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Multiple lineaire regressie dummyvariabele

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 22 Dec 2007 05:21:34 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/22/t1198325019mhaxxeolg80zkcx.htm/, Retrieved Sat, 22 Dec 2007 13:03:50 +0100

User-defined keywords:

Dataseries X:

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106,5 0 112,3 0 102,8 0 96,5 0 101,0 0 98,9 0 105,1 0 103,0 0 99,0 0 104,3 0 94,6 0 90,4 0 108,9 0 111,4 0 100,8 0 102,5 0 98,2 0 98,7 0 113,3 0 104,6 0 99,3 0 111,8 0 97,3 0 97,7 0 115,6 0 111,9 0 107,0 0 107,1 0 100,6 0 99,2 0 108,4 0 103,0 0 99,8 0 115,0 0 90,8 0 95,9 0 114,4 0 108,2 0 112,6 0 109,1 0 105,0 1 105,0 1 118,5 1 103,7 1 112,5 1 116,6 1 96,6 1 101,9 1 116,5 1 119,3 1 115,4 1 108,5 1 111,5 1 108,8 1 121,8 1 109,6 1 112,2 1 119,6 1 103,4 1 105,3 1 113,5 1

Text written by user:

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 compuational 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

Industriële_productie[t] = + 103.9375 + 6.78630952380952x[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)	103.9375	1.06455	97.6351	0	0
x	6.78630952380952	1.814352	3.7403	0.000418	0.000209

Multiple Linear Regression - Regression Statistics
Multiple R	0.43780409846228
R-squared	0.19167242863037
Adjusted R-squared	0.177971961319020
F-TEST (value)	13.9902110106555
F-TEST (DF numerator)	1
F-TEST (DF denominator)	59
p-value	0.000417895249223532
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.73280842155216
Sum Squared Residuals	2674.51184523810

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	106.5	103.9375	2.56250000000008
2	112.3	103.9375	8.3625
3	102.8	103.9375	-1.13750000000000
4	96.5	103.9375	-7.4375
5	101	103.9375	-2.9375
6	98.9	103.9375	-5.0375
7	105.1	103.9375	1.16249999999999
8	103	103.9375	-0.937500000000001
9	99	103.9375	-4.9375
10	104.3	103.9375	0.362499999999996
11	94.6	103.9375	-9.3375
12	90.4	103.9375	-13.5375
13	108.9	103.9375	4.9625
14	111.4	103.9375	7.4625
15	100.8	103.9375	-3.13750000000000
16	102.5	103.9375	-1.43750000000000
17	98.2	103.9375	-5.7375
18	98.7	103.9375	-5.2375
19	113.3	103.9375	9.3625
20	104.6	103.9375	0.662499999999993
21	99.3	103.9375	-4.6375
22	111.8	103.9375	7.8625
23	97.3	103.9375	-6.6375
24	97.7	103.9375	-6.2375
25	115.6	103.9375	11.6625
26	111.9	103.9375	7.9625
27	107	103.9375	3.0625
28	107.1	103.9375	3.16249999999999
29	100.6	103.9375	-3.33750000000001
30	99.2	103.9375	-4.7375
31	108.4	103.9375	4.4625
32	103	103.9375	-0.937500000000001
33	99.8	103.9375	-4.13750000000000
34	115	103.9375	11.0625
35	90.8	103.9375	-13.1375
36	95.9	103.9375	-8.0375
37	114.4	103.9375	10.4625
38	108.2	103.9375	4.2625
39	112.6	103.9375	8.6625
40	109.1	103.9375	5.16249999999999
41	105	110.723809523810	-5.72380952380952
42	105	110.723809523810	-5.72380952380952
43	118.5	110.723809523810	7.77619047619048
44	103.7	110.723809523810	-7.02380952380952
45	112.5	110.723809523810	1.77619047619048
46	116.6	110.723809523810	5.87619047619047
47	96.6	110.723809523810	-14.1238095238095
48	101.9	110.723809523810	-8.82380952380952
49	116.5	110.723809523810	5.77619047619048
50	119.3	110.723809523810	8.57619047619047
51	115.4	110.723809523810	4.67619047619048
52	108.5	110.723809523810	-2.22380952380952
53	111.5	110.723809523810	0.776190476190478
54	108.8	110.723809523810	-1.92380952380952
55	121.8	110.723809523810	11.0761904761905
56	109.6	110.723809523810	-1.12380952380953
57	112.2	110.723809523810	1.47619047619048
58	119.6	110.723809523810	8.87619047619047
59	103.4	110.723809523810	-7.32380952380952
60	105.3	110.723809523810	-5.42380952380953
61	113.5	110.723809523810	2.77619047619048

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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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