Home » date » 2007 » Nov » 18 » attachments

export België gerelateerd aan inflatie

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 08:14:24 -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/18/t1195398587tue0fq7ow5axcdk.htm/, Retrieved Sun, 18 Nov 2007 16:09:47 +0100

User-defined keywords:

export, België, inflatie

Dataseries X:

» Textbox « » Textfile « » CSV «

12103 1 12989 1 11610 1 10206 1 11356 1 11307 1 12649 1 11947 1 11714 0 12193 1 11269 1 9097 1 12640 1 13040 1 11687 1 11192 1 11392 1 11793 1 13933 1 12778 1 11810 2 13698 2 11957 2 10724 2 13939 1 13980 2 13807 2 12974 1 12510 2 12934 2 14908 2 13772 2 13013 2 14050 2 11817 2 11593 2 14466 2 13616 2 14734 2 13881 2 13528 2 13584 2 16170 2 13261 2 14742 2 15487 2 13155 2 12621 2 15032 1 15452 1 15428 2 13106 2 14717 1 14180 1 16202 1 15036 1 15915 1 16468 1 14730 1 13705 1

Text written by user:

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	7 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 9033.29419953596 -101.495359628771x[t] + 2865.40413766434M1[t] + 2990.73936581593M2[t] + 2574.47459396752M3[t] + 1298.41167826759M4[t] + 1652.84783449343M5[t] + 1637.48399071926M6[t] + 3575.92014694509M7[t] + 2087.95630317092M8[t] + 2093.59245939675M9[t] + 2979.92768754834M10[t] + 1111.96384377417M11[t] + 74.3638437741686t + 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)	9033.29419953596	311.834726	28.9682	0	0
x	-101.495359628771	132.805895	-0.7642	0.448628	0.224314
M1	2865.40413766434	323.489321	8.8578	0	0
M2	2990.73936581593	320.950123	9.3184	0	0
M3	2574.47459396752	320.435791	8.0343	0	0
M4	1298.41167826759	320.247166	4.0544	0.000192	9.6e-05
M5	1652.84783449343	319.971676	5.1656	5e-06	3e-06
M6	1637.48399071926	319.747027	5.1212	6e-06	3e-06
M7	3575.92014694509	319.573326	11.1897	0	0
M8	2087.95630317092	319.450657	6.5361	0	0
M9	2093.59245939675	319.379079	6.5552	0	0
M10	2979.92768754834	318.467604	9.3571	0	0
M11	1111.96384377417	318.390675	3.4925	0.001069	0.000534
t	74.3638437741686	4.041155	18.4016	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.960293179246709
R-squared	0.922162990107751
Adjusted R-squared	0.900165574268637
F-TEST (value)	41.9214237186917
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	503.379307808244
Sum Squared Residuals	11655973.4663573

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12103	11871.5668213457	231.433178654281
2	12989	12071.2658932715	917.734106728538
3	11610	11729.3649651972	-119.364965197215
4	10206	10527.6658932715	-321.665893271461
5	11356	10956.4658932715	399.534106728539
6	11307	11015.4658932715	291.534106728539
7	12649	13028.2658932715	-379.265893271461
8	11947	11614.6658932715	332.334106728538
9	11714	11796.1612529002	-82.1612529002318
10	12193	12655.3649651972	-462.364965197215
11	11269	10861.7649651972	407.235034802785
12	9097	9824.16496519721	-727.164965197215
13	12640	12763.9329466357	-123.932946635728
14	13040	12963.6320185615	76.3679814385146
15	11687	12621.7310904872	-934.731090487239
16	11192	11420.0320185615	-228.032018561485
17	11392	11848.8320185615	-456.832018561485
18	11793	11907.8320185615	-114.832018561485
19	13933	13920.6320185615	12.3679814385150
20	12778	12507.0320185615	270.967981438515
21	11810	12485.5366589327	-675.536658932714
22	13698	13446.2357308585	251.764269141531
23	11957	11652.6357308585	304.364269141531
24	10724	10615.0357308585	108.964269141531
25	13939	13656.2990719258	282.700928074249
26	13980	13754.5027842227	225.497215777263
27	13807	13412.6018561485	394.398143851508
28	12974	12312.3981438515	661.601856148492
29	12510	12639.7027842227	-129.702784222738
30	12934	12698.7027842227	235.297215777263
31	14908	14711.5027842227	196.497215777262
32	13772	13297.9027842227	474.097215777262
33	13013	13377.9027842227	-364.902784222738
34	14050	14338.6018561485	-288.601856148492
35	11817	12545.0018561485	-728.001856148492
36	11593	11507.4018561485	85.5981438515079
37	14466	14447.169837587	18.8301624129955
38	13616	14646.8689095128	-1030.86890951276
39	14734	14304.9679814385	429.032018561485
40	13881	13103.2689095128	777.731090487239
41	13528	13532.0689095128	-4.06890951276136
42	13584	13591.0689095128	-7.0689095127609
43	16170	15603.8689095128	566.131090487239
44	13261	14190.2689095128	-929.26890951276
45	14742	14270.2689095128	471.731090487239
46	15487	15230.9679814385	256.032018561484
47	13155	13437.3679814385	-282.367981438516
48	12621	12399.7679814385	221.232018561485
49	15032	15441.0313225058	-409.031322505798
50	15452	15640.7303944316	-188.730394431555
51	15428	15197.3341067285	230.665893271461
52	13106	13995.6350348028	-889.635034802785
53	14717	14525.9303944316	191.069605568445
54	14180	14584.9303944316	-404.930394431556
55	16202	16597.7303944316	-395.730394431555
56	15036	15184.1303944316	-148.130394431555
57	15915	15264.1303944316	650.869605568446
58	16468	16224.8294663573	243.170533642691
59	14730	14431.2294663573	298.770533642691
60	13705	13393.6294663573	311.370533642690

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/1v3ro1195398853.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/1v3ro1195398853.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/2ev0o1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/2ev0o1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/39u2p1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/39u2p1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/4b3uu1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/4b3uu1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/5q1wm1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/5q1wm1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/6guzj1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/6guzj1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/7iwfc1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/7iwfc1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/8iwfl1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/8iwfl1195398854.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/9nkuw1195398854.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195398587tue0fq7ow5axcdk/9nkuw1195398854.ps (open in new window)

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

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