Home » date » 2007 » Nov » 28 » attachments

Multiple regression Werkloosheid-toetreding nieuwe EUlanden (Seizoenaliteit)

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

Title produced by software: Multiple Regression

Date of computation: Wed, 28 Nov 2007 07:50:59 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/28/t119626088029teliq6tsulztw.htm/, Retrieved Wed, 28 Nov 2007 15:41:30 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

467037 0 460070 0 447988 0 442867 0 436087 0 431328 0 484015 0 509673 0 512927 0 502831 0 470984 0 471067 0 476049 0 474605 0 470439 0 461251 0 454724 0 455626 0 516847 0 525192 0 522975 0 518585 0 509239 0 512238 0 519164 0 517009 0 509933 0 509127 0 500857 0 506971 0 569323 0 579714 0 577992 0 565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 1 542722 1 593530 1 610763 1 612613 1 611324 1 594167 1 595454 1 590865 1 589379 1 584428 1 573100 1 567456 1 569028 1 620735 1 628884 1 628232 1 612117 1 595404 1 597141 1 593408 1 590072 1 579799 1 574205 1 572775 1 572942 1 619567 1 625809 1 619916 1 587625 1 565742 1 557274 1

Text written by user:

paper

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 compuational 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

Werkloosheid[t] = + 505931.171474359 + 84124.9903846154EUlanden[t] + 835.165064102585M1[t] -1974.66826923081M2[t] -9319.6682692308M3[t] -16614.6682692308M4[t] -36566.8333333334M5[t] -34890.8333333333M6[t] + 19342.5000000000M7[t] + 32012.1666666666M8[t] + 31115.5M9[t] + 18330.6666666667M10[t] -847.000000000007M11[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)	505931.171474359	12702.293789	39.8299	0	0
EUlanden	84124.9903846154	7169.587706	11.7336	0	0
M1	835.165064102585	17274.921182	0.0483	0.961604	0.480802
M2	-1974.66826923081	17274.921182	-0.1143	0.909381	0.454691
M3	-9319.6682692308	17274.921182	-0.5395	0.591578	0.295789
M4	-16614.6682692308	17274.921182	-0.9618	0.340086	0.170043
M5	-36566.8333333334	17233.544066	-2.1218	0.038061	0.01903
M6	-34890.8333333333	17233.544066	-2.0246	0.047444	0.023722
M7	19342.5000000000	17233.544066	1.1224	0.26625	0.133125
M8	32012.1666666666	17233.544066	1.8575	0.068226	0.034113
M9	31115.5	17233.544066	1.8055	0.076096	0.038048
M10	18330.6666666667	17233.544066	1.0637	0.291816	0.145908
M11	-847.000000000007	17233.544066	-0.0491	0.960967	0.480484

Multiple Linear Regression - Regression Statistics
Multiple R	0.870341412865593
R-squared	0.757494174948876
Adjusted R-squared	0.70817095629441
F-TEST (value)	15.3577604141268
F-TEST (DF numerator)	12
F-TEST (DF denominator)	59
p-value	5.59552404411079e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	29849.3739164386
Sum Squared Residuals	52568122268.9984

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	467037	506766.336538461	-39729.3365384614
2	460070	503956.503205128	-43886.5032051283
3	447988	496611.503205128	-48623.5032051282
4	442867	489316.503205128	-46449.5032051281
5	436087	469364.338141026	-33277.3381410257
6	431328	471040.338141026	-39712.3381410256
7	484015	525273.671474359	-41258.671474359
8	509673	537943.338141026	-28270.3381410257
9	512927	537046.671474359	-24119.6714743590
10	502831	524261.838141026	-21430.8381410256
11	470984	505084.171474359	-34100.1714743589
12	471067	505931.171474359	-34864.171474359
13	476049	506766.336538462	-30717.3365384616
14	474605	503956.503205128	-29351.5032051282
15	470439	496611.503205128	-26172.5032051282
16	461251	489316.503205128	-28065.5032051282
17	454724	469364.338141026	-14640.3381410256
18	455626	471040.338141026	-15414.3381410256
19	516847	525273.671474359	-8426.67147435898
20	525192	537943.338141026	-12751.3381410256
21	522975	537046.671474359	-14071.6714743590
22	518585	524261.838141026	-5676.83814102565
23	509239	505084.171474359	4154.82852564102
24	512238	505931.171474359	6306.828525641
25	519164	506766.336538462	12397.6634615384
26	517009	503956.503205128	13052.4967948718
27	509933	496611.503205128	13321.4967948718
28	509127	489316.503205128	19810.4967948718
29	500857	469364.338141026	31492.6618589744
30	506971	471040.338141026	35930.6618589744
31	569323	525273.671474359	44049.328525641
32	579714	537943.338141026	41770.6618589744
33	577992	537046.671474359	40945.328525641
34	565464	524261.838141026	41202.1618589743
35	547344	505084.171474359	42259.828525641
36	554788	505931.171474359	48856.828525641
37	562325	506766.336538462	55558.6634615384
38	560854	503956.503205128	56897.4967948718
39	555332	496611.503205128	58720.4967948718
40	543599	489316.503205128	54282.4967948718
41	536662	553489.328525641	-16827.328525641
42	542722	555165.328525641	-12443.3285256410
43	593530	609398.661858974	-15868.6618589744
44	610763	622068.328525641	-11305.3285256410
45	612613	621171.661858974	-8558.66185897436
46	611324	608386.828525641	2937.17147435897
47	594167	589209.161858974	4957.83814102564
48	595454	590056.161858974	5397.83814102562
49	590865	590891.326923077	-26.3269230769674
50	589379	588081.493589744	1297.50641025640
51	584428	580736.493589744	3691.50641025642
52	573100	573441.493589744	-341.493589743584
53	567456	553489.328525641	13966.671474359
54	569028	555165.328525641	13862.6714743590
55	620735	609398.661858974	11336.3381410256
56	628884	622068.328525641	6815.67147435899
57	628232	621171.661858974	7060.33814102564
58	612117	608386.828525641	3730.17147435897
59	595404	589209.161858974	6194.83814102563
60	597141	590056.161858974	7084.83814102562
61	593408	590891.326923077	2516.67307692304
62	590072	588081.493589744	1990.50641025640
63	579799	580736.493589744	-937.49358974358
64	574205	573441.493589744	763.506410256416
65	572775	553489.328525641	19285.6714743590
66	572942	555165.328525641	17776.6714743590
67	619567	609398.661858974	10168.3381410256
68	625809	622068.328525641	3740.67147435899
69	619916	621171.661858974	-1255.66185897437
70	587625	608386.828525641	-20761.8285256410
71	565742	589209.161858974	-23467.1618589744
72	557274	590056.161858974	-32782.1618589744

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/1dvzv1196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/1dvzv1196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/2qhg71196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/2qhg71196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/3b6sn1196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/3b6sn1196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/4zx401196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/4zx401196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/58yt31196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/58yt31196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/6dbnm1196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/6dbnm1196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/7909y1196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/7909y1196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/8k54p1196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/8k54p1196261455.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/98wox1196261455.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/28/t119626088029teliq6tsulztw/98wox1196261455.ps (open in new window)

Parameters:

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

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