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*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 16 Dec 2009 11:39:45 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0.htm/, Retrieved Wed, 16 Dec 2009 19:40:31 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

19 0 18 0 19 0 19 0 22 0 23 0 20 0 14 0 14 0 14 0 15 0 11 0 17 0 16 0 20 0 24 0 23 0 20 0 21 0 19 0 23 0 23 0 23 0 23 0 27 0 26 0 17 0 24 0 26 0 24 0 27 0 27 0 26 0 24 0 23 0 23 0 24 1 17 1 21 1 19 1 22 1 22 1 18 1 16 1 14 1 12 1 14 1 16 1 8 1 3 1 0 1 5 1 1 1 1 1 3 1 6 1 7 1 8 1 14 1 14 1 13 1 15 1

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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

consumentenvertrouwen[t] = + 20.9444444444445 -8.9059829059829`financiële_crisis`[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)	20.9444444444445	0.938589	22.3148	0	0
`financiële_crisis`	-8.9059829059829	1.449388	-6.1447	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.621475316509173
R-squared	0.386231569030177
Adjusted R-squared	0.37600209518068
F-TEST (value)	37.7567384904324
F-TEST (DF numerator)	1
F-TEST (DF denominator)	60
p-value	7.03481710662146e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.63153387534638
Sum Squared Residuals	1902.85042735043

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	19	20.9444444444444	-1.94444444444437
2	18	20.9444444444445	-2.94444444444445
3	19	20.9444444444444	-1.94444444444445
4	19	20.9444444444444	-1.94444444444445
5	22	20.9444444444444	1.05555555555555
6	23	20.9444444444444	2.05555555555555
7	20	20.9444444444444	-0.944444444444446
8	14	20.9444444444444	-6.94444444444445
9	14	20.9444444444444	-6.94444444444445
10	14	20.9444444444444	-6.94444444444445
11	15	20.9444444444444	-5.94444444444445
12	11	20.9444444444444	-9.94444444444445
13	17	20.9444444444444	-3.94444444444445
14	16	20.9444444444444	-4.94444444444445
15	20	20.9444444444444	-0.944444444444446
16	24	20.9444444444444	3.05555555555555
17	23	20.9444444444444	2.05555555555555
18	20	20.9444444444444	-0.944444444444446
19	21	20.9444444444444	0.0555555555555537
20	19	20.9444444444444	-1.94444444444445
21	23	20.9444444444444	2.05555555555555
22	23	20.9444444444444	2.05555555555555
23	23	20.9444444444444	2.05555555555555
24	23	20.9444444444444	2.05555555555555
25	27	20.9444444444444	6.05555555555555
26	26	20.9444444444444	5.05555555555555
27	17	20.9444444444444	-3.94444444444445
28	24	20.9444444444444	3.05555555555555
29	26	20.9444444444444	5.05555555555555
30	24	20.9444444444444	3.05555555555555
31	27	20.9444444444444	6.05555555555555
32	27	20.9444444444444	6.05555555555555
33	26	20.9444444444444	5.05555555555555
34	24	20.9444444444444	3.05555555555555
35	23	20.9444444444444	2.05555555555555
36	23	20.9444444444444	2.05555555555555
37	24	12.0384615384615	11.9615384615385
38	17	12.0384615384615	4.96153846153846
39	21	12.0384615384615	8.96153846153846
40	19	12.0384615384615	6.96153846153846
41	22	12.0384615384615	9.96153846153846
42	22	12.0384615384615	9.96153846153846
43	18	12.0384615384615	5.96153846153846
44	16	12.0384615384615	3.96153846153846
45	14	12.0384615384615	1.96153846153846
46	12	12.0384615384615	-0.0384615384615388
47	14	12.0384615384615	1.96153846153846
48	16	12.0384615384615	3.96153846153846
49	8	12.0384615384615	-4.03846153846154
50	3	12.0384615384615	-9.03846153846154
51	0	12.0384615384615	-12.0384615384615
52	5	12.0384615384615	-7.03846153846154
53	1	12.0384615384615	-11.0384615384615
54	1	12.0384615384615	-11.0384615384615
55	3	12.0384615384615	-9.03846153846154
56	6	12.0384615384615	-6.03846153846154
57	7	12.0384615384615	-5.03846153846154
58	8	12.0384615384615	-4.03846153846154
59	14	12.0384615384615	1.96153846153846
60	14	12.0384615384615	1.96153846153846
61	13	12.0384615384615	0.961538461538461
62	15	12.0384615384615	2.96153846153846

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/1q89v1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/1q89v1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/2t21a1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/2t21a1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/3mjm31260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/3mjm31260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/4efon1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/4efon1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/5krvx1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/5krvx1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/6uefn1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/6uefn1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/76nje1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/76nje1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/8zbbg1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/8zbbg1260988781.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/9cese1260988781.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609888213zfefmvb6qpzvt0/9cese1260988781.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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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