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Ouput 2: Zonder trend en met seizoensinvloeden

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 02:37:54 -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/21/t1195637449e8u3wblxp85bu85.htm/, Retrieved Wed, 21 Nov 2007 10:30:59 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,2286 1 1,1702 1 1,1692 1 1,1222 1 1,1139 1 1,1372 1 1,1663 1 1,1582 1 1,0848 1 1,0807 1 1,0773 1 1,0622 1 1,0183 1 1,0014 1 0,9811 1 0,9808 1 0,9778 1 0,9922 1 0,9554 1 0,9170 1 0,8858 1 0,8758 1 0,8700 1 0,8833 1 0,8924 1 0,8883 1 0,9059 1 0,9111 1 0,9005 0 0,8607 0 0,8532 0 0,8742 0 0,8920 0 0,9095 0 0,9217 0 0,9383 0 0,8973 0 0,8564 0 0,8552 0 0,8721 0 0,9041 0 0,9397 0 0,9492 0 0,9060 0 0,9470 0 0,9643 0 0,9834 0 1,0137 0 1,0110 0 1,0338 0 1,0706 0 1,0501 0 1,0604 0 1,0353 0 1,0378 0 1,0628 0 1,0704 0 1,0883 0 1,1208 0 1,1608 0

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

dollarkoers[t] = + 0.992076666666667 + 0.0489583333333333dummy[t] -0.011931666666667M1[t] -0.0314316666666667M2[t] -0.0250516666666668M3[t] -0.0341916666666667M4[t] -0.0203200000000001M5[t] -0.0186400000000001M6[t] -0.0192800000000001M7[t] -0.0280200000000001M8[t] -0.0356600000000001M9[t] -0.0279400000000001M10[t] -0.0170200000000001M11[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)	0.992076666666667	0.050398	19.6848	0	0
dummy	0.0489583333333333	0.028905	1.6937	0.096932	0.048466
M1	-0.011931666666667	0.069613	-0.1714	0.864646	0.432323
M2	-0.0314316666666667	0.069613	-0.4515	0.653693	0.326846
M3	-0.0250516666666668	0.069613	-0.3599	0.720557	0.360279
M4	-0.0341916666666667	0.069613	-0.4912	0.625595	0.312798
M5	-0.0203200000000001	0.069373	-0.2929	0.77088	0.38544
M6	-0.0186400000000001	0.069373	-0.2687	0.789342	0.394671
M7	-0.0192800000000001	0.069373	-0.2779	0.782294	0.391147
M8	-0.0280200000000001	0.069373	-0.4039	0.688115	0.344057
M9	-0.0356600000000001	0.069373	-0.514	0.609637	0.304818
M10	-0.0279400000000001	0.069373	-0.4028	0.688957	0.344479
M11	-0.0170200000000001	0.069373	-0.2453	0.807261	0.40363

Multiple Linear Regression - Regression Statistics
Multiple R	0.257668500891859
R-squared	0.0663930563518578
Adjusted R-squared	-0.171974673941285
F-TEST (value)	0.278532065855593
F-TEST (DF numerator)	12
F-TEST (DF denominator)	47
p-value	0.99009948052604
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.109688079512926
Sum Squared Residuals	0.565479315

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.2286	1.02910333333333	0.199496666666666
2	1.1702	1.00960333333333	0.160596666666667
3	1.1692	1.01598333333333	0.153216666666667
4	1.1222	1.00684333333333	0.115356666666667
5	1.1139	1.020715	0.093185
6	1.1372	1.022395	0.114805
7	1.1663	1.021755	0.144545
8	1.1582	1.013015	0.145185
9	1.0848	1.005375	0.079425
10	1.0807	1.013095	0.067605
11	1.0773	1.024015	0.053285
12	1.0622	1.041035	0.0211650000000000
13	1.0183	1.02910333333333	-0.0108033333333331
14	1.0014	1.00960333333333	-0.00820333333333332
15	0.9811	1.01598333333333	-0.0348833333333333
16	0.9808	1.00684333333333	-0.0260433333333334
17	0.9778	1.020715	-0.042915
18	0.9922	1.022395	-0.0301950000000001
19	0.9554	1.021755	-0.0663549999999999
20	0.917	1.013015	-0.096015
21	0.8858	1.005375	-0.119575
22	0.8758	1.013095	-0.137295
23	0.87	1.024015	-0.154015
24	0.8833	1.041035	-0.157735
25	0.8924	1.02910333333333	-0.136703333333333
26	0.8883	1.00960333333333	-0.121303333333333
27	0.9059	1.01598333333333	-0.110083333333333
28	0.9111	1.00684333333333	-0.0957433333333334
29	0.9005	0.971756666666667	-0.0712566666666667
30	0.8607	0.973436666666667	-0.112736666666667
31	0.8532	0.972796666666667	-0.119596666666667
32	0.8742	0.964056666666667	-0.0898566666666667
33	0.892	0.956416666666667	-0.0644166666666666
34	0.9095	0.964136666666667	-0.0546366666666667
35	0.9217	0.975056666666667	-0.0533566666666667
36	0.9383	0.992076666666667	-0.0537766666666667
37	0.8973	0.980145	-0.0828449999999997
38	0.8564	0.960645	-0.104245
39	0.8552	0.967025	-0.111825
40	0.8721	0.957885	-0.085785
41	0.9041	0.971756666666667	-0.0676566666666666
42	0.9397	0.973436666666667	-0.0337366666666667
43	0.9492	0.972796666666667	-0.0235966666666666
44	0.906	0.964056666666667	-0.0580566666666666
45	0.947	0.956416666666667	-0.00941666666666668
46	0.9643	0.964136666666667	0.000163333333333397
47	0.9834	0.975056666666667	0.00834333333333342
48	1.0137	0.992076666666667	0.0216233333333333
49	1.011	0.980145	0.0308550000000001
50	1.0338	0.960645	0.073155
51	1.0706	0.967025	0.103575
52	1.0501	0.957885	0.092215
53	1.0604	0.971756666666667	0.0886433333333334
54	1.0353	0.973436666666667	0.0618633333333334
55	1.0378	0.972796666666667	0.0650033333333334
56	1.0628	0.964056666666667	0.0987433333333333
57	1.0704	0.956416666666667	0.113983333333333
58	1.0883	0.964136666666667	0.124163333333333
59	1.1208	0.975056666666667	0.145743333333333
60	1.1608	0.992076666666667	0.168723333333333

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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

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