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

Title produced by software: Multiple Regression

Date of computation: Wed, 12 Dec 2007 12:02:10 -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/12/t1197485305sr69zw8ml5v2gc4.htm/, Retrieved Wed, 12 Dec 2007 19:48:26 +0100

User-defined keywords:

s0650062

Dataseries X:

» Textbox « » Textfile « » CSV «

1,3 0 1,2 0 1,6 0 1,7 0 1,5 0 0,9 0 1,5 0 1,4 0 1,6 0 1,7 0 1,4 0 1,8 0 1,7 0 1,4 0 1,2 0 1,0 0 1,7 0 2,4 0 2,0 0 2,1 0 2,0 0 1,8 0 2,7 0 2,3 0 1,9 0 2,0 0 2,3 0 2,8 0 2,4 0 2,3 0 2,7 0 2,7 0 2,9 0 3,0 1 2,2 0 2,3 0 2,8 0 2,8 0 2,8 0 2,2 0 2,6 0 2,8 0 2,5 0 2,4 0 2,3 0 1,9 0 1,7 0 2,0 0 2,1 0 1,7 0 1,8 0 1,8 0 1,8 0 1,3 0 1,3 0 1,3 0 1,2 0 1,4 0 2,2 0 2,9 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	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.96610169491525 + 1.03389830508475x[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)	1.96610169491525	0.070508	27.8847	0	0
x	1.03389830508475	0.546155	1.893	0.063344	0.031672

Multiple Linear Regression - Regression Statistics
Multiple R	0.241228855223658
R-squared	0.0581913605925166
Adjusted R-squared	0.0419532806027325
F-TEST (value)	3.58363554244876
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0.063344176187855
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.541584574696143
Sum Squared Residuals	17.0122033898305

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.3	1.96610169491526	-0.666101694915256
2	1.2	1.96610169491525	-0.766101694915254
3	1.6	1.96610169491525	-0.366101694915254
4	1.7	1.96610169491525	-0.266101694915254
5	1.5	1.96610169491525	-0.466101694915254
6	0.9	1.96610169491525	-1.06610169491525
7	1.5	1.96610169491525	-0.466101694915254
8	1.4	1.96610169491525	-0.566101694915254
9	1.6	1.96610169491525	-0.366101694915254
10	1.7	1.96610169491525	-0.266101694915254
11	1.4	1.96610169491525	-0.566101694915254
12	1.8	1.96610169491525	-0.166101694915254
13	1.7	1.96610169491525	-0.266101694915254
14	1.4	1.96610169491525	-0.566101694915254
15	1.2	1.96610169491525	-0.766101694915254
16	1	1.96610169491525	-0.966101694915254
17	1.7	1.96610169491525	-0.266101694915254
18	2.4	1.96610169491525	0.433898305084746
19	2	1.96610169491525	0.0338983050847458
20	2.1	1.96610169491525	0.133898305084746
21	2	1.96610169491525	0.0338983050847458
22	1.8	1.96610169491525	-0.166101694915254
23	2.7	1.96610169491525	0.733898305084746
24	2.3	1.96610169491525	0.333898305084746
25	1.9	1.96610169491525	-0.0661016949152543
26	2	1.96610169491525	0.0338983050847458
27	2.3	1.96610169491525	0.333898305084746
28	2.8	1.96610169491525	0.833898305084746
29	2.4	1.96610169491525	0.433898305084746
30	2.3	1.96610169491525	0.333898305084746
31	2.7	1.96610169491525	0.733898305084746
32	2.7	1.96610169491525	0.733898305084746
33	2.9	1.96610169491525	0.933898305084746
34	3	3	-3.01475966586751e-17
35	2.2	1.96610169491525	0.233898305084746
36	2.3	1.96610169491525	0.333898305084746
37	2.8	1.96610169491525	0.833898305084746
38	2.8	1.96610169491525	0.833898305084746
39	2.8	1.96610169491525	0.833898305084746
40	2.2	1.96610169491525	0.233898305084746
41	2.6	1.96610169491525	0.633898305084746
42	2.8	1.96610169491525	0.833898305084746
43	2.5	1.96610169491525	0.533898305084746
44	2.4	1.96610169491525	0.433898305084746
45	2.3	1.96610169491525	0.333898305084746
46	1.9	1.96610169491525	-0.0661016949152543
47	1.7	1.96610169491525	-0.266101694915254
48	2	1.96610169491525	0.0338983050847458
49	2.1	1.96610169491525	0.133898305084746
50	1.7	1.96610169491525	-0.266101694915254
51	1.8	1.96610169491525	-0.166101694915254
52	1.8	1.96610169491525	-0.166101694915254
53	1.8	1.96610169491525	-0.166101694915254
54	1.3	1.96610169491525	-0.666101694915254
55	1.3	1.96610169491525	-0.666101694915254
56	1.3	1.96610169491525	-0.666101694915254
57	1.2	1.96610169491525	-0.766101694915254
58	1.4	1.96610169491525	-0.566101694915254
59	2.2	1.96610169491525	0.233898305084746
60	2.9	1.96610169491525	0.933898305084746

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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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