Home » date » 2007 » Nov » 21 » attachments

workshop2

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 05:32:03 -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/t1195647962dmuxhlat9b47d2u.htm/, Retrieved Wed, 21 Nov 2007 13:26:12 +0100
 
User-defined keywords:
textiel
 
Dataseries X:
» Textbox « » Textfile « » CSV «
101.5 0 99.2 0 107.8 0 92.3 0 99.2 0 101.6 0 87 0 71.4 0 104.7 0 115.1 0 102.5 0 75.3 0 96.7 1 94.6 1 98.6 1 99.5 1 92 1 93.6 1 89.3 1 66.9 1 108.8 1 113.2 1 105.5 1 77.8 1 102.1 1 97 1 95.5 1 99.3 1 86.4 1 92.4 1 85.7 1 61.9 1 104.9 1 107.9 1 95.6 1 79.8 1 94.8 1 93.7 1 108.1 1 96.9 1 88.8 1 106.7 1 86.8 1 69.8 1 110.9 1 105.4 1 99.2 1 84.4 1 87.2 1 91.9 1 97.9 1 94.5 1 85 1 100.3 1 78.7 1 65.8 1 104.8 1 96 1 103.3 1 82.9 1 91.4 1 94.5 1 109.3 1 92.1 1 99.3 1 109.6 1 87.5 1 73.1 1 110.7 1 111.6 1 110.7 1 84 1 101.6 1 102.1 1 113.9 1 99 1 100.4 1 109.5 1 93 1 76.8 1 105.3 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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 96.4666666666666 -1.47826086956518x[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)96.46666666666663.50905427.490800
x-1.478260869565183.801964-0.38880.6984590.349229


Multiple Linear Regression - Regression Statistics
Multiple R0.0437033195659165
R-squared0.00190998014108062
Adjusted R-squared-0.0107240707432097
F-TEST (value)0.151177176550365
F-TEST (DF numerator)1
F-TEST (DF denominator)79
p-value0.698458914502653
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation12.1557182414647
Sum Squared Residuals11673.1573913043


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1101.596.46666666666715.0333333333329
299.296.46666666666662.73333333333336
3107.896.466666666666611.3333333333334
492.396.4666666666666-4.16666666666663
599.296.46666666666662.73333333333337
6101.696.46666666666665.13333333333336
78796.4666666666666-9.46666666666663
871.496.4666666666666-25.0666666666666
9104.796.46666666666668.23333333333337
10115.196.466666666666618.6333333333334
11102.596.46666666666666.03333333333337
1275.396.4666666666666-21.1666666666666
1396.794.98840579710141.71159420289855
1494.694.9884057971014-0.388405797101454
1598.694.98840579710143.61159420289855
1699.594.98840579710144.51159420289855
179294.9884057971014-2.98840579710145
1893.694.9884057971014-1.38840579710145
1989.394.9884057971014-5.68840579710145
2066.994.9884057971014-28.0884057971014
21108.894.988405797101413.8115942028985
22113.294.988405797101418.2115942028986
23105.594.988405797101410.5115942028986
2477.894.9884057971014-17.1884057971015
25102.194.98840579710147.11159420289855
269794.98840579710142.01159420289855
2795.594.98840579710140.511594202898552
2899.394.98840579710144.31159420289855
2986.494.9884057971014-8.58840579710144
3092.494.9884057971014-2.58840579710144
3185.794.9884057971014-9.28840579710145
3261.994.9884057971014-33.0884057971015
33104.994.98840579710149.91159420289856
34107.994.988405797101412.9115942028986
3595.694.98840579710140.611594202898546
3679.894.9884057971014-15.1884057971015
3794.894.9884057971014-0.188405797101451
3893.794.9884057971014-1.28840579710145
39108.194.988405797101413.1115942028985
4096.994.98840579710141.91159420289856
4188.894.9884057971014-6.18840579710145
42106.794.988405797101411.7115942028986
4386.894.9884057971014-8.18840579710145
4469.894.9884057971014-25.1884057971015
45110.994.988405797101415.9115942028986
46105.494.988405797101410.4115942028986
4799.294.98840579710144.21159420289855
4884.494.9884057971014-10.5884057971014
4987.294.9884057971014-7.78840579710145
5091.994.9884057971014-3.08840579710144
5197.994.98840579710142.91159420289856
5294.594.9884057971014-0.488405797101448
538594.9884057971014-9.98840579710145
54100.394.98840579710145.31159420289855
5578.794.9884057971014-16.2884057971014
5665.894.9884057971014-29.1884057971015
57104.894.98840579710149.81159420289855
589694.98840579710141.01159420289855
59103.394.98840579710148.31159420289855
6082.994.9884057971014-12.0884057971014
6191.494.9884057971014-3.58840579710144
6294.594.9884057971014-0.488405797101448
63109.394.988405797101414.3115942028985
6492.194.9884057971014-2.88840579710145
6599.394.98840579710144.31159420289855
66109.694.988405797101414.6115942028985
6787.594.9884057971014-7.48840579710145
6873.194.9884057971014-21.8884057971015
69110.794.988405797101415.7115942028986
70111.694.988405797101416.6115942028985
71110.794.988405797101415.7115942028986
728494.9884057971014-10.9884057971014
73101.694.98840579710146.61159420289855
74102.194.98840579710147.11159420289855
75113.994.988405797101418.9115942028986
769994.98840579710144.01159420289855
77100.494.98840579710145.41159420289856
78109.594.988405797101414.5115942028986
799394.9884057971014-1.98840579710145
8076.894.9884057971014-18.1884057971015
81105.394.988405797101410.3115942028985
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/1tru41195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/1tru41195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/2do4z1195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/2do4z1195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/3ytp21195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/3ytp21195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/4behg1195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/4behg1195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/5tf2v1195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/5tf2v1195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/6uttx1195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/6uttx1195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/737mi1195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/737mi1195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/8qb441195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/8qb441195648317.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/9zi341195648317.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/21/t1195647962dmuxhlat9b47d2u/9zi341195648317.ps (open in new window)


 
Parameters:
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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