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Paper: multiple linear regression prijsindexcijfers grondstoffen

*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: Thu, 18 Dec 2008 04:09:27 -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/18/t1229598808537o1w3o298agx4.htm/, Retrieved Thu, 18 Dec 2008 12:13:56 +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/18/t1229598808537o1w3o298agx4.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 «
90.8 0 96.4 0 90 0 92.1 0 97.2 0 95.1 0 88.5 0 91 0 90.5 1 75 1 66.3 1 66 0 68.4 0 70.6 0 83.9 0 90.1 0 90.6 0 87.1 0 90.8 0 94.1 0 99.8 0 96.8 0 87 0 96.3 0 107.1 0 115.2 0 106.1 1 89.5 1 91.3 1 97.6 1 100.7 1 104.6 1 94.7 1 101.8 1 102.5 1 105.3 1 110.3 1 109.8 1 117.3 1 118.8 1 131.3 1 125.9 1 133.1 1 147 1 145.8 1 164.4 1 149.8 1 137.7 1 151.7 1 156.8 1 180 1 180.4 1 170.4 1 191.6 1 199.5 1 218.2 1 217.5 1 205 1 194 1 199.3 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 92.7881818181819 + 46.8863636363636t -5.88272727272737M1[t] -1.78272727272727M2[t] -5.46000000000002M3[t] -6.74000000000003M4[t] -4.76000000000004M5[t] -1.46000000000003M6[t] + 1.59999999999998M7[t] + 10.0600000000000M8[t] -0.637272727272797M9[t] -1.69727272727277M10[t] -10.3772727272728M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)92.788181818181918.0416135.1435e-063e-06
t46.886363636363610.416334.50124.4e-052.2e-05
M1-5.8827272727273724.025396-0.24490.8076350.403817
M2-1.7827272727272724.025396-0.07420.9411650.470582
M3-5.4600000000000223.934905-0.22810.8205440.410272
M4-6.7400000000000323.934905-0.28160.7794890.389744
M5-4.7600000000000423.934905-0.19890.843220.42161
M6-1.4600000000000323.934905-0.0610.9516190.475809
M71.5999999999999823.9349050.06680.9469860.473493
M810.060000000000023.9349050.42030.6761770.338088
M9-0.63727272727279724.025396-0.02650.9789510.489475
M10-1.6972727272727724.025396-0.07060.943980.47199
M11-10.377272727272824.025396-0.43190.6677680.333884


Multiple Linear Regression - Regression Statistics
Multiple R0.569875575470858
R-squared0.324758171518242
Adjusted R-squared0.152356002544176
F-TEST (value)1.88372439541114
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.061421781836675
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation37.8444075368895
Sum Squared Residuals67313.3615454545


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
190.886.90545454545483.89454545454518
296.491.00545454545445.39454545454557
39087.32818181818182.67181818181818
492.186.04818181818186.05181818181817
597.288.02818181818189.17181818181817
695.191.32818181818183.77181818181818
788.594.3881818181818-5.88818181818182
891102.848181818182-11.8481818181818
990.5139.037272727273-48.5372727272728
1075137.977272727273-62.9772727272727
1166.3129.297272727273-62.9972727272727
126692.7881818181818-26.7881818181818
1368.486.9054545454545-18.5054545454545
1470.691.0054545454546-20.4054545454546
1583.987.3281818181818-3.42818181818181
1690.186.04818181818184.05181818181817
1790.688.02818181818182.57181818181818
1887.191.3281818181818-4.22818181818182
1990.894.3881818181818-3.58818181818181
2094.1102.848181818182-8.74818181818182
2199.892.1509090909097.64909090909092
2296.891.0909090909095.70909090909092
238782.41090909090914.58909090909089
2496.392.78818181818183.51181818181815
25107.186.905454545454520.1945454545455
26115.291.005454545454624.1945454545454
27106.1134.214545454545-28.1145454545455
2889.5132.934545454545-43.4345454545455
2991.3134.914545454545-43.6145454545454
3097.6138.214545454545-40.6145454545455
31100.7141.274545454545-40.5745454545454
32104.6149.734545454545-45.1345454545454
3394.7139.037272727273-44.3372727272727
34101.8137.977272727273-36.1772727272727
35102.5129.297272727273-26.7972727272727
36105.3139.674545454545-34.3745454545455
37110.3133.791818181818-23.4918181818181
38109.8137.891818181818-28.0918181818182
39117.3134.214545454545-16.9145454545455
40118.8132.934545454545-14.1345454545455
41131.3134.914545454545-3.61454545454543
42125.9138.214545454545-12.3145454545454
43133.1141.274545454545-8.17454545454545
44147149.734545454545-2.73454545454544
45145.8139.0372727272736.7627272727273
46164.4137.97727272727326.4227272727273
47149.8129.29727272727320.5027272727273
48137.7139.674545454545-1.97454545454549
49151.7133.79181818181817.9081818181819
50156.8137.89181818181818.9081818181818
51180134.21454545454545.7854545454545
52180.4132.93454545454547.4654545454545
53170.4134.91454545454535.4854545454545
54191.6138.21454545454553.3854545454545
55199.5141.27454545454558.2254545454546
56218.2149.73454545454568.4654545454545
57217.5139.03727272727378.4627272727272
58205137.97727272727367.0227272727273
59194129.29727272727364.7027272727273
60199.3139.67454545454559.6254545454545


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.05220121207847090.1044024241569420.947798787921529
170.01515319952108090.03030639904216170.98484680047892
180.00420315080498990.00840630160997980.99579684919501
190.0009749936269894440.001949987253978890.99902500637301
200.0002124854531424790.0004249709062849570.999787514546858
214.15938514427031e-058.31877028854063e-050.999958406148557
229.84089157083578e-061.96817831416716e-050.99999015910843
231.90561936816029e-063.81123873632057e-060.999998094380632
244.44408544601107e-068.88817089202213e-060.999995555914554
256.5666734138744e-061.31333468277488e-050.999993433326586
261.08035257406464e-052.16070514812929e-050.99998919647426
271.32880486068361e-052.65760972136722e-050.999986711951393
285.02086047424913e-061.00417209484983e-050.999994979139526
291.87257014502639e-063.74514029005279e-060.999998127429855
308.51309731405404e-071.70261946281081e-060.999999148690269
314.81366772870414e-079.62733545740829e-070.999999518633227
323.71001670497966e-077.42003340995931e-070.99999962899833
333.42871811367738e-076.85743622735476e-070.999999657128189
345.54082236267273e-071.10816447253455e-060.999999445917764
351.3123887471066e-062.6247774942132e-060.999998687611253
362.08749566129524e-064.17499132259049e-060.99999791250434
371.31958807548039e-062.63917615096079e-060.999998680411925
387.18818309983695e-071.43763661996739e-060.99999928118169
391.02033203750534e-062.04066407501067e-060.999998979667962
401.90051741052438e-063.80103482104876e-060.99999809948259
413.10675406517404e-066.21350813034808e-060.999996893245935
428.3933566966478e-061.67867133932956e-050.999991606643303
433.7544384370212e-057.5088768740424e-050.99996245561563
440.0004053572146554210.0008107144293108420.999594642785345


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level270.93103448275862NOK
5% type I error level280.96551724137931NOK
10% type I error level280.96551724137931NOK
 
Charts produced by software:
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Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
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))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$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')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$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()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
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')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 





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Software written by Ed van Stee & Patrick Wessa


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