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5

*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 06:31:33 -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/t12298663392m6vko6l3mikznr.htm/, Retrieved Sun, 21 Dec 2008 14:32:27 +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/t12298663392m6vko6l3mikznr.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 «

274412 0 272433 0 268361 0 268586 0 264768 0 269974 0 304744 0 309365 0 308347 0 298427 0 289231 0 291975 0 294912 0 293488 0 290555 0 284736 0 281818 0 287854 0 316263 0 325412 0 326011 0 328282 0 317480 0 317539 0 313737 0 312276 0 309391 0 302950 0 300316 0 304035 0 333476 0 337698 0 335932 0 323931 0 313927 0 314485 0 313218 0 309664 0 302963 0 298989 0 298423 0 301631 0 329765 0 335083 0 327616 0 309119 0 295916 0 291413 0 291542 1 284678 1 276475 1 272566 1 264981 1 263290 1 296806 1 303598 1 286994 1 276427 1 266424 1 267153 1 268381 1 262522 1 255542 1 253158 1 243803 1 250741 1 280445 1 285257 1 270976 1 261076 1 255603 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	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

WerklozenVrouwen[t] = + 304185.979166667 -32949.5443840580Kredietcrisis[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)	304185.979166667	2619.903227	116.1058	0	0
Kredietcrisis	-32949.5443840580	4603.101022	-7.1581	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.652795020079306
R-squared	0.426141338240342
Adjusted R-squared	0.417824546040926
F-TEST (value)	51.2386660653008
F-TEST (DF numerator)	1
F-TEST (DF denominator)	69
p-value	6.87142120980866e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	18151.2220032716
Sum Squared Residuals	22733213354.6314

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	274412	304185.979166668	-29773.9791666679
2	272433	304185.979166667	-31752.9791666666
3	268361	304185.979166667	-35824.9791666666
4	268586	304185.979166667	-35599.9791666666
5	264768	304185.979166667	-39417.9791666666
6	269974	304185.979166667	-34211.9791666666
7	304744	304185.979166667	558.020833333358
8	309365	304185.979166667	5179.02083333336
9	308347	304185.979166667	4161.02083333336
10	298427	304185.979166667	-5758.97916666664
11	289231	304185.979166667	-14954.9791666666
12	291975	304185.979166667	-12210.9791666666
13	294912	304185.979166667	-9273.97916666664
14	293488	304185.979166667	-10697.9791666666
15	290555	304185.979166667	-13630.9791666666
16	284736	304185.979166667	-19449.9791666666
17	281818	304185.979166667	-22367.9791666666
18	287854	304185.979166667	-16331.9791666666
19	316263	304185.979166667	12077.0208333334
20	325412	304185.979166667	21226.0208333334
21	326011	304185.979166667	21825.0208333334
22	328282	304185.979166667	24096.0208333334
23	317480	304185.979166667	13294.0208333334
24	317539	304185.979166667	13353.0208333334
25	313737	304185.979166667	9551.02083333336
26	312276	304185.979166667	8090.02083333336
27	309391	304185.979166667	5205.02083333336
28	302950	304185.979166667	-1235.97916666664
29	300316	304185.979166667	-3869.97916666664
30	304035	304185.979166667	-150.979166666642
31	333476	304185.979166667	29290.0208333334
32	337698	304185.979166667	33512.0208333334
33	335932	304185.979166667	31746.0208333334
34	323931	304185.979166667	19745.0208333334
35	313927	304185.979166667	9741.02083333336
36	314485	304185.979166667	10299.0208333334
37	313218	304185.979166667	9032.02083333336
38	309664	304185.979166667	5478.02083333336
39	302963	304185.979166667	-1222.97916666664
40	298989	304185.979166667	-5196.97916666664
41	298423	304185.979166667	-5762.97916666664
42	301631	304185.979166667	-2554.97916666664
43	329765	304185.979166667	25579.0208333334
44	335083	304185.979166667	30897.0208333334
45	327616	304185.979166667	23430.0208333334
46	309119	304185.979166667	4933.02083333336
47	295916	304185.979166667	-8269.97916666664
48	291413	304185.979166667	-12772.9791666666
49	291542	271236.434782609	20305.5652173913
50	284678	271236.434782609	13441.5652173913
51	276475	271236.434782609	5238.56521739131
52	272566	271236.434782609	1329.56521739131
53	264981	271236.434782609	-6255.4347826087
54	263290	271236.434782609	-7946.4347826087
55	296806	271236.434782609	25569.5652173913
56	303598	271236.434782609	32361.5652173913
57	286994	271236.434782609	15757.5652173913
58	276427	271236.434782609	5190.56521739131
59	266424	271236.434782609	-4812.43478260869
60	267153	271236.434782609	-4083.43478260869
61	268381	271236.434782609	-2855.43478260869
62	262522	271236.434782609	-8714.4347826087
63	255542	271236.434782609	-15694.4347826087
64	253158	271236.434782609	-18078.4347826087
65	243803	271236.434782609	-27433.4347826087
66	250741	271236.434782609	-20495.4347826087
67	280445	271236.434782609	9208.56521739131
68	285257	271236.434782609	14020.5652173913
69	270976	271236.434782609	-260.434782608694
70	261076	271236.434782609	-10160.4347826087
71	255603	271236.434782609	-15633.4347826087

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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