Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2009 » Dec » 16 »

*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 10:12:08 -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/t1260983688i6927q7dwlsen28.htm/, Retrieved Wed, 16 Dec 2009 18:14:59 +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/t1260983688i6927q7dwlsen28.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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

consumentenvertrouwen[t] = + 19.9166666666667 -10.3452380952381`financiële_crisis`[t] + 1.85972222222223M1[t] -0.351984126984132M2[t] -1.59464285714286M3[t] + 1.16031746031746M4[t] + 1.71527777777778M5[t] + 0.870238095238092M6[t] + 0.62519841269841M7[t] -0.819841269841272M8[t] -0.464880952380954M9[t] -1.10992063492063M10[t] + 0.44503968253968M11[t] + 0.0450396825396822t + 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)	19.9166666666667	3.516726	5.6634	1e-06	0
`financiële_crisis`	-10.3452380952381	3.192629	-3.2404	0.002171	0.001086
M1	1.85972222222223	3.807474	0.4884	0.627462	0.313731
M2	-0.351984126984132	3.791701	-0.0928	0.926425	0.463212
M3	-1.59464285714286	3.982264	-0.4004	0.690612	0.345306
M4	1.16031746031746	3.965441	0.2926	0.771083	0.385542
M5	1.71527777777778	3.950538	0.4342	0.666097	0.333049
M6	0.870238095238092	3.937576	0.221	0.826023	0.413012
M7	0.62519841269841	3.926575	0.1592	0.874162	0.437081
M8	-0.819841269841272	3.917551	-0.2093	0.83512	0.41756
M9	-0.464880952380954	3.910518	-0.1189	0.905867	0.452933
M10	-1.10992063492063	3.905487	-0.2842	0.777483	0.388742
M11	0.44503968253968	3.902465	0.114	0.909681	0.454841
t	0.0450396825396822	0.088684	0.5079	0.613873	0.306937

Multiple Linear Regression - Regression Statistics
Multiple R	0.640966321583416
R-squared	0.410837825404175
Adjusted R-squared	0.251273069784472
F-TEST (value)	2.57474041688342
F-TEST (DF numerator)	13
F-TEST (DF denominator)	48
p-value	0.00874013524307227
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.16874562768215
Sum Squared Residuals	1826.56428571429

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	19	21.8214285714285	-2.82142857142852
2	18	19.6547619047619	-1.65476190476191
3	19	18.4571428571429	0.542857142857136
4	19	21.2571428571429	-2.25714285714286
5	22	21.8571428571429	0.142857142857144
6	23	21.0571428571429	1.94285714285714
7	20	20.8571428571429	-0.857142857142862
8	14	19.4571428571429	-5.45714285714286
9	14	19.8571428571429	-5.85714285714287
10	14	19.2571428571429	-5.25714285714286
11	15	20.8571428571429	-5.85714285714286
12	11	20.4571428571429	-9.45714285714287
13	17	22.3619047619048	-5.36190476190477
14	16	20.1952380952381	-4.19523809523809
15	20	18.9976190476191	1.00238095238095
16	24	21.7976190476191	2.20238095238095
17	23	22.3976190476190	0.60238095238095
18	20	21.5976190476190	-1.59761904761905
19	21	21.3976190476190	-0.397619047619046
20	19	19.9976190476191	-0.997619047619049
21	23	20.3976190476190	2.60238095238095
22	23	19.7976190476190	3.20238095238095
23	23	21.3976190476190	1.60238095238095
24	23	20.9976190476191	2.00238095238095
25	27	22.9023809523810	4.09761904761903
26	26	20.7357142857143	5.26428571428572
27	17	19.5380952380952	-2.53809523809524
28	24	22.3380952380952	1.66190476190476
29	26	22.9380952380952	3.06190476190476
30	24	22.1380952380952	1.86190476190476
31	27	21.9380952380952	5.06190476190477
32	27	20.5380952380952	6.46190476190476
33	26	20.9380952380952	5.06190476190477
34	24	20.3380952380952	3.66190476190476
35	23	21.9380952380952	1.06190476190476
36	23	21.5380952380952	1.46190476190476
37	24	13.0976190476191	10.9023809523809
38	17	10.9309523809524	6.06904761904762
39	21	9.73333333333333	11.2666666666667
40	19	12.5333333333333	6.46666666666667
41	22	13.1333333333333	8.86666666666667
42	22	12.3333333333333	9.66666666666667
43	18	12.1333333333333	5.86666666666667
44	16	10.7333333333333	5.26666666666666
45	14	11.1333333333333	2.86666666666667
46	12	10.5333333333333	1.46666666666667
47	14	12.1333333333333	1.86666666666667
48	16	11.7333333333333	4.26666666666666
49	8	13.6380952380953	-5.63809523809525
50	3	11.4714285714286	-8.47142857142857
51	0	10.2738095238095	-10.2738095238095
52	5	13.0738095238095	-8.07380952380952
53	1	13.6738095238095	-12.6738095238095
54	1	12.8738095238095	-11.8738095238095
55	3	12.6738095238095	-9.67380952380952
56	6	11.2738095238095	-5.27380952380952
57	7	11.6738095238095	-4.67380952380952
58	8	11.0738095238095	-3.07380952380952
59	14	12.6738095238095	1.32619047619048
60	14	12.2738095238095	1.72619047619048
61	13	14.1785714285714	-1.17857142857144
62	15	12.0119047619048	2.98809523809524

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/1j29x1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/1j29x1260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/28twy1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/28twy1260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/3iyx41260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/3iyx41260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/45o5a1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/45o5a1260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/5q5pe1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/5q5pe1260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/6e46b1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/6e46b1260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/7nycx1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/7nycx1260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/8ij841260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/8ij841260983523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/95xdw1260983523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260983688i6927q7dwlsen28/95xdw1260983523.ps (open in new window)

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

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