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Multiple regression Werkloosheid-toetreding nieuwe EUlanden(seizoenaliteit en trend)

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 07:54:20 -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/t119626106700gef05lvbjpnz8.htm/, Retrieved Wed, 28 Nov 2007 15:44:41 +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] = + 457765.301103989 + 11876.1848290599Eulanden[t] + 10869.7213912630M1[t] + 6052.97679249759M2[t] -3298.93447293448M3[t] -12600.8457383666M4[t] -22518.4544753087M5[t] -22849.3657407407M6[t] + 29377.0563271605M7[t] + 40039.811728395M8[t] + 37136.2337962963M9[t] + 22344.4891975309M10[t] + 1159.91126543210M11[t] + 2006.9112654321t + 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)	457765.301103989	9668.577393	47.3457	0	0
Eulanden	11876.1848290599	9066.188726	1.3099	0.19538	0.09769
M1	10869.7213912630	11130.337097	0.9766	0.33283	0.166415
M2	6052.97679249759	11111.272566	0.5448	0.588007	0.294004
M3	-3298.93447293448	11096.421953	-0.2973	0.767302	0.383651
M4	-12600.8457383666	11085.802193	-1.1367	0.260353	0.130176
M5	-22518.4544753087	11154.731138	-2.0187	0.048146	0.024073
M6	-22849.3657407407	11127.243369	-2.0535	0.044546	0.022273
M7	29377.0563271605	11103.931339	2.6456	0.010476	0.005238
M8	40039.811728395	11084.821394	3.6121	0.000635	0.000318
M9	37136.2337962963	11069.935297	3.3547	0.001405	0.000703
M10	22344.4891975309	11059.290102	2.0204	0.047965	0.023983
M11	1159.91126543210	11052.898064	0.1049	0.916784	0.458392
t	2006.9112654321	217.057555	9.246	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.949724010267909
R-squared	0.901975695679359
Adjusted R-squared	0.880004730917835
F-TEST (value)	41.0530764338102
F-TEST (DF numerator)	13
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	19140.4891497739
Sum Squared Residuals	21248782843.7715

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	467037	470641.933760684	-3604.93376068378
2	460070	467832.100427350	-7762.10042735052
3	447988	460487.100427350	-12499.1004273505
4	442867	453192.100427350	-10325.1004273504
5	436087	445281.402955840	-9194.40295584049
6	431328	446957.402955840	-15629.4029558404
7	484015	501190.736289174	-17175.7362891738
8	509673	513860.40295584	-4187.40295584049
9	512927	512963.736289174	-36.7362891737525
10	502831	500178.90295584	2652.09704415958
11	470984	481001.236289174	-10017.2362891738
12	471067	481848.236289174	-10781.2362891738
13	476049	494724.868945869	-18675.8689458689
14	474605	491915.035612536	-17310.0356125355
15	470439	484570.035612536	-14131.0356125356
16	461251	477275.035612536	-16024.0356125356
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	-5676.83814102564
23	509239	505084.171474359	4154.82852564102
24	512238	505931.171474359	6306.82852564102
25	519164	518807.804131054	356.195868945878
26	517009	515997.970797721	1011.0292022792
27	509933	508652.970797721	1280.02920227921
28	509127	501357.970797721	7769.0292022792
29	500857	493447.273326211	7409.72667378918
30	506971	495123.273326211	11847.7266737892
31	569323	549356.606659544	19966.3933404558
32	579714	562026.273326211	17687.7266737892
33	577992	561129.606659544	16862.3933404558
34	565464	548344.773326211	17119.2266737892
35	547344	529167.106659544	18176.8933404558
36	554788	530014.106659544	24773.8933404558
37	562325	542890.739316239	19434.2606837607
38	560854	540080.905982906	20773.094017094
39	555332	532735.905982906	22596.0940170940
40	543599	525440.905982906	18158.094017094
41	536662	529406.393340456	7255.60665954417
42	542722	531082.393340456	11639.6066595442
43	593530	585315.726673789	8214.27332621082
44	610763	597985.393340456	12777.6066595442
45	612613	597088.726673789	15524.2733262108
46	611324	584303.893340456	27020.1066595442
47	594167	565126.226673789	29040.7733262108
48	595454	565973.226673789	29480.7733262108
49	590865	578849.859330484	12015.1406695157
50	589379	576040.025997151	13338.974002849
51	584428	568695.025997151	15732.974002849
52	573100	561400.025997151	11699.974002849
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	6194.83814102564
60	597141	590056.161858974	7084.83814102564
61	593408	602932.794515669	-9524.7945156695
62	590072	600122.961182336	-10050.9611823362
63	579799	592777.961182336	-12978.9611823362
64	574205	585482.961182336	-11277.9611823362
65	572775	577572.263710826	-4797.2637108262
66	572942	579248.263710826	-6306.26371082622
67	619567	633481.59704416	-13914.5970441596
68	625809	646151.263710826	-20342.2637108262
69	619916	645254.59704416	-25338.5970441595
70	587625	632469.763710826	-44844.7637108262
71	565742	613292.09704416	-47550.0970441595
72	557274	614139.097044160	-56865.0970441595

Charts produced by software:

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Parameters:

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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