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brood met trend met dummie 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 09:04:38 -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/t1197993802kh6ck8usdflehx5.htm/, Retrieved Tue, 18 Dec 2007 17:03:22 +0100

User-defined keywords:

Dataseries X:

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1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,5 1,43 0 0,51 1,43 0 0,51 1,43 0 0,5 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,51 1,43 0 0,52 1,43 0 0,52 1,44 0 0,52 1,48 0 0,53 1,48 0 0,53 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,52 1,48 0 0,53 1,48 0 0,53 1,48 0 0,53 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,54 1,48 0 0,53 1,48 0 0,53 1,48 0 0,53 1,48 0 0,53 1,48 0 0,53 1,57 0 0,54 1,58 0 0,55 1,58 0 0,55 1,58 0 0,55 1,58 0 0,55 1,59 1 0,55 1,6 1 0,55 1,6 1 0,55 1,61 1 0,55 1,61 1 0,56 1,61 1 0,56 1,62 1 0,56 1,63 1 0,56 1,63 1 0,56 1,64 1 0,55 1,64 1 0,56 1,64 1 0,55 1,64 1 0,55 1,64 1 0,56 1,65 1 0,55 1,65 1 0,55 1,65 1 0,55 1,65 1 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.01583420916727 + 0.074205333797495x1[t] + 0.782453795876532x2[t] + 0.00164324049146559t + 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)	1.01583420916727	0.19569	5.191	2e-06	1e-06
x1	0.074205333797495	0.008458	8.7732	0	0
x2	0.782453795876532	0.387913	2.0171	0.047637	0.023818
t	0.00164324049146559	0.000339	4.8501	8e-06	4e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.966096496623152
R-squared	0.933342440787529
Adjusted R-squared	0.93040166611639
F-TEST (value)	317.379787695945
F-TEST (DF numerator)	3
F-TEST (DF denominator)	68
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0204509693490157
Sum Squared Residuals	0.0284404660173777

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.41652888555577	0.0134711144442342
2	1.43	1.41817212604723	0.0118278739527655
3	1.43	1.4198153665387	0.0101846334613000
4	1.43	1.42145860703017	0.00854139296983443
5	1.43	1.42310184752163	0.00689815247836882
6	1.43	1.42474508801310	0.00525491198690322
7	1.43	1.42638832850456	0.00361167149543763
8	1.43	1.42803156899603	0.00196843100397204
9	1.43	1.42185027152873	0.00814972847127176
10	1.43	1.43131804997896	-0.00131804997895915
11	1.43	1.43296129047042	-0.00296129047042474
12	1.43	1.42677999300312	0.00322000699687498
13	1.43	1.43624777145336	-0.00624777145335593
14	1.43	1.43789101194482	-0.00789101194482152
15	1.43	1.43953425243629	-0.00953425243628712
16	1.43	1.44117749292775	-0.0111774929277527
17	1.43	1.45064527137798	-0.0206452713779836
18	1.43	1.45228851186945	-0.0222885118694492
19	1.44	1.45393175236091	-0.0139317523609148
20	1.48	1.46339953081115	0.0166004691888543
21	1.48	1.46504277130261	0.0149572286973887
22	1.48	1.45886147383531	0.0211385261646885
23	1.48	1.46050471432678	0.0194952856732229
24	1.48	1.46214795481824	0.0178520451817573
25	1.48	1.46379119530971	0.0162088046902917
26	1.48	1.46543443580117	0.0145655641988261
27	1.48	1.46707767629264	0.0129223237073605
28	1.48	1.46872091678411	0.0112790832158949
29	1.48	1.47036415727557	0.00963584272442931
30	1.48	1.47200739776704	0.00799260223296372
31	1.48	1.47365063825850	0.00634936174149813
32	1.48	1.48311841670873	-0.00311841670873279
33	1.48	1.48476165720020	-0.00476165720019838
34	1.48	1.48640489769166	-0.00640489769166398
35	1.48	1.49587267614189	-0.0158726761418949
36	1.48	1.49751591663336	-0.0175159166333605
37	1.48	1.49915915712483	-0.0191591571248261
38	1.48	1.50080239761629	-0.0208023976162917
39	1.48	1.50244563810776	-0.0224456381077573
40	1.48	1.50408887859922	-0.0240888785992229
41	1.48	1.50573211909069	-0.0257321190906884
42	1.48	1.50737535958215	-0.0273753595821540
43	1.48	1.50901860007362	-0.0290186000736196
44	1.48	1.51066184056509	-0.0306618405650852
45	1.48	1.50448054309779	-0.0244805430977855
46	1.48	1.50612378358925	-0.0261237835892511
47	1.48	1.50776702408072	-0.0277670240807167
48	1.48	1.50941026457218	-0.0294102645721823
49	1.48	1.51105350506365	-0.0310535050636479
50	1.57	1.52052128351388	0.0494787164861213
51	1.58	1.52998906196411	0.0500109380358904
52	1.58	1.53163230245558	0.0483676975444248
53	1.58	1.53327554294704	0.0467244570529592
54	1.58	1.53491878343851	0.0450812165614936
55	1.59	1.61076735772747	-0.0207673577274670
56	1.6	1.61241059821893	-0.0124105982189325
57	1.6	1.61405383871040	-0.0140538387103981
58	1.61	1.61569707920186	-0.00569707920186373
59	1.61	1.62516485765209	-0.0151648576520946
60	1.61	1.62680809814356	-0.0168080981435602
61	1.62	1.62845133863503	-0.00845133863502581
62	1.63	1.63009457912649	-9.45791264916076e-05
63	1.63	1.63173781961796	-0.0017378196179572
64	1.64	1.62555652215066	0.0144434778493425
65	1.64	1.63502430060089	0.00497569939911162
66	1.64	1.62884300313359	0.0111569968664113
67	1.64	1.63048624362505	0.00951375637494576
68	1.64	1.63995402207529	4.59779247148431e-05
69	1.65	1.63377272460799	0.0162272753920146
70	1.65	1.63541596509945	0.0145840349005490
71	1.65	1.63705920559092	0.0129407944090834
72	1.65	1.63870244608238	0.0112975539176178

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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

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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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