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Paper - Multiple Regression - Olie zonder trend & monthly dummies

*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: Sun, 21 Dec 2008 08:50:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t1229874692h8eo7jyra95uqeo.htm/, Retrieved Sun, 21 Dec 2008 16:51:41 +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/2008/Dec/21/t1229874692h8eo7jyra95uqeo.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

20.7246301 0 21.44580352 0 22.09413114 0 21.53321848 0 23.3470789 0 23.5656163 0 26.42117166 0 25.21193138 0 26.43574082 0 29.33500366 0 29.40056488 0 33.05013946 0 28.38072368 0 26.0059506 0 29.31314992 0 30.36212944 0 35.74543406 0 36.15337054 0 34.20838768 0 37.90895432 0 38.70297354 0 42.11944156 0 42.16314904 0 39.79566054 0 37.36261082 0 38.3533137 0 42.60022384 0 41.24529196 0 42.15586446 0 46.94183352 0 47.42990038 0 47.0583868 0 50.18347162 0 50.12519498 0 43.22669772 0 40.04333626 0 40.37114236 0 42.2141411 0 36.99838182 0 39.74466848 0 42.68035422 0 46.2935059 0 46.97097184 0 48.72655562 0 52.36884562 1 50.05234918 1 54.03701444 1 57.78128856 1 64.71620872 1 63.4122689 1 64.3592643 1 66.02743312 1 72.13919574 1 76.60464328 1 86.97060062 1 93.48301514 1 95.58825876 1 81.88596378 1 70.5511573 1 50.38015528 1 36.24807008 0

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Olie[t] = + 36.2310727266667 + 32.5412811945833Dumivariabele[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)	36.2310727266667	1.580906	22.9179	0	0
Dumivariabele	32.5412811945833	3.086818	10.542	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.80821693233158
R-squared	0.65321460970747
Adjusted R-squared	0.647336891227935
F-TEST (value)	111.134041547225
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	3.44169137633799e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	10.6050427667741
Sum Squared Residuals	6635.54899302141

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	20.7246301	36.2310727266667	-15.5064426266667
2	21.44580352	36.2310727266667	-14.7852692066667
3	22.09413114	36.2310727266667	-14.1369415866667
4	21.53321848	36.2310727266667	-14.6978542466667
5	23.3470789	36.2310727266667	-12.8839938266667
6	23.5656163	36.2310727266667	-12.6654564266667
7	26.42117166	36.2310727266667	-9.80990106666667
8	25.21193138	36.2310727266667	-11.0191413466667
9	26.43574082	36.2310727266667	-9.79533190666667
10	29.33500366	36.2310727266667	-6.89606906666666
11	29.40056488	36.2310727266667	-6.83050784666666
12	33.05013946	36.2310727266667	-3.18093326666667
13	28.38072368	36.2310727266667	-7.85034904666667
14	26.0059506	36.2310727266667	-10.2251221266667
15	29.31314992	36.2310727266667	-6.91792280666666
16	30.36212944	36.2310727266667	-5.86894328666667
17	35.74543406	36.2310727266667	-0.485638666666665
18	36.15337054	36.2310727266667	-0.0777021866666687
19	34.20838768	36.2310727266667	-2.02268504666666
20	37.90895432	36.2310727266667	1.67788159333333
21	38.70297354	36.2310727266667	2.47190081333334
22	42.11944156	36.2310727266667	5.88836883333333
23	42.16314904	36.2310727266667	5.93207631333333
24	39.79566054	36.2310727266667	3.56458781333333
25	37.36261082	36.2310727266667	1.13153809333333
26	38.3533137	36.2310727266667	2.12224097333333
27	42.60022384	36.2310727266667	6.36915111333333
28	41.24529196	36.2310727266667	5.01421923333334
29	42.15586446	36.2310727266667	5.92479173333333
30	46.94183352	36.2310727266667	10.7107607933333
31	47.42990038	36.2310727266667	11.1988276533333
32	47.0583868	36.2310727266667	10.8273140733333
33	50.18347162	36.2310727266667	13.9523988933333
34	50.12519498	36.2310727266667	13.8941222533333
35	43.22669772	36.2310727266667	6.99562499333333
36	40.04333626	36.2310727266667	3.81226353333333
37	40.37114236	36.2310727266667	4.14006963333333
38	42.2141411	36.2310727266667	5.98306837333333
39	36.99838182	36.2310727266667	0.767309093333333
40	39.74466848	36.2310727266667	3.51359575333334
41	42.68035422	36.2310727266667	6.44928149333333
42	46.2935059	36.2310727266667	10.0624331733333
43	46.97097184	36.2310727266667	10.7398991133333
44	48.72655562	36.2310727266667	12.4954828933333
45	52.36884562	68.77235392125	-16.40350830125
46	50.05234918	68.77235392125	-18.72000474125
47	54.03701444	68.77235392125	-14.73533948125
48	57.78128856	68.77235392125	-10.99106536125
49	64.71620872	68.77235392125	-4.05614520125
50	63.4122689	68.77235392125	-5.36008502125
51	64.3592643	68.77235392125	-4.41308962124999
52	66.02743312	68.77235392125	-2.74492080125000
53	72.13919574	68.77235392125	3.36684181875
54	76.60464328	68.77235392125	7.83228935875
55	86.97060062	68.77235392125	18.19824669875
56	93.48301514	68.77235392125	24.71066121875
57	95.58825876	68.77235392125	26.81590483875
58	81.88596378	68.77235392125	13.11360985875
59	70.5511573	68.77235392125	1.77880337875000
60	50.38015528	68.77235392125	-18.39219864125
61	36.24807008	36.2310727266667	0.0169973533333319

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly 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')

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Software written by Ed van Stee & Patrick Wessa

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