Home » date » 2007 » Dec » 13 » attachments

wisselkoers paper

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

Title produced by software: Multiple Regression

Date of computation: Thu, 13 Dec 2007 02:57:05 -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/13/t1197539151xmsa4ynwq1350qi.htm/, Retrieved Thu, 13 Dec 2007 10:45:52 +0100

User-defined keywords:

s0650062

Dataseries X:

» Textbox « » Textfile « » CSV «

1.0014 0 1.0183 0 1.0622 0 1.0773 0 1.0807 0 1.0848 0 1.1582 0 1.1663 0 1.1372 0 1.1139 0 1.1222 0 1.1692 0 1.1702 0 1.2286 0 1.2613 0 1.2646 0 1.2262 0 1.1985 0 1.2007 0 1.2138 0 1.2266 0 1.2176 0 1.2218 0 1.249 0 1.2991 0 1.3408 0 1.3119 0 1.3014 0 1.3201 0 1.2938 0 1.2694 0 1.2165 0 1.2037 0 1.2292 0 1.2256 0 1.2015 0 1.1786 0 1.1856 0 1.2103 0 1.1938 0 1.202 0 1.2271 0 1.277 0 1.265 0 1.2684 0 1.2811 0 1.2727 0 1.2611 0 1.2881 0 1.3213 0 1.2999 0 1.3074 1 1.3242 1 1.3516 1 1.3511 1 1.3419 1 1.3716 1 1.3622 1 1.3896 1 1.4227 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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.11826 + 0.0325999999999999x[t] -0.0251688888888893M1[t] + 0.00249555555555545M2[t] + 0.00891999999999998M3[t] -0.00159555555555566M4[t] -0.00363111111111115M5[t] -0.00688666666666672M6[t] + 0.00945777777777772M7[t] -0.00489777777777787M8[t] -0.00787333333333342M9[t] -0.0123488888888890M10[t] -0.0105444444444445M11[t] + 0.00377555555555556t + 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)	1.11826	0.031235	35.8012	0	0
x	0.0325999999999999	0.027395	1.19	0.240155	0.120077
M1	-0.0251688888888893	0.037114	-0.6781	0.501076	0.250538
M2	0.00249555555555545	0.037076	0.0673	0.946628	0.473314
M3	0.00891999999999998	0.037047	0.2408	0.810798	0.405399
M4	-0.00159555555555566	0.037026	-0.0431	0.965814	0.482907
M5	-0.00363111111111115	0.036962	-0.0982	0.92217	0.461085
M6	-0.00688666666666672	0.036907	-0.1866	0.8528	0.4264
M7	0.00945777777777772	0.036861	0.2566	0.798645	0.399323
M8	-0.00489777777777787	0.036822	-0.133	0.894765	0.447383
M9	-0.00787333333333342	0.036793	-0.214	0.831499	0.41575
M10	-0.0123488888888890	0.036771	-0.3358	0.738527	0.369264
M11	-0.0105444444444445	0.036759	-0.2869	0.775511	0.387755
t	0.00377555555555556	0.000559	6.7517	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.82296196892034
R-squared	0.677266402289243
Adjusted R-squared	0.586059081197073
F-TEST (value)	7.42557060309693
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	1.45631275816349e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.058113846787197
Sum Squared Residuals	0.155352082666667

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.0014	1.09686666666667	-0.0954666666666679
2	1.0183	1.12830666666667	-0.110006666666667
3	1.0622	1.13850666666667	-0.0763066666666666
4	1.0773	1.13176666666667	-0.0544666666666666
5	1.0807	1.13350666666667	-0.0528066666666666
6	1.0848	1.13402666666667	-0.0492266666666666
7	1.1582	1.15414666666667	0.00405333333333334
8	1.1663	1.14356666666667	0.0227333333333333
9	1.1372	1.14436666666667	-0.00716666666666657
10	1.1139	1.14366666666667	-0.0297666666666667
11	1.1222	1.14924666666667	-0.0270466666666665
12	1.1692	1.16356666666667	0.00563333333333335
13	1.1702	1.14217333333333	0.0280266666666670
14	1.2286	1.17361333333333	0.0549866666666667
15	1.2613	1.18381333333333	0.0774866666666668
16	1.2646	1.17707333333333	0.0875266666666667
17	1.2262	1.17881333333333	0.0473866666666666
18	1.1985	1.17933333333333	0.0191666666666666
19	1.2007	1.19945333333333	0.00124666666666681
20	1.2138	1.18887333333333	0.0249266666666667
21	1.2266	1.18967333333333	0.0369266666666667
22	1.2176	1.18897333333333	0.0286266666666667
23	1.2218	1.19455333333333	0.0272466666666667
24	1.249	1.20887333333333	0.0401266666666667
25	1.2991	1.18748	0.111620000000000
26	1.3408	1.21892	0.12188
27	1.3119	1.22912	0.08278
28	1.3014	1.22238	0.07902
29	1.3201	1.22412	0.09598
30	1.2938	1.22464	0.06916
31	1.2694	1.24476	0.0246400000000001
32	1.2165	1.23418	-0.0176800000000000
33	1.2037	1.23498	-0.03128
34	1.2292	1.23428	-0.00507999999999993
35	1.2256	1.23986	-0.01426
36	1.2015	1.25418	-0.0526800000000001
37	1.1786	1.23278666666667	-0.0541866666666663
38	1.1856	1.26422666666667	-0.0786266666666667
39	1.2103	1.27442666666667	-0.0641266666666668
40	1.1938	1.26768666666667	-0.0738866666666667
41	1.202	1.26942666666667	-0.0674266666666668
42	1.2271	1.26994666666667	-0.0428466666666667
43	1.277	1.29006666666667	-0.0130666666666668
44	1.265	1.27948666666667	-0.0144866666666668
45	1.2684	1.28028666666667	-0.0118866666666667
46	1.2811	1.27958666666667	0.00151333333333315
47	1.2727	1.28516666666667	-0.0124666666666668
48	1.2611	1.29948666666667	-0.0383866666666667
49	1.2881	1.27809333333333	0.0100066666666669
50	1.3213	1.30953333333333	0.0117666666666665
51	1.2999	1.31973333333333	-0.0198333333333334
52	1.3074	1.34559333333333	-0.0381933333333333
53	1.3242	1.34733333333333	-0.0231333333333333
54	1.3516	1.34785333333333	0.00374666666666657
55	1.3511	1.36797333333333	-0.0168733333333334
56	1.3419	1.35739333333333	-0.0154933333333332
57	1.3716	1.35819333333333	0.0134066666666666
58	1.3622	1.35749333333333	0.00470666666666675
59	1.3896	1.36307333333333	0.0265266666666666
60	1.4227	1.37739333333333	0.0453066666666667

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/1z4db1197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/1z4db1197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/2cj5u1197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/2cj5u1197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/3qpxa1197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/3qpxa1197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/4fe101197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/4fe101197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/5lgkh1197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/5lgkh1197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/6rht21197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/6rht21197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/7gngr1197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/7gngr1197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/8z7631197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/8z7631197539816.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/9eumh1197539816.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197539151xmsa4ynwq1350qi/9eumh1197539816.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')

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