Home » date » 2008 » Dec » 16 »

Regressiemodel (met seasonal dummies en lineaire trend)

*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: Tue, 16 Dec 2008 02:36:46 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t1229420293bd8s5ljmo22v2iq.htm/, Retrieved Tue, 16 Dec 2008 10:38:13 +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/2008/Dec/16/t1229420293bd8s5ljmo22v2iq.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

117 0 103.8 0 100.8 0 110.6 0 104 0 112.6 0 107.3 0 98.9 0 109.8 0 104.9 0 102.2 0 123.9 0 124.9 0 112.7 0 121.9 0 100.6 0 104.3 0 120.4 0 107.5 0 102.9 0 125.6 0 107.5 0 108.8 0 128.4 1 121.1 1 119.5 1 128.7 1 108.7 1 105.5 1 119.8 1 111.3 1 110.6 1 120.1 1 97.5 1 107.7 1 127.3 1 117.2 1 119.8 1 116.2 1 111 1 112.4 1 130.6 1 109.1 1 118.8 1 123.9 1 101.6 1 112.8 1 128 1 129.6 1 125.8 1 119.5 1 115.7 1 113.6 1 129.7 1 112 1 116.8 1 127 1 112.9 1 113.3 1 121.7 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	12 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Cons[t] = + 117.858505494505 -0.186593406593408Reg[t] -1.44680586080589M1[t] -7.31321611721612M2[t] -6.43962637362638M3[t] -14.7660366300366M4[t] -16.3524468864469M5[t] -1.91885714285715M6[t] -15.3252673992674M7[t] -15.3916776556777M8[t] -3.93808791208792M9[t] -20.5644981684982M10[t] -16.7109084249084M11[t] + 0.226410256410257t + 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)	117.858505494505	2.650881	44.4601	0	0
Reg	-0.186593406593408	2.589051	-0.0721	0.942858	0.471429
M1	-1.44680586080589	3.221007	-0.4492	0.655412	0.327706
M2	-7.31321611721612	3.213411	-2.2758	0.027559	0.013779
M3	-6.43962637362638	3.20749	-2.0077	0.050572	0.025286
M4	-14.7660366300366	3.203254	-4.6097	3.2e-05	1.6e-05
M5	-16.3524468864469	3.20071	-5.109	6e-06	3e-06
M6	-1.91885714285715	3.199862	-0.5997	0.55167	0.275835
M7	-15.3252673992674	3.20071	-4.7881	1.8e-05	9e-06
M8	-15.3916776556777	3.203254	-4.805	1.7e-05	8e-06
M9	-3.93808791208792	3.20749	-1.2278	0.225776	0.112888
M10	-20.5644981684982	3.213411	-6.3996	0	0
M11	-16.7109084249084	3.221007	-5.1881	5e-06	2e-06
t	0.226410256410257	0.073694	3.0723	0.003563	0.001781

Multiple Linear Regression - Regression Statistics
Multiple R	0.868945960631488
R-squared	0.75506708249778
Adjusted R-squared	0.685846910160196
F-TEST (value)	10.9081942011839
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	4.48466486169252e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.04145259252864
Sum Squared Residuals	1169.14723516483

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	117	116.63810989011	0.361890109890025
2	103.8	110.998109890110	-7.19810989010989
3	100.8	112.098109890110	-11.2981098901099
4	110.6	103.998109890110	6.6018901098901
5	104	102.638109890110	1.36189010989011
6	112.6	117.29810989011	-4.69810989010989
7	107.3	104.118109890110	3.18189010989012
8	98.9	104.278109890110	-5.37810989010988
9	109.8	115.958109890110	-6.15810989010989
10	104.9	99.55810989011	5.34189010989011
11	102.2	103.638109890110	-1.43810989010989
12	123.9	120.575428571429	3.32457142857143
13	124.9	119.355032967033	5.54496703296706
14	112.7	113.715032967033	-1.01503296703296
15	121.9	114.815032967033	7.08496703296704
16	100.6	106.715032967033	-6.11503296703297
17	104.3	105.355032967033	-1.05503296703297
18	120.4	120.015032967033	0.384967032967043
19	107.5	106.835032967033	0.664967032967032
20	102.9	106.995032967033	-4.09503296703296
21	125.6	118.675032967033	6.92496703296703
22	107.5	102.275032967033	5.22496703296703
23	108.8	106.355032967033	2.44496703296703
24	128.4	123.105758241758	5.29424175824176
25	121.1	121.885362637363	-0.78536263736262
26	119.5	116.245362637363	3.25463736263737
27	128.7	117.345362637363	11.3546373626373
28	108.7	109.245362637363	-0.545362637362631
29	105.5	107.885362637363	-2.38536263736264
30	119.8	122.545362637363	-2.74536263736264
31	111.3	109.365362637363	1.93463736263736
32	110.6	109.525362637363	1.07463736263736
33	120.1	121.205362637363	-1.10536263736264
34	97.5	104.805362637363	-7.30536263736263
35	107.7	108.885362637363	-1.18536263736263
36	127.3	125.822681318681	1.47731868131867
37	117.2	124.602285714286	-7.40228571428569
38	119.8	118.962285714286	0.837714285714283
39	116.2	120.062285714286	-3.86228571428571
40	111	111.962285714286	-0.962285714285713
41	112.4	110.602285714286	1.79771428571429
42	130.6	125.262285714286	5.33771428571428
43	109.1	112.082285714286	-2.98228571428572
44	118.8	112.242285714286	6.55771428571428
45	123.9	123.922285714286	-0.0222857142857087
46	101.6	107.522285714286	-5.92228571428572
47	112.8	111.602285714286	1.19771428571428
48	128	128.539604395604	-0.539604395604402
49	129.6	127.319208791209	2.28079120879122
50	125.8	121.679208791209	4.1207912087912
51	119.5	122.779208791209	-3.27920879120880
52	115.7	114.679208791209	1.02079120879121
53	113.6	113.319208791209	0.280791208791202
54	129.7	127.979208791209	1.72079120879120
55	112	114.799208791209	-2.79920879120879
56	116.8	114.959208791209	1.84079120879120
57	127	126.639208791209	0.360791208791207
58	112.9	110.239208791209	2.66079120879121
59	113.3	114.319208791209	-1.01920879120879
60	121.7	131.256527472527	-9.55652747252748

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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

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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.

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