Home » date » 2008 » Dec » 20 »

Investeringsgoederen met seizoenale en lineaire 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: Sat, 20 Dec 2008 07:18:37 -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/20/t1229782807ksor6ns3dyaisv3.htm/, Retrieved Sat, 20 Dec 2008 15:20:17 +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/20/t1229782807ksor6ns3dyaisv3.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 «
97.7 0 101.5 0 119.6 0 108.1 0 117.8 0 125.5 0 89.2 0 92.3 0 104.6 0 122.8 0 96.0 0 94.6 0 93.3 0 101.1 0 114.2 0 104.7 0 113.3 0 118.2 0 83.6 0 73.9 0 99.5 0 97.7 0 103.0 0 106.3 0 92.2 0 101.8 0 122.8 0 111.8 0 106.3 0 121.5 0 81.9 0 85.4 0 110.9 0 117.3 0 106.3 0 105.5 0 101.3 0 105.9 0 126.3 0 111.9 0 108.9 0 127.2 0 94.2 0 85.7 0 116.2 0 107.2 0 110.6 0 112.0 0 104.5 0 112.0 0 132.8 0 110.8 0 128.7 0 136.8 0 94.9 0 88.8 0 123.2 0 125.3 0 122.7 0 125.7 0 116.3 0 118.7 0 142.0 0 127.9 0 131.9 0 152.3 0 110.8 1 99.1 1 135.0 1 133.2 1 131.0 1 133.9 1 119.9 1 136.9 1 148.9 1 145.1 1 142.4 1 159.6 1 120.7 1 109.0 1 142.0 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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 97.0556224899598 + 11.2265060240964X[t] -7.4573101931536M1[t] -0.263817173455726M2[t] + 17.7868187033849M3[t] + 5.12316886593993M4[t] + 8.93094759992352M5[t] + 21.7101549053356M6[t] -18.2001386498374M7[t] -24.4066456301396M8[t] + 3.42970453241538M9[t] + 4.92015681774718M10[t] -1.06492159112641M11[t] + 0.33507840887359t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)97.05562248995982.90247733.438900
X11.22650602409642.4163814.6461.6e-058e-06
M1-7.45731019315363.442468-2.16630.0338520.016926
M2-0.2638171734557263.440839-0.07670.9391130.469556
M317.78681870338493.4396715.17112e-061e-06
M45.123168865939933.4389641.48970.1409850.070492
M58.930947599923523.438722.59720.0115440.005772
M621.71015490533563.4389376.31300
M7-18.20013864983743.448464-5.27782e-061e-06
M8-24.40664563013963.446921-7.080700
M93.429704532415383.4458380.99530.3231630.161581
M104.920156817747183.5691441.37850.1726270.086313
M11-1.064921591126413.568476-0.29840.7663030.383151
t0.335078408873590.0398558.407400


Multiple Linear Regression - Regression Statistics
Multiple R0.946900247831163
R-squared0.896620079342718
Adjusted R-squared0.876561288767424
F-TEST (value)44.6996081831119
F-TEST (DF numerator)13
F-TEST (DF denominator)67
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation6.18039698072037
Sum Squared Residuals2559.21955823293


