Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Nov » 21 »

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 21 Nov 2010 14:26:52 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa.htm/, Retrieved Sun, 21 Nov 2010 15:32:47 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1.39 1.08 1.34 1.12 1.33 1.12 1.3 1.16 1.28 1.16 1.29 1.16 1.29 1.16 1.28 1.15 1.27 1.17 1.26 1.16 1.29 1.19 1.36 1.13 1.33 1.14 1.35 1.13 1.31 1.16 1.3 1.17 1.32 1.14 1.33 1.14 1.36 1.11 1.35 1.12 1.4 1.08 1.41 1.07 1.4 1.09 1.4 1.08 1.4 1.08 1.41 1.08 1.4 1.09 1.39 1.08 1.41 1.07 1.42 1.07 1.43 1.07 1.42 1.08 1.42 1.07 1.43 1.06 1.43 1.06 1.43 1.06 1.46 1.04 1.47 1.03 1.47 1.03 1.46 1.04 1.47 1.03 1.49 1.02 1.5 1.01 1.47 1.03 1.48 1.02 1.49 1.01 1.49 1.02 1.5 1.01 1.48 1.02 1.46 1.03 1.43 1.04 1.44 1.04 1.43 1.03

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 computational 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

us/ch[t] = + 2.02985011486707 -0.667154578273706`eu/us`[t] -0.00680891095066132M1[t] -0.00445108084454656M2[t] -0.00609910567771565M3[t] -0.00240989388469514M4[t] -0.0113805179958427M5[t] -0.00135072858549389M6[t] -0.00265053878131491M7[t] -0.0047970998796629M8[t] -0.006096910075484M9[t] -0.0124003796083579M10[t] + 0.00629615085876827M11[t] -0.000360757575757605t + 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)	2.02985011486707	0.060496	33.5535	0	0
`eu/us`	-0.667154578273706	0.046327	-14.4011	0	0
M1	-0.00680891095066132	0.006609	-1.0302	0.30925	0.154625
M2	-0.00445108084454656	0.006588	-0.6756	0.503255	0.251628
M3	-0.00609910567771565	0.006664	-0.9152	0.365706	0.182853
M4	-0.00240989388469514	0.006793	-0.3548	0.724674	0.362337
M5	-0.0113805179958427	0.006792	-1.6756	0.10182	0.05091
M6	-0.00135072858549389	0.006992	-0.1932	0.847816	0.423908
M7	-0.00265053878131491	0.006956	-0.381	0.705248	0.352624
M8	-0.0047970998796629	0.007049	-0.6806	0.500163	0.250081
M9	-0.006096910075484	0.006988	-0.8725	0.388287	0.194144
M10	-0.0124003796083579	0.00698	-1.7765	0.083455	0.041727
M11	0.00629615085876827	0.006974	0.9028	0.372168	0.186084
t	-0.000360757575757605	0.000208	-1.7303	0.091482	0.045741

Multiple Linear Regression - Regression Statistics
Multiple R	0.986902872755255
R-squared	0.973977280252575
Adjusted R-squared	0.965303040336767
F-TEST (value)	112.283876132773
F-TEST (DF numerator)	13
F-TEST (DF denominator)	39
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.00980647641668609
Sum Squared Residuals	0.0037505122087298

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.08	1.09533558254020	-0.0153355825402015
2	1.12	1.13069038398425	-0.0106903839842470
3	1.12	1.13535314735806	-0.0153531473580573
4	1.16	1.15869623892353	0.00130376107646838
5	1.16	1.16270794880210	-0.00270794880210057
6	1.16	1.16570543485395	-0.00570543485395473
7	1.16	1.16404486708238	-0.00404486708237612
8	1.15	1.16820909419101	-0.0182090941910076
9	1.17	1.17322007220217	-0.00322007220216594
10	1.16	1.17322739087627	-0.0132273908762715
11	1.19	1.17154852641943	0.0184514735805711
12	1.13	1.11819079750574	0.0118092024942564
13	1.14	1.13103576632754	0.00896423367246417
14	1.13	1.11968974729242	0.0103102527075811
15	1.16	1.14436714801444	0.0156328519855596
16	1.17	1.15436714801444	0.0156328519855596
17	1.14	1.13169267476206	0.00830732523793893
18	1.14	1.13469016081392	0.00530983918608477
19	1.11	1.11301495569413	-0.00301495569412521
20	1.12	1.11717918280276	0.00282081719724333
21	1.08	1.08216088611749	-0.00216088611749282
22	1.07	1.06882511322612	0.00117488677387572
23	1.09	1.09383243190023	-0.00383243190022987
24	1.08	1.08717552346570	-0.007175523465704
25	1.08	1.08000585493929	-5.85493928507703e-06
26	1.08	1.07533138168691	0.00466861831309483
27	1.09	1.07999414506072	0.0100058549392845
28	1.08	1.08999414506072	-0.00999414506071551
29	1.07	1.06731967180834	0.0026803281916638
30	1.07	1.07031715786019	-0.000317157860190356
31	1.07	1.06198504430587	0.00801495569412533
32	1.08	1.06614927141451	0.0138507285854939
33	1.07	1.06448870364293	0.00551129635707257
34	1.06	1.05115293075156	0.0088470692484411
35	1.06	1.06948870364293	-0.00948870364292744
36	1.06	1.06283179520840	-0.00283179520840156
37	1.04	1.03564748933377	0.00435251066622854
38	1.03	1.03097301608139	-0.000973016081391561
39	1.03	1.02896423367246	0.00103576632753514
40	1.04	1.03896423367246	0.00103576632753518
41	1.03	1.02296130620282	0.00703869379717742
42	1.02	1.01928724647194	0.00071275352806032
43	1.01	1.01095513291762	-0.00095513291762400
44	1.03	1.02846245159173	0.00153754840827041
45	1.02	1.02013033803741	-0.000130338037413814
46	1.01	1.00679456514605	0.00320543485395472
47	1.02	1.02513033803741	-0.00513033803741382
48	1.01	1.01180188382015	-0.00180188382015088
49	1.02	1.01797530685921	0.00202469314079392
50	1.03	1.03331547095504	-0.00331547095503737
51	1.04	1.05132132589432	-0.0113213258943219
52	1.04	1.04797823432885	-0.00797823432884769
53	1.03	1.04531839842468	-0.0153183984246796

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/1sejd1290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/1sejd1290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/2loig1290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/2loig1290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/3loig1290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/3loig1290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/4vfz11290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/4vfz11290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/5vfz11290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/5vfz11290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/6vfz11290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/6vfz11290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/7o6y41290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/7o6y41290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/8o6y41290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/8o6y41290349607.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/9o6y41290349607.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349957br52t6l8f97mboa/9o6y41290349607.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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