Home » date » 2008 » Dec » 16 »

Paper: Multiple Regression met dummy: Toetreding van Slovenië tot de EU (zonder LT)

*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 11:26:09 -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/t1229452165pejs55h55w7dk5w.htm/, Retrieved Tue, 16 Dec 2008 19:29:25 +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/t1229452165pejs55h55w7dk5w.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 «

17.3 0 15.4 0 16.9 0 20.8 0 16.4 0 11.3 0 17.5 0 16.6 0 17.5 0 19.5 0 18.8 0 20.2 0 19.2 0 14.4 0 24.5 0 25.7 0 27.1 0 21 0 18.6 0 20 0 21.8 0 20.4 0 18 1 21.5 1 19.1 1 19.7 1 26 1 26.3 1 24.6 1 22.4 1 32 1 24 1 30 1 24.1 1 26.3 1 29.8 1 21.9 1 22.8 1 29.2 1 27.5 1 27.4 1 31 1 26.1 1 22.2 1 34 1 26.9 1 31.9 1 34.2 1 31.2 1 28.5 1 37.1 1 36 1 34.8 1 32.1 1 37.2 1 36.3 1 39.5 1 37.1 1 35.6 1 36.2 1 35.9 1 32.5 1 39.2 1 39.4 1 42.8 1 34.5 1 43.7 1 46.3 1 40.8 1 48.4 1 43.2 1 48.1 1 42.8 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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 20.8533123028391 + 12.9760252365931x[t] -3.35047318611987M1[t] -7.28732912723449M2[t] -0.68732912723449M3[t] -0.220662460567823M4[t] -0.653995793901157M5[t] -4.12066246056782M6[t] -0.320662460567822M7[t] -1.93732912723449M8[t] + 1.09600420609884M9[t] -0.103995793901157M10[t] -2.7M11[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)	20.8533123028391	3.248691	6.419	0	0
x	12.9760252365931	1.813153	7.1566	0	0
M1	-3.35047318611987	3.925176	-0.8536	0.39673	0.198365
M2	-7.28732912723449	4.078394	-1.7868	0.07902	0.03951
M3	-0.68732912723449	4.078394	-0.1685	0.866734	0.433367
M4	-0.220662460567823	4.078394	-0.0541	0.957031	0.478516
M5	-0.653995793901157	4.078394	-0.1604	0.873139	0.43657
M6	-4.12066246056782	4.078394	-1.0104	0.316378	0.158189
M7	-0.320662460567822	4.078394	-0.0786	0.937593	0.468796
M8	-1.93732912723449	4.078394	-0.475	0.636496	0.318248
M9	1.09600420609884	4.078394	0.2687	0.789056	0.394528
M10	-0.103995793901157	4.078394	-0.0255	0.979741	0.489871
M11	-2.7	4.067183	-0.6639	0.509329	0.254665

Multiple Linear Regression - Regression Statistics
Multiple R	0.705897895720123
R-squared	0.498291839182098
Adjusted R-squared	0.397950207018517
F-TEST (value)	4.96595309880713
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	1.21898229794581e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	7.04456831125253
Sum Squared Residuals	2977.55656151420

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	17.3	17.5028391167192	-0.202839116719223
2	15.4	13.5659831756046	1.83401682439538
3	16.9	20.1659831756046	-3.26598317560463
4	20.8	20.6326498422713	0.167350157728706
5	16.4	20.1993165089380	-3.79931650893796
6	11.3	16.7326498422713	-5.43264984227129
7	17.5	20.5326498422713	-3.03264984227130
8	16.6	18.9159831756046	-2.31598317560463
9	17.5	21.9493165089380	-4.44931650893796
10	19.5	20.7493165089380	-1.24931650893796
11	18.8	18.1533123028391	0.646687697160881
12	20.2	20.8533123028391	-0.653312302839119
13	19.2	17.5028391167192	1.69716088328075
14	14.4	13.5659831756046	0.834016824395372
15	24.5	20.1659831756046	4.33401682439537
16	25.7	20.6326498422713	5.0673501577287
17	27.1	20.1993165089380	6.90068349106204
18	21	16.7326498422713	4.26735015772871
19	18.6	20.5326498422713	-1.93264984227129
20	20	18.9159831756046	1.08401682439537
21	21.8	21.9493165089380	-0.149316508937960
22	20.4	20.7493165089380	-0.349316508937961
23	18	31.1293375394322	-13.1293375394322
24	21.5	33.8293375394322	-12.3293375394322
25	19.1	30.4788643533123	-11.3788643533123
26	19.7	26.5420084121977	-6.84200841219769
27	26	33.1420084121977	-7.14200841219769
28	26.3	33.6086750788644	-7.30867507886435
29	24.6	33.175341745531	-8.57534174553102
30	22.4	29.7086750788644	-7.30867507886435
31	32	33.5086750788644	-1.50867507886435
32	24	31.8920084121977	-7.89200841219769
33	30	34.925341745531	-4.92534174553102
34	24.1	33.725341745531	-9.62534174553102
35	26.3	31.1293375394322	-4.82933753943218
36	29.8	33.8293375394322	-4.02933753943218
37	21.9	30.4788643533123	-8.5788643533123
38	22.8	26.5420084121977	-3.74200841219769
39	29.2	33.1420084121977	-3.94200841219769
40	27.5	33.6086750788644	-6.10867507886435
41	27.4	33.175341745531	-5.77534174553102
42	31	29.7086750788644	1.29132492113565
43	26.1	33.5086750788644	-7.40867507886435
44	22.2	31.8920084121977	-9.69200841219769
45	34	34.925341745531	-0.92534174553102
46	26.9	33.725341745531	-6.82534174553102
47	31.9	31.1293375394322	0.77066246056782
48	34.2	33.8293375394322	0.370662460567829
49	31.2	30.4788643533123	0.721135646687695
50	28.5	26.5420084121977	1.95799158780231
51	37.1	33.1420084121977	3.95799158780232
52	36	33.6086750788644	2.39132492113565
53	34.8	33.175341745531	1.62465825446898
54	32.1	29.7086750788644	2.39132492113565
55	37.2	33.5086750788644	3.69132492113565
56	36.3	31.8920084121977	4.40799158780231
57	39.5	34.925341745531	4.57465825446898
58	37.1	33.725341745531	3.37465825446898
59	35.6	31.1293375394322	4.47066246056782
60	36.2	33.8293375394322	2.37066246056783
61	35.9	30.4788643533123	5.42113564668769
62	32.5	26.5420084121977	5.95799158780231
63	39.2	33.1420084121977	6.05799158780232
64	39.4	33.6086750788644	5.79132492113565
65	42.8	33.175341745531	9.62465825446898
66	34.5	29.7086750788644	4.79132492113565
67	43.7	33.5086750788644	10.1913249211356
68	46.3	31.8920084121977	14.4079915878023
69	40.8	34.925341745531	5.87465825446898
70	48.4	33.725341745531	14.6746582544690
71	43.2	31.1293375394322	12.0706624605678
72	48.1	33.8293375394322	14.2706624605678
73	42.8	30.4788643533123	12.3211356466877

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229452165pejs55h55w7dk5w/4w5ao1229451960.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229452165pejs55h55w7dk5w/57pfn1229451960.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229452165pejs55h55w7dk5w/8rlck1229451960.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229452165pejs55h55w7dk5w/90i1f1229451960.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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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.

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