Home » date » 2008 » Dec » 12 »

Paper Hoofdstuk 5 Multiple regression werkloosheid met dummies en trend

*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: Fri, 12 Dec 2008 04:53:38 -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/12/t12290828914alxp7u99vu5bi0.htm/, Retrieved Fri, 12 Dec 2008 12:55:08 +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/12/t12290828914alxp7u99vu5bi0.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 «

493.000 0 481.000 0 462.000 0 457.000 0 442.000 0 439.000 0 488.000 0 521.000 0 501.000 0 485.000 0 464.000 0 460.000 0 467.000 0 460.000 0 448.000 0 443.000 0 436.000 0 431.000 0 484.000 0 510.000 0 513.000 0 503.000 0 471.000 0 471.000 0 476.000 0 475.000 0 470.000 0 461.000 0 455.000 0 456.000 0 517.000 1 525.000 1 523.000 1 519.000 1 509.000 1 512.000 1 519.000 1 517.000 1 510.000 1 509.000 1 501.000 1 507.000 1 569.000 1 580.000 1 578.000 1 565.000 1 547.000 1 555.000 1 562.000 1 561.000 1 555.000 1 544.000 1 537.000 1 543.000 1 594.000 1 611.000 1 613.000 1 611.000 1 594.000 1 595.000 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

y[t] = + 441.766666666666 + 16.7222222222221x[t] + 8.55555555555529M1[t] + 2.10000000000004M2[t] -9.55555555555553M3[t] -17.6111111111111M4[t] -28.0666666666667M5[t] -28.9222222222222M6[t] + 21.0777777777778M7[t] + 38.2222222222223M8[t] + 32.5666666666667M9[t] + 21.7111111111111M10[t] + 0.255555555555560M11[t] + 1.85555555555556t + 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)	441.766666666666	9.983276	44.2507	0	0
x	16.7222222222221	9.606412	1.7407	0.088416	0.044208
M1	8.55555555555529	11.650456	0.7344	0.46646	0.23323
M2	2.10000000000004	11.620714	0.1807	0.857388	0.428694
M3	-9.55555555555553	11.597529	-0.8239	0.414231	0.207115
M4	-17.6111111111111	11.58094	-1.5207	0.13518	0.06759
M5	-28.0666666666667	11.570975	-2.4256	0.019264	0.009632
M6	-28.9222222222222	11.567651	-2.5003	0.016037	0.008018
M7	21.0777777777778	11.610784	1.8154	0.07599	0.037995
M8	38.2222222222223	11.58094	3.3004	0.00187	0.000935
M9	32.5666666666667	11.557675	2.8178	0.007105	0.003552
M10	21.7111111111111	11.541029	1.8812	0.066281	0.033141
M11	0.255555555555560	11.531029	0.0222	0.982414	0.491207
t	1.85555555555556	0.277313	6.6912	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.94589715318519
R-squared	0.894721424403847
Adjusted R-squared	0.8649687834745
F-TEST (value)	30.0720002143174
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	18.2268846397703
Sum Squared Residuals	15282.0888888887

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	493	452.177777777779	40.822222222221
2	481	447.577777777778	33.4222222222223
3	462	437.777777777778	24.2222222222223
4	457	431.577777777778	25.4222222222223
5	442	422.977777777778	19.0222222222223
6	439	423.977777777778	15.0222222222222
7	488	475.833333333333	12.1666666666668
8	521	494.833333333333	26.1666666666667
9	501	491.033333333333	9.96666666666676
10	485	482.033333333333	2.96666666666668
11	464	462.433333333333	1.56666666666674
12	460	464.033333333333	-4.0333333333333
13	467	474.444444444444	-7.4444444444441
14	460	469.844444444444	-9.84444444444445
15	448	460.044444444444	-12.0444444444444
16	443	453.844444444444	-10.8444444444444
17	436	445.244444444444	-9.24444444444442
18	431	446.244444444444	-15.2444444444444
19	484	498.1	-14.1
20	510	517.1	-7.1
21	513	513.3	-0.300000000000018
22	503	504.3	-1.29999999999999
23	471	484.7	-13.7
24	471	486.3	-15.3
25	476	496.711111111111	-20.7111111111108
26	475	492.111111111111	-17.1111111111111
27	470	482.311111111111	-12.3111111111111
28	461	476.111111111111	-15.1111111111111
29	455	467.511111111111	-12.5111111111111
30	456	468.511111111111	-12.5111111111111
31	517	537.088888888889	-20.0888888888889
32	525	556.088888888889	-31.0888888888889
33	523	552.288888888889	-29.2888888888889
34	519	543.288888888889	-24.2888888888888
35	509	523.688888888889	-14.6888888888889
36	512	525.288888888889	-13.2888888888889
37	519	535.7	-16.6999999999997
38	517	531.1	-14.1
39	510	521.3	-11.3
40	509	515.1	-6.09999999999999
41	501	506.5	-5.5
42	507	507.5	-0.499999999999985
43	569	559.355555555556	9.64444444444441
44	580	578.355555555556	1.64444444444443
45	578	574.555555555556	3.44444444444441
46	565	565.555555555556	-0.555555555555569
47	547	545.955555555556	1.04444444444442
48	555	547.555555555556	7.44444444444441
49	562	557.966666666666	4.0333333333336
50	561	553.366666666667	7.63333333333327
51	555	543.566666666667	11.4333333333333
52	544	537.366666666667	6.63333333333328
53	537	528.766666666667	8.23333333333327
54	543	529.766666666667	13.2333333333333
55	594	581.622222222222	12.3777777777777
56	611	600.622222222222	10.3777777777777
57	613	596.822222222222	16.1777777777777
58	611	587.822222222222	23.1777777777777
59	594	568.222222222222	25.7777777777777
60	595	569.822222222222	25.1777777777777

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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