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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 14:12:17 +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/t1290349867hos8w8rht5ubb8v.htm/, Retrieved Sun, 21 Nov 2010 15:31:07 +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/t1290349867hos8w8rht5ubb8v.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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

us/ch[t] = + 2.10935943686758 -0.734389206628538`eu/us`[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)	2.10935943686758	0.028181	74.851	0	0
`eu/us`	-0.734389206628538	0.02018	-36.3916	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.981284059913598
R-squared	0.962918406240514
Adjusted R-squared	0.962191316166798
F-TEST (value)	1324.34541613257
F-TEST (DF numerator)	1
F-TEST (DF denominator)	51
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0102367726314117
Sum Squared Residuals	0.00534436720926818

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.08	1.08855843965391	-0.00855843965390603
2	1.12	1.12527789998534	-0.00527789998533491
3	1.12	1.13262179205162	-0.0126217920516204
4	1.16	1.15465346825048	0.0053465317495233
5	1.16	1.16934125238305	-0.00934125238304747
6	1.16	1.16199736031676	-0.00199736031676208
7	1.16	1.16199736031676	-0.00199736031676208
8	1.15	1.16934125238305	-0.0193412523830475
9	1.17	1.17668514444933	-0.00668514444933284
10	1.16	1.18402903651562	-0.0240290365156182
11	1.19	1.16199736031676	0.0280026396832379
12	1.13	1.11059011585276	0.0194098841472356
13	1.14	1.13262179205162	0.00737820794837944
14	1.13	1.11793400791905	0.0120659920809502
15	1.16	1.14730957618419	0.0126904238158087
16	1.17	1.15465346825048	0.0153465317495233
17	1.14	1.13996568411791	3.43158820940604e-05
18	1.14	1.13262179205162	0.00737820794837944
19	1.11	1.11059011585276	-0.000590115852764199
20	1.12	1.11793400791905	0.00206599208095043
21	1.08	1.08121454758762	-0.00121454758762286
22	1.07	1.07387065552134	-0.00387065552133748
23	1.09	1.08121454758762	0.00878545241237715
24	1.08	1.08121454758762	-0.00121454758762286
25	1.08	1.08121454758762	-0.00121454758762286
26	1.08	1.07387065552134	0.00612934447866253
27	1.09	1.08121454758762	0.00878545241237715
28	1.08	1.08855843965391	-0.00855843965390824
29	1.07	1.07387065552134	-0.00387065552133748
30	1.07	1.06652676345505	0.00347323654494791
31	1.07	1.05918287138877	0.0108171286112333
32	1.08	1.06652676345505	0.0134732365449479
33	1.07	1.06652676345505	0.00347323654494791
34	1.06	1.05918287138877	0.000817128611233281
35	1.06	1.05918287138877	0.000817128611233281
36	1.06	1.05918287138877	0.000817128611233281
37	1.04	1.03715119518991	0.00284880481008941
38	1.03	1.02980730312363	0.000192696876374789
39	1.03	1.02980730312363	0.000192696876374789
40	1.04	1.03715119518991	0.00284880481008941
41	1.03	1.02980730312363	0.000192696876374789
42	1.02	1.01511951899105	0.00488048100894554
43	1.01	1.00777562692477	0.00222437307523091
44	1.03	1.02980730312363	0.000192696876374789
45	1.02	1.02246341105734	-0.00246341105733985
46	1.01	1.01511951899105	-0.00511951899105447
47	1.02	1.01511951899105	0.00488048100894554
48	1.01	1.00777562692477	0.00222437307523091
49	1.02	1.02246341105734	-0.00246341105733985
50	1.03	1.03715119518991	-0.0071511951899106
51	1.04	1.05918287138877	-0.0191828713887667
52	1.04	1.05183897932248	-0.0118389793224814
53	1.03	1.05918287138877	-0.0291828713887667

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/1v6kn1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/1v6kn1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/26xjq1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/26xjq1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/36xjq1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/36xjq1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/4z7it1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/4z7it1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/5z7it1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/5z7it1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/6z7it1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/6z7it1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/7rghw1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/7rghw1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/8rghw1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/8rghw1290348729.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/9rghw1290348729.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290349867hos8w8rht5ubb8v/9rghw1290348729.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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

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