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Broodprijs dummy liberalisering

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

Title produced by software: Multiple Regression

Date of computation: Fri, 14 Dec 2007 09:09:40 -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/14/t1197649592owaqmf2jdmfly3p.htm/, Retrieved Fri, 14 Dec 2007 17:26:42 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,43 0 1,44 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,48 0 1,57 0 1,58 0 1,58 0 1,58 0 1,58 0 1,59 1 1,6 1 1,6 1 1,61 1 1,61 1 1,61 1 1,62 1 1,63 1 1,63 1 1,64 1 1,64 1 1,64 1 1,64 1 1,64 1 1,65 1 1,65 1 1,65 1 1,65 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

Broodprijs[t] = + 1.48357142857143 + 0.144206349206349Dummy[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)	1.48357142857143	0.005394	275.0422	0	0
Dummy	0.144206349206349	0.009848	14.6432	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.887184293010393
R-squared	0.78709596976435
Adjusted R-squared	0.783425210622356
F-TEST (value)	214.423213105940
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0349569678381563
Sum Squared Residuals	0.0708753968253977

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.48357142857144	-0.0535714285714358
2	1.43	1.48357142857143	-0.0535714285714285
3	1.43	1.48357142857143	-0.0535714285714284
4	1.43	1.48357142857143	-0.0535714285714284
5	1.43	1.48357142857143	-0.0535714285714284
6	1.43	1.48357142857143	-0.0535714285714284
7	1.44	1.48357142857143	-0.0435714285714284
8	1.48	1.48357142857143	-0.00357142857142839
9	1.48	1.48357142857143	-0.00357142857142839
10	1.48	1.48357142857143	-0.00357142857142839
11	1.48	1.48357142857143	-0.00357142857142839
12	1.48	1.48357142857143	-0.00357142857142839
13	1.48	1.48357142857143	-0.00357142857142839
14	1.48	1.48357142857143	-0.00357142857142839
15	1.48	1.48357142857143	-0.00357142857142839
16	1.48	1.48357142857143	-0.00357142857142839
17	1.48	1.48357142857143	-0.00357142857142839
18	1.48	1.48357142857143	-0.00357142857142839
19	1.48	1.48357142857143	-0.00357142857142839
20	1.48	1.48357142857143	-0.00357142857142839
21	1.48	1.48357142857143	-0.00357142857142839
22	1.48	1.48357142857143	-0.00357142857142839
23	1.48	1.48357142857143	-0.00357142857142839
24	1.48	1.48357142857143	-0.00357142857142839
25	1.48	1.48357142857143	-0.00357142857142839
26	1.48	1.48357142857143	-0.00357142857142839
27	1.48	1.48357142857143	-0.00357142857142839
28	1.48	1.48357142857143	-0.00357142857142839
29	1.48	1.48357142857143	-0.00357142857142839
30	1.48	1.48357142857143	-0.00357142857142839
31	1.48	1.48357142857143	-0.00357142857142839
32	1.48	1.48357142857143	-0.00357142857142839
33	1.48	1.48357142857143	-0.00357142857142839
34	1.48	1.48357142857143	-0.00357142857142839
35	1.48	1.48357142857143	-0.00357142857142839
36	1.48	1.48357142857143	-0.00357142857142839
37	1.48	1.48357142857143	-0.00357142857142839
38	1.57	1.48357142857143	0.0864285714285717
39	1.58	1.48357142857143	0.0964285714285717
40	1.58	1.48357142857143	0.0964285714285717
41	1.58	1.48357142857143	0.0964285714285717
42	1.58	1.48357142857143	0.0964285714285717
43	1.59	1.62777777777778	-0.0377777777777777
44	1.6	1.62777777777778	-0.0277777777777777
45	1.6	1.62777777777778	-0.0277777777777777
46	1.61	1.62777777777778	-0.0177777777777777
47	1.61	1.62777777777778	-0.0177777777777777
48	1.61	1.62777777777778	-0.0177777777777777
49	1.62	1.62777777777778	-0.00777777777777766
50	1.63	1.62777777777778	0.00222222222222213
51	1.63	1.62777777777778	0.00222222222222213
52	1.64	1.62777777777778	0.0122222222222221
53	1.64	1.62777777777778	0.0122222222222221
54	1.64	1.62777777777778	0.0122222222222221
55	1.64	1.62777777777778	0.0122222222222221
56	1.64	1.62777777777778	0.0122222222222221
57	1.65	1.62777777777778	0.0222222222222221
58	1.65	1.62777777777778	0.0222222222222221
59	1.65	1.62777777777778	0.0222222222222221
60	1.65	1.62777777777778	0.0222222222222221

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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