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broodprijs dummy trend

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 11:42:31 -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/t1197657045k9acdgviyip177w.htm/, Retrieved Fri, 14 Dec 2007 19:30:45 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,43 0 1 1,43 0 2 1,43 0 3 1,43 0 4 1,43 0 5 1,43 0 6 1,44 0 7 1,48 0 8 1,48 0 9 1,48 0 10 1,48 0 11 1,48 0 12 1,48 0 13 1,48 0 14 1,48 0 15 1,48 0 16 1,48 0 17 1,48 0 18 1,48 0 19 1,48 0 20 1,48 0 21 1,48 0 22 1,48 0 23 1,48 0 24 1,48 0 25 1,48 0 26 1,48 0 27 1,48 0 28 1,48 0 29 1,48 0 30 1,48 0 31 1,48 0 32 1,48 0 33 1,48 0 34 1,48 0 35 1,48 0 36 1,48 0 37 1,57 0 38 1,58 0 39 1,58 0 40 1,58 0 41 1,58 0 42 1,59 1 43 1,6 1 44 1,6 1 45 1,61 1 46 1,61 1 47 1,61 1 48 1,62 1 49 1,63 1 50 1,63 1 51 1,64 1 52 1,64 1 53 1,64 1 54 1,64 1 55 1,64 1 56 1,65 1 57 1,65 1 58 1,65 1 59 1,65 1 60

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	11 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 1.42928029408608 + 0.0684512778314429dummy[t] + 0.00252516904583021trend[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)	1.42928029408608	0.006822	209.5187	0	0
dummy	0.0684512778314429	0.010348	6.6151	0	0
trend	0.00252516904583021	0.000274	9.2223	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.95633086280211
R-squared	0.914568719147827
Adjusted R-squared	0.911571130345996
F-TEST (value)	305.101459743010
F-TEST (DF numerator)	2
F-TEST (DF denominator)	57
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0223371027233623
Sum Squared Residuals	0.0284399310102203

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1.43	1.43180546313191	-0.00180546313191148
2	1.43	1.43433063217774	-0.00433063217773951
3	1.43	1.43685580122357	-0.0068558012235697
4	1.43	1.4393809702694	-0.00938097026939987
5	1.43	1.44190613931523	-0.0119061393152301
6	1.43	1.44443130836106	-0.0144313083610603
7	1.44	1.44695647740689	-0.00695647740689049
8	1.48	1.44948164645272	0.0305183535472793
9	1.48	1.45200681549855	0.0279931845014491
10	1.48	1.45453198454438	0.0254680154556189
11	1.48	1.45705715359021	0.0229428464097887
12	1.48	1.45958232263604	0.0204176773639585
13	1.48	1.46210749168187	0.0178925083181283
14	1.48	1.46463266072770	0.0153673392722981
15	1.48	1.46715782977353	0.0128421702264679
16	1.48	1.46968299881936	0.0103170011806376
17	1.48	1.47220816786519	0.00779183213480743
18	1.48	1.47473333691102	0.00526666308897722
19	1.48	1.47725850595685	0.00274149404314701
20	1.48	1.47978367500268	0.000216324997316798
21	1.48	1.48230884404851	-0.00230884404851341
22	1.48	1.48483401309434	-0.00483401309434362
23	1.48	1.48735918214017	-0.00735918214017384
24	1.48	1.48988435118600	-0.00988435118600405
25	1.48	1.49240952023183	-0.0124095202318343
26	1.48	1.49493468927766	-0.0149346892776645
27	1.48	1.49745985832349	-0.0174598583234947
28	1.48	1.49998502736932	-0.0199850273693249
29	1.48	1.50251019641516	-0.0225101964151551
30	1.48	1.50503536546099	-0.0250353654609853
31	1.48	1.50756053450682	-0.0275605345068155
32	1.48	1.51008570355265	-0.0300857035526457
33	1.48	1.51261087259848	-0.0326108725984759
34	1.48	1.51513604164431	-0.0351360416443062
35	1.48	1.51766121069014	-0.0376612106901364
36	1.48	1.52018637973597	-0.0401863797359666
37	1.48	1.52271154878180	-0.0427115487817968
38	1.57	1.52523671782763	0.0447632821723731
39	1.58	1.52776188687346	0.0522381131265429
40	1.58	1.53028705591929	0.0497129440807127
41	1.58	1.53281222496512	0.0471877750348825
42	1.58	1.53533739401095	0.0446626059890523
43	1.59	1.60631384088822	-0.0163138408882209
44	1.6	1.60883900993405	-0.00883900993405108
45	1.6	1.61136417897988	-0.0113641789798813
46	1.61	1.61388934802571	-0.0038893480257115
47	1.61	1.61641451707154	-0.00641451707154171
48	1.61	1.61893968611737	-0.00893968611737192
49	1.62	1.62146485516320	-0.00146485516320212
50	1.63	1.62399002420903	0.00600997579096745
51	1.63	1.62651519325486	0.00348480674513724
52	1.64	1.62904036230069	0.0109596376993070
53	1.64	1.63156553134652	0.00843446865347683
54	1.64	1.63409070039235	0.00590929960764662
55	1.64	1.63661586943818	0.00338413056181641
56	1.64	1.63914103848401	0.000858961515986199
57	1.65	1.64166620752984	0.008333792470156
58	1.65	1.64419137657567	0.00580862342432578
59	1.65	1.64671654562150	0.00328345437849558
60	1.65	1.64924171466733	0.000758285332665363

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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