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Workshop 3 Q3 uitvoer dummy

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 05:04:30 -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/22/t1195732656h4fbp2oatr9zs1o.htm/, Retrieved Thu, 22 Nov 2007 12:57:46 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0,9808 0 0,9811 0 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 1 1,2613 1 1,2646 1 1,2262 1 1,1985 0 1,2007 0 1,2138 1 1,2266 1 1,2176 1 1,2218 1 1,2490 1 1,2991 1 1,3408 1 1,3119 1 1,3014 1 1,3201 1 1,2938 1 1,2694 1 1,2165 1 1,2037 1 1,2292 1 1,2256 1 1,2015 1 1,1786 0 1,1856 0 1,2103 1 1,1938 0 1,2020 0 1,2271 1 1,2770 1 1,2650 1 1,2684 1 1,2811 1 1,2727 1 1,2611 1 1,2881 1 1,3213 1 1,2999 1 1,3074 1 1,3242 1 1,3516 1 1,3511 1 1,3419 1 1,3716 1 1,3622 1 1,3896 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.11823809523810 + 0.159114404761905x[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)	1.11823809523810	0.013241	84.4521	0	0
x	0.159114404761905	0.016352	9.7309	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.784926126611354
R-squared	0.616109024237103
Adjusted R-squared	0.609602397529258
F-TEST (value)	94.6894684298083
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	7.07212066686225e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0606782971943308
Sum Squared Residuals	0.217229489273809

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	0.9808	1.11823809523809	-0.137438095238092
2	0.9811	1.11823809523810	-0.137138095238096
3	1.0014	1.11823809523810	-0.116838095238095
4	1.0183	1.11823809523810	-0.0999380952380954
5	1.0622	1.11823809523810	-0.0560380952380954
6	1.0773	1.11823809523810	-0.0409380952380955
7	1.0807	1.11823809523810	-0.0375380952380954
8	1.0848	1.11823809523810	-0.0334380952380954
9	1.1582	1.11823809523810	0.0399619047619045
10	1.1663	1.11823809523810	0.0480619047619045
11	1.1372	1.11823809523810	0.0189619047619046
12	1.1139	1.11823809523810	-0.00433809523809552
13	1.1222	1.11823809523810	0.00396190476190468
14	1.1692	1.11823809523810	0.0509619047619046
15	1.1702	1.11823809523810	0.0519619047619045
16	1.2286	1.2773525	-0.0487525000000001
17	1.2613	1.2773525	-0.0160524999999999
18	1.2646	1.2773525	-0.0127525000000000
19	1.2262	1.2773525	-0.0511525
20	1.1985	1.11823809523810	0.0802619047619045
21	1.2007	1.11823809523810	0.0824619047619047
22	1.2138	1.2773525	-0.0635525
23	1.2266	1.2773525	-0.0507525000000001
24	1.2176	1.2773525	-0.0597525
25	1.2218	1.2773525	-0.0555525
26	1.249	1.2773525	-0.0283524999999999
27	1.2991	1.2773525	0.0217474999999999
28	1.3408	1.2773525	0.0634475
29	1.3119	1.2773525	0.0345475000000001
30	1.3014	1.2773525	0.0240474999999999
31	1.3201	1.2773525	0.0427475000000001
32	1.2938	1.2773525	0.0164475000000001
33	1.2694	1.2773525	-0.0079524999999999
34	1.2165	1.2773525	-0.0608525
35	1.2037	1.2773525	-0.0736525
36	1.2292	1.2773525	-0.0481524999999999
37	1.2256	1.2773525	-0.0517525
38	1.2015	1.2773525	-0.0758525
39	1.1786	1.11823809523810	0.0603619047619047
40	1.1856	1.11823809523810	0.0673619047619046
41	1.2103	1.2773525	-0.0670525
42	1.1938	1.11823809523810	0.0755619047619046
43	1.202	1.11823809523810	0.0837619047619046
44	1.2271	1.2773525	-0.0502524999999999
45	1.277	1.2773525	-0.000352500000000066
46	1.265	1.2773525	-0.0123525000000001
47	1.2684	1.2773525	-0.0089525
48	1.2811	1.2773525	0.00374749999999993
49	1.2727	1.2773525	-0.00465250000000004
50	1.2611	1.2773525	-0.0162524999999999
51	1.2881	1.2773525	0.0107475000000000
52	1.3213	1.2773525	0.0439474999999999
53	1.2999	1.2773525	0.0225475000000001
54	1.3074	1.2773525	0.0300474999999999
55	1.3242	1.2773525	0.0468475000000001
56	1.3516	1.2773525	0.0742475
57	1.3511	1.2773525	0.0737475
58	1.3419	1.2773525	0.0645475000000001
59	1.3716	1.2773525	0.0942475
60	1.3622	1.2773525	0.0848475000000001
61	1.3896	1.2773525	0.1122475

Charts produced by software:

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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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