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brood met vier dummies, trend en bakmeel

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

Title produced by software: Multiple Regression

Date of computation: Tue, 18 Dec 2007 09:47:50 -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/Dec/18/t1197995456h4owqevtfip9w7p.htm/, Retrieved Tue, 18 Dec 2007 17:31:07 +0100

User-defined keywords:

Dataseries X:

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1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,5 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,5 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,51 1,43 0 0 0 0 0,52 1,43 0 0 0 0 0,52 1,44 0 0 0 0 0,52 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,52 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,54 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,48 1 0 0 0 0,53 1,57 1 1 0 0 0,54 1,58 1 1 0 0 0,55 1,58 1 1 0 0 0,55 1,58 1 1 0 0 0,55 1,58 1 1 0 0 0,55 1,59 1 1 0 0 0,55 1,6 1 1 1 1 0,55 1,6 1 1 1 2 0,55 1,61 1 1 1 3 0,55 1,61 1 1 1 4 0,56 1,61 1 1 1 5 0,56 1,62 1 1 1 6 0,56 1,63 1 1 1 7 0,56 1,63 1 1 1 8 0,56 1,64 1 1 1 9 0,55 1,64 1 1 1 10 0,56 1,64 1 1 1 11 0,55 1,64 1 1 1 12 0,55 1,64 1 1 1 13 0,56 1,65 1 1 1 14 0,55 1,65 1 1 1 15 0,55 1,65 1 1 1 16 0,55 1,65 1 1 1 17 0,55

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.39151998080862 + 0.0478035703125428x1[t] + 0.09846595983763x2[t] + 0.0184894550635091x3[t] + 0.00344250663472741x4[t] + 0.0762561542764317x5[t] + 7.5561481834617e-06t + 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)	1.39151998080862	0.035335	39.3812	0	0
x1	0.0478035703125428	0.001804	26.4999	0	0
x2	0.09846595983763	0.001897	51.9142	0	0
x3	0.0184894550635091	0.002149	8.6037	0	0
x4	0.00344250663472741	0.000179	19.2291	0	0
x5	0.0762561542764317	0.069938	1.0903	0.279592	0.139796
t	7.5561481834617e-06	7.2e-05	0.1056	0.916194	0.458097

Multiple Linear Regression - Regression Statistics
Multiple R	0.999212635065156
R-squared	0.998425890073853
Adjusted R-squared	0.998280587619131
F-TEST (value)	6871.36285473646
F-TEST (DF numerator)	6
F-TEST (DF denominator)	65
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.00321443391090483
Sum Squared Residuals	0.000671618048892368

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.43041817563778	-0.00041817563777877
2	1.43	1.43042573178597	-0.000425731785965638
3	1.43	1.43043328793415	-0.000433287934149580
4	1.43	1.43044084408233	-0.000440844082332907
5	1.43	1.43044840023052	-0.000448400230516382
6	1.43	1.4304559563787	-0.000455956378699815
7	1.43	1.43046351252688	-0.000463512526883277
8	1.43	1.43047106867507	-0.000471068675066738
9	1.43	1.42971606328049	0.000283936719514118
10	1.43	1.43048618097143	-0.000486180971433661
11	1.43	1.43049373711962	-0.000493737119617123
12	1.43	1.42973873172504	0.000261268274963733
13	1.43	1.43050884941598	-0.000508849415984046
14	1.43	1.43051640556417	-0.000516405564167508
15	1.43	1.43052396171235	-0.000523961712350969
16	1.43	1.43053151786053	-0.000531517860534431
17	1.43	1.43130163555148	-0.00130163555148221
18	1.43	1.43130919169967	-0.00130919169966567
19	1.44	1.43131674784785	0.00868325215215088
20	1.48	1.47989043585134	0.000109564148660195
21	1.48	1.47989799199952	0.000102008000476733
22	1.48	1.47914298660494	0.000857013395057588
23	1.48	1.47915054275313	0.000849457246874127
24	1.48	1.47915809890131	0.000841901098690665
25	1.48	1.47916565504949	0.000834344950507203
26	1.48	1.47917321119768	0.000826788802323742
27	1.48	1.47918076734586	0.00081923265414028
28	1.48	1.47918832349404	0.000811676505956818
29	1.48	1.47919587964223	0.000804120357773356
30	1.48	1.47920343579041	0.000796564209589895
31	1.48	1.47921099193859	0.000789008061406433
32	1.48	1.47998110962954	1.88903704586545e-05
33	1.48	1.47998866577772	1.13342222751928e-05
34	1.48	1.47999622192591	3.77807409173111e-06
35	1.48	1.48076633961686	-0.000766339616856048
36	1.48	1.48077389576504	-0.00077389576503951
37	1.48	1.48078145191322	-0.000781451913222971
38	1.48	1.48078900806141	-0.000789008061406433
39	1.48	1.48079656420959	-0.000796564209589895
40	1.48	1.48080412035777	-0.000804120357773356
41	1.48	1.48081167650596	-0.000811676505956818
42	1.48	1.48081923265414	-0.00081923265414028
43	1.48	1.48082678880232	-0.000826788802323741
44	1.48	1.48083434495051	-0.000834344950507203
45	1.48	1.48007933955593	-7.93395559263474e-05
46	1.48	1.48008689570411	-8.68957041098091e-05
47	1.48	1.48009445185229	-9.44518522932708e-05
48	1.48	1.48010200800048	-0.000102008000476732
49	1.48	1.48010956414866	-0.000109564148660194
50	1.57	1.57934564167724	-0.00934564167723776
51	1.58	1.58011575936819	-0.000115759368185527
52	1.58	1.58012331551637	-0.000123315516368989
53	1.58	1.58013087166455	-0.000130871664552451
54	1.58	1.58013842781274	-0.000138427812735912
55	1.59	1.58014598396092	0.00985401603908064
56	1.6	1.60208550180734	-0.00208550180733934
57	1.6	1.60553556459025	-0.00553556459025022
58	1.61	1.60898562737316	0.00101437262683892
59	1.61	1.61319825169884	-0.00319825169883627
60	1.61	1.61664831448175	-0.00664831448174715
61	1.62	1.62009837726466	-9.83772646580127e-05
62	1.63	1.62354844004757	0.0064515599524309
63	1.63	1.62699850283048	0.00300149716952003
64	1.64	1.62968600407063	0.0103139959293735
65	1.64	1.6338986283963	0.00610137160369828
66	1.64	1.63658612963645	0.00341387036355172
67	1.64	1.64003619241936	-3.61924193591546e-05
68	1.64	1.64424881674503	-0.00424881674503435
69	1.65	1.64693631798518	0.00306368201481911
70	1.65	1.65038638076809	-0.000386380768091772
71	1.65	1.65383644355100	-0.00383644355100264
72	1.65	1.65728650633391	-0.00728650633391352

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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.

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