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3

*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 06:27:04 -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/t12298660685ymos03inwszz2f.htm/, Retrieved Sun, 21 Dec 2008 14:27:56 +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/t12298660685ymos03inwszz2f.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 «

244752 0 244576 0 241572 0 240541 0 236089 0 236997 0 264579 0 270349 0 269645 0 267037 0 258113 0 262813 0 267413 0 267366 0 264777 0 258863 0 254844 0 254868 0 277267 0 285351 0 286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 0 280190 0 280408 0 276836 0 275216 0 274352 0 271311 0 289802 0 290726 0 292300 0 278506 0 269826 0 265861 0 269034 1 264176 1 255198 1 253353 1 246057 1 235372 1 258556 1 260993 1 254663 1 250643 1 243422 1 247105 1 248541 1 245039 1 237080 1 237085 1 225554 1 226839 1 247934 1 248333 1 246969 1 245098 1 246263 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

WerklozenMannen[t] = + 270666.8125 -23131.7255434782Kredietcrisis[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)	270666.8125	1990.606847	135.972	0	0
Kredietcrisis	-23131.7255434782	3497.443844	-6.6139	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.622889950233052
R-squared	0.387991890101335
Adjusted R-squared	0.37912220734918
F-TEST (value)	43.7436040209089
F-TEST (DF numerator)	1
F-TEST (DF denominator)	69
p-value	6.61418353420373e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	13791.3287907150
Sum Squared Residuals	13123851737.1386

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	244752	270666.812500001	-25914.8125000009
2	244576	270666.8125	-26090.8125
3	241572	270666.8125	-29094.8125
4	240541	270666.8125	-30125.8125
5	236089	270666.8125	-34577.8125
6	236997	270666.8125	-33669.8125
7	264579	270666.8125	-6087.81249999998
8	270349	270666.8125	-317.812499999982
9	269645	270666.8125	-1021.81249999998
10	267037	270666.8125	-3629.81249999998
11	258113	270666.8125	-12553.8125000000
12	262813	270666.8125	-7853.81249999998
13	267413	270666.8125	-3253.81249999998
14	267366	270666.8125	-3300.81249999998
15	264777	270666.8125	-5889.81249999998
16	258863	270666.8125	-11803.8125000000
17	254844	270666.8125	-15822.8125000000
18	254868	270666.8125	-15798.8125000000
19	277267	270666.8125	6600.18750000002
20	285351	270666.8125	14684.1875000000
21	286602	270666.8125	15935.1875000000
22	283042	270666.8125	12375.1875000000
23	276687	270666.8125	6020.18750000002
24	277915	270666.8125	7248.18750000002
25	277128	270666.8125	6461.18750000002
26	277103	270666.8125	6436.18750000002
27	275037	270666.8125	4370.18750000002
28	270150	270666.8125	-516.812499999982
29	267140	270666.8125	-3526.81249999998
30	264993	270666.8125	-5673.81249999998
31	287259	270666.8125	16592.1875000000
32	291186	270666.8125	20519.1875
33	292300	270666.8125	21633.1875000000
34	288186	270666.8125	17519.1875000000
35	281477	270666.8125	10810.1875000000
36	282656	270666.8125	11989.1875000000
37	280190	270666.8125	9523.18750000002
38	280408	270666.8125	9741.18750000002
39	276836	270666.8125	6169.18750000002
40	275216	270666.8125	4549.18750000002
41	274352	270666.8125	3685.18750000002
42	271311	270666.8125	644.187500000018
43	289802	270666.8125	19135.1875
44	290726	270666.8125	20059.1875000000
45	292300	270666.8125	21633.1875000000
46	278506	270666.8125	7839.18750000002
47	269826	270666.8125	-840.812499999982
48	265861	270666.8125	-4805.81249999998
49	269034	247535.086956522	21498.9130434783
50	264176	247535.086956522	16640.9130434783
51	255198	247535.086956522	7662.91304347826
52	253353	247535.086956522	5817.91304347826
53	246057	247535.086956522	-1478.08695652174
54	235372	247535.086956522	-12163.0869565217
55	258556	247535.086956522	11020.9130434783
56	260993	247535.086956522	13457.9130434783
57	254663	247535.086956522	7127.91304347826
58	250643	247535.086956522	3107.91304347826
59	243422	247535.086956522	-4113.08695652174
60	247105	247535.086956522	-430.086956521739
61	248541	247535.086956522	1005.91304347826
62	245039	247535.086956522	-2496.08695652174
63	237080	247535.086956522	-10455.0869565217
64	237085	247535.086956522	-10450.0869565217
65	225554	247535.086956522	-21981.0869565217
66	226839	247535.086956522	-20696.0869565217
67	247934	247535.086956522	398.913043478261
68	248333	247535.086956522	797.913043478261
69	246969	247535.086956522	-566.086956521739
70	245098	247535.086956522	-2437.08695652174
71	246263	247535.086956522	-1272.08695652174

Charts produced by software:

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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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