63 1 1,63 1 1,64 1 1,64 1 1,64 1 1,64 1 1,64 1 1,65 1 1,65 1 1,65 1 1,65 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
y[t] = + 1.40222222222222 + 0.0783333333333335x[t] + 0.00250000000000066M1[t] + 0.0169444444444444M2[t] + 0.0163888888888888M3[t] + 0.0158333333333333M4[t] + 0.0136111111111111M5[t] + 0.0113888888888889M6[t] -0.000555555555555579M7[t] + 0.00555555555555554M8[t] + 0.00499999999999998M9[t] + 0.00444444444444443M10[t] + 0.00222222222222222M11[t] + 0.00222222222222222t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)1.402222222222220.010685131.237100
x0.07833333333333350.0090448.661100
M10.002500000000000660.0126040.19830.8434660.421733
M20.01694444444444440.0125911.34570.1836340.091817
M30.01638888888888880.0125821.30260.1978610.09893
M40.01583333333333330.0125751.25910.2130230.106512
M50.01361111111111110.0125711.08280.2833870.141693
M60.01138888888888890.0125690.90610.3686310.184316
M7-0.0005555555555555790.012564-0.04420.9648830.482441
M80.005555555555555540.0125510.44260.6596850.329843
M90.004999999999999980.0125420.39870.6915990.3458
M100.004444444444444430.0125350.35460.7241950.362098
M110.002222222222222220.012530.17730.8598540.429927
t0.002222222222222220.00018811.850400


Multiple Linear Regression - Regression Statistics
Multiple R0.96746207394789
R-squared0.935982864527553
Adjusted R-squared0.921634196232005
F-TEST (value)65.2313403061898
F-TEST (DF numerator)13
F-TEST (DF denominator)58
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0217009013355194
Sum Squared Residuals0.0273138888888891


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.431.406944444444440.0230555555555585
21.431.423611111111110.00638888888888877
31.431.425277777777780.00472222222222195
41.431.426944444444440.00305555555555539
51.431.426944444444440.00305555555555547
61.431.426944444444440.0030555555555554
71.431.417222222222220.0127777777777777
81.431.425555555555560.0044444444444443
91.431.427222222222220.00277777777777762
101.431.428888888888890.00111111111111095
111.431.428888888888890.00111111111111097
121.431.428888888888890.00111111111111097
131.431.43361111111111-0.00361111111111185
141.431.45027777777778-0.0202777777777779
151.431.45194444444444-0.0219444444444445
161.431.45361111111111-0.0236111111111112
171.431.45361111111111-0.0236111111111112
181.431.45361111111111-0.0236111111111112
191.441.44388888888889-0.00388888888888897
201.481.452222222222220.0277777777777777
211.481.453888888888890.0261111111111111
221.481.455555555555560.0244444444444444
231.481.455555555555560.0244444444444444
241.481.455555555555560.0244444444444444
251.481.460277777777780.0197222222222216
261.481.476944444444440.00305555555555555
271.481.478611111111110.00138888888888892
281.481.48027777777778-0.000277777777777775
291.481.48027777777778-0.000277777777777789
301.481.48027777777778-0.000277777777777771
311.481.470555555555560.00944444444444446
321.481.478888888888890.00111111111111112
331.481.48055555555556-0.000555555555555545
341.481.48222222222222-0.00222222222222221
351.481.48222222222222-0.00222222222222222
361.481.48222222222222-0.00222222222222221
371.481.48694444444445-0.00694444444444504
381.481.50361111111111-0.0236111111111111
391.481.50527777777778-0.0252777777777777
401.481.50694444444444-0.0269444444444444
411.481.50694444444444-0.0269444444444444
421.481.50694444444444-0.0269444444444444
431.481.49722222222222-0.0172222222222221
441.481.50555555555556-0.0255555555555555
451.481.50722222222222-0.0272222222222221
461.481.50888888888889-0.0288888888888888
471.481.50888888888889-0.0288888888888888
481.481.50888888888889-0.0288888888888888
491.481.51361111111111-0.0336111111111116
501.571.530277777777780.0397222222222224
511.581.531944444444440.0480555555555558
521.581.533611111111110.0463888888888891
531.581.533611111111110.0463888888888891
541.581.533611111111110.0463888888888891
551.591.60222222222222-0.0122222222222221
561.61.61055555555556-0.0105555555555554
571.61.61222222222222-0.0122222222222221
581.611.61388888888889-0.00388888888888877
591.611.61388888888889-0.00388888888888877
601.611.61388888888889-0.00388888888888876
611.621.618611111111110.00138888888888843
621.631.63527777777778-0.00527777777777783
631.631.63694444444444-0.00694444444444445
641.641.638611111111110.00138888888888886
651.641.638611111111110.00138888888888886
661.641.638611111111110.00138888888888887
671.641.628888888888890.0111111111111111
681.641.637222222222220.00277777777777776
691.651.638888888888890.0111111111111111
701.651.640555555555560.00944444444444444
711.651.640555555555560.00944444444444445
721.651.640555555555560.00944444444444444
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/1bpvx1195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/1bpvx1195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/2zi081195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/2zi081195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/329q91195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/329q91195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/4pck41195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/4pck41195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/5p34g1195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/5p34g1195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/60cu11195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/60cu11195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/7gkma1195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/7gkma1195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/842wc1195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/842wc1195653368.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/9ebwf1195653368.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195652918jhygpn9emb95gue/9ebwf1195653368.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')
 





Copyright

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.


FreeStatistics.org is powered by