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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 07:45:31 -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/t1229870785almhnvrl9pngmy4.htm/, Retrieved Sun, 21 Dec 2008 15:46:33 +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/t1229870785almhnvrl9pngmy4.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 0 50.05234918 0 54.03701444 0 57.78128856 0 64.71620872 0 63.4122689 0 64.3592643 0 66.02743312 0 72.13919574 0 76.60464328 0 86.97060062 0 93.48301514 0 95.58825876 0 81.88596378 1 70.5511573 1 50.38015528 1 36.24807008 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Olie[t] = + 43.7138699824561 + 16.0524666275439Dumivariabele[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)	43.7138699824561	2.324501	18.8057	0	0
Dumivariabele	16.0524666275439	9.077467	1.7684	0.082166	0.041083

Multiple Linear Regression - Regression Statistics
Multiple R	0.224355255896349
R-squared	0.0503352808483162
Adjusted R-squared	0.0342392686593046
F-TEST (value)	3.12718953348451
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	0.0821659618270217
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	17.549598283773
Sum Squared Residuals	18171.3155953867

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	20.7246301	43.7138699824561	-22.9892398824561
2	21.44580352	43.7138699824561	-22.2680664624561
3	22.09413114	43.7138699824561	-21.6197388424561
4	21.53321848	43.7138699824561	-22.1806515024561
5	23.3470789	43.7138699824561	-20.3667910824561
6	23.5656163	43.7138699824561	-20.1482536824561
7	26.42117166	43.7138699824561	-17.2926983224561
8	25.21193138	43.7138699824561	-18.5019386024561
9	26.43574082	43.7138699824561	-17.2781291624561
10	29.33500366	43.7138699824561	-14.3788663224561
11	29.40056488	43.7138699824561	-14.3133051024561
12	33.05013946	43.7138699824561	-10.6637305224561
13	28.38072368	43.7138699824561	-15.3331463024561
14	26.0059506	43.7138699824561	-17.7079193824561
15	29.31314992	43.7138699824561	-14.4007200624561
16	30.36212944	43.7138699824561	-13.3517405424561
17	35.74543406	43.7138699824561	-7.96843592245614
18	36.15337054	43.7138699824561	-7.56049944245614
19	34.20838768	43.7138699824561	-9.50548230245614
20	37.90895432	43.7138699824561	-5.80491566245614
21	38.70297354	43.7138699824561	-5.01089644245614
22	42.11944156	43.7138699824561	-1.59442842245614
23	42.16314904	43.7138699824561	-1.55072094245614
24	39.79566054	43.7138699824561	-3.91820944245614
25	37.36261082	43.7138699824561	-6.35125916245614
26	38.3533137	43.7138699824561	-5.36055628245614
27	42.60022384	43.7138699824561	-1.11364614245614
28	41.24529196	43.7138699824561	-2.46857802245614
29	42.15586446	43.7138699824561	-1.55800552245614
30	46.94183352	43.7138699824561	3.22796353754386
31	47.42990038	43.7138699824561	3.71603039754386
32	47.0583868	43.7138699824561	3.34451681754386
33	50.18347162	43.7138699824561	6.46960163754386
34	50.12519498	43.7138699824561	6.41132499754386
35	43.22669772	43.7138699824561	-0.487172262456142
36	40.04333626	43.7138699824561	-3.67053372245614
37	40.37114236	43.7138699824561	-3.34272762245614
38	42.2141411	43.7138699824561	-1.49972888245614
39	36.99838182	43.7138699824561	-6.71548816245614
40	39.74466848	43.7138699824561	-3.96920150245614
41	42.68035422	43.7138699824561	-1.03351576245614
42	46.2935059	43.7138699824561	2.57963591754386
43	46.97097184	43.7138699824561	3.25710185754386
44	48.72655562	43.7138699824561	5.01268563754386
45	52.36884562	43.7138699824561	8.65497563754386
46	50.05234918	43.7138699824561	6.33847919754386
47	54.03701444	43.7138699824561	10.3231444575439
48	57.78128856	43.7138699824561	14.0674185775439
49	64.71620872	43.7138699824561	21.0023387375439
50	63.4122689	43.7138699824561	19.6983989175439
51	64.3592643	43.7138699824561	20.6453943175439
52	66.02743312	43.7138699824561	22.3135631375439
53	72.13919574	43.7138699824561	28.4253257575439
54	76.60464328	43.7138699824561	32.8907732975439
55	86.97060062	43.7138699824561	43.2567306375439
56	93.48301514	43.7138699824561	49.7691451575439
57	95.58825876	43.7138699824561	51.8743887775439
58	81.88596378	59.76633661	22.11962717
59	70.5511573	59.76633661	10.78482069
60	50.38015528	59.76633661	-9.38618133
61	36.24807008	59.76633661	-23.51826653

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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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