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wisselkoers paper

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

Title produced by software: Multiple Regression

Date of computation: Thu, 13 Dec 2007 02:48:46 -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/13/t1197538437yhhl5mrkxfrq8m3.htm/, Retrieved Thu, 13 Dec 2007 10:33:57 +0100

User-defined keywords:

s0650062

Dataseries X:

» Textbox « » Textfile « » CSV «

1,0014 0 1,0183 0 1,0622 0 1,0773 0 1,0807 0 1,0848 0 1,1582 0 1,1663 0 1,1372 0 1,1139 0 1,1222 0 1,1692 0 1,1702 0 1,2286 0 1,2613 0 1,2646 0 1,2262 0 1,1985 0 1,2007 0 1,2138 0 1,2266 0 1,2176 0 1,2218 0 1,249 0 1,2991 0 1,3408 0 1,3119 0 1,3014 0 1,3201 0 1,2938 0 1,2694 0 1,2165 0 1,2037 0 1,2292 0 1,2256 0 1,2015 0 1,1786 0 1,1856 0 1,2103 0 1,1938 0 1,202 0 1,2271 0 1,277 0 1,265 0 1,2684 0 1,2811 0 1,2727 0 1,2611 0 1,2881 0 1,3213 0 1,2999 0 1,3074 1 1,3242 1 1,3516 1 1,3511 1 1,3419 1 1,3716 1 1,3622 1 1,3896 1 1,4227 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.21207058823529 + 0.145962745098039x[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)	1.21207058823529	0.010375	116.8301	0	0
x	0.145962745098039	0.026787	5.449	1e-06	1e-06

Multiple Linear Regression - Regression Statistics
Multiple R	0.581883831454452
R-squared	0.338588793308113
Adjusted R-squared	0.327185151813426
F-TEST (value)	29.6912870740318
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	1.08148881550196e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0740897668352098
Sum Squared Residuals	0.318379025882354

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.0014	1.21207058823530	-0.210670588235296
2	1.0183	1.21207058823529	-0.193770588235294
3	1.0622	1.21207058823529	-0.149870588235294
4	1.0773	1.21207058823529	-0.134770588235294
5	1.0807	1.21207058823529	-0.131370588235294
6	1.0848	1.21207058823529	-0.127270588235294
7	1.1582	1.21207058823529	-0.0538705882352942
8	1.1663	1.21207058823529	-0.0457705882352942
9	1.1372	1.21207058823529	-0.0748705882352941
10	1.1139	1.21207058823529	-0.0981705882352942
11	1.1222	1.21207058823529	-0.089870588235294
12	1.1692	1.21207058823529	-0.0428705882352941
13	1.1702	1.21207058823529	-0.0418705882352942
14	1.2286	1.21207058823529	0.0165294117647059
15	1.2613	1.21207058823529	0.049229411764706
16	1.2646	1.21207058823529	0.0525294117647059
17	1.2262	1.21207058823529	0.0141294117647059
18	1.1985	1.21207058823529	-0.0135705882352942
19	1.2007	1.21207058823529	-0.0113705882352940
20	1.2138	1.21207058823529	0.00172941176470592
21	1.2266	1.21207058823529	0.0145294117647058
22	1.2176	1.21207058823529	0.00552941176470595
23	1.2218	1.21207058823529	0.00972941176470593
24	1.249	1.21207058823529	0.0369294117647060
25	1.2991	1.21207058823529	0.0870294117647059
26	1.3408	1.21207058823529	0.128729411764706
27	1.3119	1.21207058823529	0.099829411764706
28	1.3014	1.21207058823529	0.0893294117647058
29	1.3201	1.21207058823529	0.108029411764706
30	1.2938	1.21207058823529	0.081729411764706
31	1.2694	1.21207058823529	0.057329411764706
32	1.2165	1.21207058823529	0.00442941176470585
33	1.2037	1.21207058823529	-0.00837058823529408
34	1.2292	1.21207058823529	0.017129411764706
35	1.2256	1.21207058823529	0.0135294117647060
36	1.2015	1.21207058823529	-0.0105705882352941
37	1.1786	1.21207058823529	-0.033470588235294
38	1.1856	1.21207058823529	-0.0264705882352941
39	1.2103	1.21207058823529	-0.00177058823529414
40	1.1938	1.21207058823529	-0.0182705882352941
41	1.202	1.21207058823529	-0.0100705882352941
42	1.2271	1.21207058823529	0.015029411764706
43	1.277	1.21207058823529	0.0649294117647058
44	1.265	1.21207058823529	0.0529294117647058
45	1.2684	1.21207058823529	0.0563294117647059
46	1.2811	1.21207058823529	0.0690294117647058
47	1.2727	1.21207058823529	0.0606294117647059
48	1.2611	1.21207058823529	0.049029411764706
49	1.2881	1.21207058823529	0.076029411764706
50	1.3213	1.21207058823529	0.109229411764706
51	1.2999	1.21207058823529	0.087829411764706
52	1.3074	1.35803333333333	-0.0506333333333334
53	1.3242	1.35803333333333	-0.0338333333333333
54	1.3516	1.35803333333333	-0.00643333333333342
55	1.3511	1.35803333333333	-0.00693333333333337
56	1.3419	1.35803333333333	-0.0161333333333332
57	1.3716	1.35803333333333	0.0135666666666666
58	1.3622	1.35803333333333	0.00416666666666674
59	1.3896	1.35803333333333	0.0315666666666666
60	1.4227	1.35803333333333	0.0646666666666667

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal 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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