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Ouput 3: met 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 02:43:11 -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/t1195637758ugboyl7lmp7400g.htm/, Retrieved Wed, 21 Nov 2007 10:36:08 +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] = + 0.995463333333333 + 0.0468416666666669dummy[t] -0.0122844444444447M1[t] -0.0317138888888889M2[t] -0.0252633333333334M3[t] -0.0343327777777778M4[t] -0.0208138888888889M5[t] -0.0190633333333333M6[t] -0.0196327777777778M7[t] -0.0283022222222223M8[t] -0.0358716666666668M9[t] -0.0280811111111112M10[t] -0.0170905555555557M11[t] -7.05555555555487e-05t + 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)	0.995463333333333	0.095662	10.4061	0	0
dummy	0.0468416666666669	0.058435	0.8016	0.426901	0.21345
M1	-0.0122844444444447	0.070868	-0.1733	0.863143	0.431572
M2	-0.0317138888888889	0.070687	-0.4487	0.65579	0.327895
M3	-0.0252633333333334	0.070546	-0.3581	0.721899	0.36095
M4	-0.0343327777777778	0.070445	-0.4874	0.628313	0.314156
M5	-0.0208138888888889	0.071109	-0.2927	0.771064	0.385532
M6	-0.0190633333333333	0.070848	-0.2691	0.789077	0.394538
M7	-0.0196327777777778	0.070627	-0.278	0.782274	0.391137
M8	-0.0283022222222223	0.070445	-0.4018	0.68972	0.34486
M9	-0.0358716666666668	0.070304	-0.5102	0.612325	0.306162
M10	-0.0280811111111112	0.070203	-0.4	0.691007	0.345504
M11	-0.0170905555555557	0.070142	-0.2437	0.80858	0.40429
t	-7.05555555555487e-05	0.001687	-0.0418	0.966818	0.483409

Multiple Linear Regression - Regression Statistics
Multiple R	0.257737388983056
R-squared	0.0664285616798033
Adjusted R-squared	-0.197406844801991
F-TEST (value)	0.251780314725829
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.995250764916281
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.110871822749110
Sum Squared Residuals	0.565457809666666

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.2286	1.02995	0.198649999999999
2	1.1702	1.01045	0.15975
3	1.1692	1.01683	0.15237
4	1.1222	1.00769	0.114510000000000
5	1.1139	1.02113833333333	0.0927616666666666
6	1.1372	1.02281833333333	0.114381666666667
7	1.1663	1.02217833333333	0.144121666666667
8	1.1582	1.01343833333333	0.144761666666667
9	1.0848	1.00579833333333	0.0790016666666667
10	1.0807	1.01351833333333	0.0671816666666667
11	1.0773	1.02443833333333	0.0528616666666667
12	1.0622	1.04145833333333	0.0207416666666667
13	1.0183	1.02910333333333	-0.0108033333333331
14	1.0014	1.00960333333333	-0.0082033333333333
15	0.9811	1.01598333333333	-0.0348833333333333
16	0.9808	1.00684333333333	-0.0260433333333334
17	0.9778	1.02029166666667	-0.0424916666666667
18	0.9922	1.02197166666667	-0.0297716666666668
19	0.9554	1.02133166666667	-0.0659316666666666
20	0.917	1.01259166666667	-0.0955916666666666
21	0.8858	1.00495166666667	-0.119151666666667
22	0.8758	1.01267166666667	-0.136871666666667
23	0.87	1.02359166666667	-0.153591666666667
24	0.8833	1.04061166666667	-0.157311666666667
25	0.8924	1.02825666666667	-0.135856666666666
26	0.8883	1.00875666666667	-0.120456666666667
27	0.9059	1.01513666666667	-0.109236666666667
28	0.9111	1.00599666666667	-0.0948966666666668
29	0.9005	0.972603333333333	-0.0721033333333333
30	0.8607	0.974283333333333	-0.113583333333333
31	0.8532	0.973643333333333	-0.120443333333333
32	0.8742	0.964903333333333	-0.0907033333333333
33	0.892	0.957263333333333	-0.0652633333333333
34	0.9095	0.964983333333333	-0.0554833333333333
35	0.9217	0.975903333333333	-0.0542033333333333
36	0.9383	0.992923333333333	-0.0546233333333333
37	0.8973	0.980568333333333	-0.083268333333333
38	0.8564	0.961068333333333	-0.104668333333333
39	0.8552	0.967448333333333	-0.112248333333333
40	0.8721	0.958308333333333	-0.0862083333333334
41	0.9041	0.971756666666667	-0.0676566666666667
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	-0.00941666666666674
46	0.9643	0.964136666666667	0.000163333333333373
47	0.9834	0.975056666666667	0.0083433333333334
48	1.0137	0.992076666666667	0.0216233333333333
49	1.011	0.979721666666666	0.0312783333333334
50	1.0338	0.960221666666667	0.0735783333333332
51	1.0706	0.966601666666667	0.103998333333333
52	1.0501	0.957461666666667	0.0926383333333333
53	1.0604	0.97091	0.089490
54	1.0353	0.97259	0.06271
55	1.0378	0.97195	0.06585
56	1.0628	0.96321	0.09959
57	1.0704	0.95557	0.11483
58	1.0883	0.96329	0.12501
59	1.1208	0.97421	0.14659
60	1.1608	0.99123	0.16957

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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