Home » date » 2007 » Dec » 20 » attachments

brood en bakmeel

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 20 Dec 2007 07:12:19 -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/20/t1198158901sjtd6sel8v70kop.htm/, Retrieved Thu, 20 Dec 2007 14:55:13 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,5 1,43 0,51 1,43 0,51 1,43 0,5 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,51 1,43 0,52 1,43 0,52 1,44 0,52 1,48 0,53 1,48 0,53 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,52 1,48 0,53 1,48 0,53 1,48 0,53 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,54 1,48 0,53 1,48 0,53 1,48 0,53 1,48 0,53 1,48 0,53 1,57 0,54 1,58 0,55 1,58 0,55 1,58 0,55 1,58 0,55 1,59 0,55 1,6 0,55 1,6 0,55 1,61 0,55 1,61 0,56 1,61 0,56 1,62 0,56 1,63 0,56 1,63 0,56 1,64 0,55 1,64 0,56 1,64 0,55 1,64 0,55 1,64 0,56 1,65 0,55 1,65 0,55 1,65 0,55 1,65 0,55

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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = -0.591894562376485 + 3.95161598776056x[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	-0.591894562376485	0.126746	-4.6699	1.4e-05	7e-06
x	3.95161598776056	0.23808	16.5978	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.892965712216058
R-squared	0.797387763193532
Adjusted R-squared	0.794493302667725
F-TEST (value)	275.487523869858
F-TEST (DF numerator)	1
F-TEST (DF denominator)	70
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0351420802494691
Sum Squared Residuals	0.0864476062982087

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.42342959138139	0.00657040861860759
2	1.43	1.4234295913814	0.006570408618601
3	1.43	1.42342959138140	0.00657040861860114
4	1.43	1.42342959138140	0.00657040861860114
5	1.43	1.42342959138140	0.00657040861860114
6	1.43	1.42342959138140	0.00657040861860114
7	1.43	1.42342959138140	0.00657040861860114
8	1.43	1.42342959138140	0.00657040861860114
9	1.43	1.38391343150379	0.0460865684962067
10	1.43	1.42342959138140	0.00657040861860114
11	1.43	1.42342959138140	0.00657040861860114
12	1.43	1.38391343150379	0.0460865684962067
13	1.43	1.42342959138140	0.00657040861860114
14	1.43	1.42342959138140	0.00657040861860114
15	1.43	1.42342959138140	0.00657040861860114
16	1.43	1.42342959138140	0.00657040861860114
17	1.43	1.46294575125900	-0.0329457512590045
18	1.43	1.46294575125900	-0.0329457512590045
19	1.44	1.46294575125900	-0.0229457512590045
20	1.48	1.50246191113661	-0.0224619111366100
21	1.48	1.50246191113661	-0.0224619111366100
22	1.48	1.46294575125900	0.0170542487409956
23	1.48	1.46294575125900	0.0170542487409956
24	1.48	1.46294575125900	0.0170542487409956
25	1.48	1.46294575125900	0.0170542487409956
26	1.48	1.46294575125900	0.0170542487409956
27	1.48	1.46294575125900	0.0170542487409956
28	1.48	1.46294575125900	0.0170542487409956
29	1.48	1.46294575125900	0.0170542487409956
30	1.48	1.46294575125900	0.0170542487409956
31	1.48	1.46294575125900	0.0170542487409956
32	1.48	1.50246191113661	-0.0224619111366100
33	1.48	1.50246191113661	-0.0224619111366100
34	1.48	1.50246191113661	-0.0224619111366100
35	1.48	1.54197807101422	-0.0619780710142156
36	1.48	1.54197807101422	-0.0619780710142156
37	1.48	1.54197807101422	-0.0619780710142156
38	1.48	1.54197807101422	-0.0619780710142156
39	1.48	1.54197807101422	-0.0619780710142156
40	1.48	1.54197807101422	-0.0619780710142156
41	1.48	1.54197807101422	-0.0619780710142156
42	1.48	1.54197807101422	-0.0619780710142156
43	1.48	1.54197807101422	-0.0619780710142156
44	1.48	1.54197807101422	-0.0619780710142156
45	1.48	1.50246191113661	-0.0224619111366100
46	1.48	1.50246191113661	-0.0224619111366100
47	1.48	1.50246191113661	-0.0224619111366100
48	1.48	1.50246191113661	-0.0224619111366100
49	1.48	1.50246191113661	-0.0224619111366100
50	1.57	1.54197807101422	0.0280219289857845
51	1.58	1.58149423089182	-0.00149423089182114
52	1.58	1.58149423089182	-0.00149423089182114
53	1.58	1.58149423089182	-0.00149423089182114
54	1.58	1.58149423089182	-0.00149423089182114
55	1.59	1.58149423089182	0.00850576910817887
56	1.6	1.58149423089182	0.0185057691081789
57	1.6	1.58149423089182	0.0185057691081789
58	1.61	1.58149423089182	0.0285057691081789
59	1.61	1.62101039076943	-0.0110103907694267
60	1.61	1.62101039076943	-0.0110103907694267
61	1.62	1.62101039076943	-0.00101039076942671
62	1.63	1.62101039076943	0.00898960923057308
63	1.63	1.62101039076943	0.00898960923057308
64	1.64	1.58149423089182	0.0585057691081787
65	1.64	1.62101039076943	0.0189896092305731
66	1.64	1.58149423089182	0.0585057691081787
67	1.64	1.58149423089182	0.0585057691081787
68	1.64	1.62101039076943	0.0189896092305731
69	1.65	1.58149423089182	0.0685057691081787
70	1.65	1.58149423089182	0.0685057691081787
71	1.65	1.58149423089182	0.0685057691081787
72	1.65	1.58149423089182	0.0685057691081787

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/18cou1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/18cou1198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/2eo7y1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/2eo7y1198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/3hwji1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/3hwji1198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/41f021198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/41f021198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/5h65l1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/5h65l1198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/629801198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/629801198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/76ylf1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/76ylf1198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/8zg5x1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/8zg5x1198159935.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/9kksw1198159935.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/20/t1198158901sjtd6sel8v70kop/9kksw1198159935.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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')

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.

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

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

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