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*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 16 Dec 2009 11:35:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic.htm/, Retrieved Wed, 16 Dec 2009 19:38:02 +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/2009/Dec/16/t12609886719nzezpqcya8kiic.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

19 0 18 0 19 0 19 0 22 0 23 0 20 0 14 0 14 0 14 0 15 0 11 0 17 0 16 0 20 0 24 0 23 0 20 0 21 0 19 0 23 0 23 0 23 0 23 0 27 0 26 0 17 0 24 0 26 0 24 0 27 0 27 0 26 0 24 0 23 0 23 0 24 1 17 1 21 1 19 1 22 1 22 1 18 1 16 1 14 1 12 1 14 1 16 1 8 1 3 1 0 1 5 1 1 1 1 1 3 1 6 1 7 1 8 1 14 1 14 1 13 1 15 1

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

consumentenvertrouwen[t] = + 20.2923172822191 -9.9987365291713`financiële_crisis`[t] + 0.0352501168770451t + 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)	20.2923172822191	1.717473	11.8152	0	0
`financiële_crisis`	-9.9987365291713	2.81151	-3.5564	0.000749	0.000374
t	0.0352501168770451	0.077525	0.4547	0.650998	0.325499

Multiple Linear Regression - Regression Statistics
Multiple R	0.623197251267524
R-squared	0.388374813987397
Adjusted R-squared	0.367641756834428
F-TEST (value)	18.7321537350690
F-TEST (DF numerator)	2
F-TEST (DF denominator)	59
p-value	5.02710718386368e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.66913406283162
Sum Squared Residuals	1896.20578031910

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	19	20.3275673990961	-1.32756739909608
2	18	20.3628175159732	-2.36281751597321
3	19	20.3980676328502	-1.39806763285025
4	19	20.4333177497273	-1.43331774972729
5	22	20.4685678666043	1.53143213339566
6	23	20.5038179834814	2.49618201651862
7	20	20.5390681003584	-0.539068100358428
8	14	20.5743182172355	-6.57431821723547
9	14	20.6095683341125	-6.60956833411252
10	14	20.6448184509896	-6.64481845098956
11	15	20.6800685678666	-5.68006856786661
12	11	20.7153186847437	-9.71531868474365
13	17	20.7505688016207	-3.7505688016207
14	16	20.7858189184977	-4.78581891849774
15	20	20.8210690353748	-0.821069035374789
16	24	20.8563191522518	3.14368084774817
17	23	20.8915692691289	2.10843073087112
18	20	20.9268193860059	-0.926819386005924
19	21	20.9620695028830	0.0379304971170308
20	19	20.99731961976	-1.99731961976001
21	23	21.0325697366371	1.96743026336294
22	23	21.0678198535141	1.93218014648589
23	23	21.1030699703912	1.89693002960885
24	23	21.1383200872682	1.86167991273180
25	27	21.1735702041452	5.82642979585476
26	26	21.2088203210223	4.79117967897771
27	17	21.2440704378993	-4.24407043789933
28	24	21.2793205547764	2.72067944522362
29	26	21.3145706716534	4.68542932834658
30	24	21.3498207885305	2.65017921146953
31	27	21.3850709054075	5.61492909459249
32	27	21.4203210222846	5.57967897771544
33	26	21.4555711391616	4.5444288608384
34	24	21.4908212560386	2.50917874396135
35	23	21.5260713729157	1.47392862708431
36	23	21.5613214897927	1.43867851020726
37	24	11.5978350774985	12.4021649225015
38	17	11.6330851943755	5.36691480562448
39	21	11.6683353112526	9.33166468874744
40	19	11.7035854281296	7.29641457187039
41	22	11.7388355450067	10.2611644549933
42	22	11.7740856618837	10.2259143381163
43	18	11.8093357787607	6.19066422123925
44	16	11.8445858956378	4.15541410436221
45	14	11.8798360125148	2.12016398748516
46	12	11.9150861293919	0.0849138706081192
47	14	11.9503362462689	2.04966375373107
48	16	11.9855863631460	4.01441363685403
49	8	12.020836480023	-4.02083648002302
50	3	12.0560865969001	-9.05608659690006
51	0	12.0913367137771	-12.0913367137771
52	5	12.1265868306542	-7.12658683065415
53	1	12.1618369475312	-11.1618369475312
54	1	12.1970870644082	-11.1970870644082
55	3	12.2323371812853	-9.23233718128528
56	6	12.2675872981623	-6.26758729816233
57	7	12.3028374150394	-5.30283741503938
58	8	12.3380875319164	-4.33808753191642
59	14	12.3733376487935	1.62666235120653
60	14	12.4085877656705	1.59141223432949
61	13	12.4438378825476	0.556162117452442
62	15	12.4790879994246	2.52091200057540

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/1rm901260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/1rm901260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/2pj1x1260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/2pj1x1260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/36q101260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/36q101260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/4wgkb1260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/4wgkb1260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/5iu1t1260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/5iu1t1260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/67skr1260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/67skr1260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/7m9d31260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/7m9d31260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/8i42i1260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/8i42i1260988528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/9h8of1260988528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609886719nzezpqcya8kiic/9h8of1260988528.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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

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