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
197.789.933390705687.76660929432007
2101.597.46196213425134.0380378657487
3119.6115.8476764199663.75232358003445
4108.1103.5191049913944.58089500860584
5117.8107.66196213425110.1380378657488
6125.5120.7762478485374.72375215146305
789.281.20103270223757.99896729776248
892.375.32960413080916.9703958691910
9104.6103.5010327022381.09896729776248
10122.8105.32656339644317.4734366035571
119699.6765633964429-3.67656339644291
1294.6101.076563396443-6.47656339644294
1393.393.954331612163-0.65433161216293
14101.1101.482903040734-0.382903040734384
15114.2119.868617326449-5.66861732644865
16104.7107.540045897877-2.84004589787722
17113.3111.6829030407341.61709695926563
18118.2124.79718875502-6.59718875502009
1983.685.2219736087206-1.62197360872060
2073.979.350545037292-5.45054503729202
2199.5107.521973608721-8.0219736087206
2297.7109.347504302926-11.6475043029260
23103103.697504302926-0.697504302925992
24106.3105.0975043029261.20249569707401
2592.297.975272518646-5.775272518646
26101.8105.503843947217-3.70384394721745
27122.8123.889558232932-1.08955823293173
28111.8111.5609868043600.239013195639700
29106.3115.703843947217-9.40384394721745
30121.5128.818129661503-7.31812966150317
3181.989.2429145152037-7.34291451520367
3285.483.37148594377512.02851405622491
33110.9111.542914515204-0.64291451520367
34117.3113.3684452094093.93155479059094
35106.3107.718445209409-1.41844520940907
36105.5109.118445209409-3.61844520940906
37101.3101.996213425129-0.696213425129082
38105.9109.524784853701-3.62478485370051
39126.3127.910499139415-1.61049913941481
40111.9115.581927710843-3.68192771084337
41108.9119.724784853701-10.8247848537005
42127.2132.839070567986-5.63907056798624
4394.293.26385542168670.936144578313256
4485.787.3924268502582-1.69242685025817
45116.2115.5638554216870.63614457831325
46107.2117.389386115892-10.1893861158921
47110.6111.739386115892-1.13938611589215
48112113.139386115892-1.13938611589214
49104.5106.017154331612-1.51715433161215
50112113.545725760184-1.54572576018359
51132.8131.9314400458980.868559954102127
52110.8119.602868617326-8.80286861732645
53128.7123.7457257601844.95427423981639
54136.8136.860011474469-0.0600114744693075
5594.997.2847963281698-2.38479632816982
5688.891.4133677567413-2.61336775674126
57123.2119.5847963281703.61520367183018
58125.3121.4103270223753.88967297762478
59122.7115.7603270223756.93967297762479
60125.7117.1603270223758.53967297762478
61116.3110.0380952380956.26190476190477
62118.7117.5666666666671.13333333333333
63142135.9523809523816.04761904761904
64127.9123.6238095238104.27619047619048
65131.9127.7666666666674.13333333333333
66152.3140.88095238095211.4190476190476
67110.8112.532243258749-1.73224325874929
6899.1106.660814687321-7.56081468732072
69135134.8322432587490.167756741250714
70133.2136.657773952955-3.45777395295468
71131131.007773952955-0.00777395295467587
72133.9132.4077739529551.49222604704533
73119.9125.285542168675-5.38554216867468
74136.9132.8141135972464.08588640275388
75148.9151.199827882960-2.29982788296041
76145.1138.8712564543896.22874354561101
77142.4143.014113597246-0.614113597246129
78159.6156.1283993115323.47160068846814
79120.7116.5531841652324.14681583476765
80109110.681755593804-1.68175559380379
81142138.8531841652323.14681583476764


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.06795006613307890.1359001322661580.93204993386692
180.05626816164825770.1125363232965150.943731838351742
190.02447000811056630.04894001622113270.975529991889434
200.5287563007291830.9424873985416340.471243699270817
210.4134593140691420.8269186281382840.586540685930858
220.9089994989050260.1820010021899480.0910005010949741
230.9654199219389530.06916015612209320.0345800780610466
240.9932042436720180.01359151265596400.00679575632798202
250.9888552946787070.02228941064258690.0111447053212934
260.9863385521186660.02732289576266810.0136614478813340
270.990676210020090.01864757995981790.00932378997990894
280.993737126317150.01252574736570060.0062628736828503
290.9914384721785450.01712305564291020.0085615278214551
300.9866578966857590.02668420662848260.0133421033142413
310.9790823500026790.0418352999946420.020917649997321
320.988372800287990.02325439942402160.0116271997120108
330.9914300617515680.01713987649686310.00856993824843156
340.9985510035436060.002897992912787010.00144899645639350
350.998349293576190.003301412847619350.00165070642380967
360.997412286124070.005175427751859740.00258771387592987
370.998030556647310.003938886705380830.00196944335269041
380.996976822169050.006046355661901720.00302317783095086
390.9968190645372130.006361870925573930.00318093546278696
400.9956746854932460.008650629013507350.00432531450675367
410.995372194058620.00925561188275960.0046278059413798
420.9932523955026170.01349520899476620.0067476044973831
430.993981105919060.01203778816188220.00601889408094108
440.9956541273323810.008691745335237710.00434587266761886
450.99600834655230.007983306895401410.00399165344770071
460.9967414752612970.006517049477405740.00325852473870287
470.9948060981344250.01038780373114920.00519390186557461
480.9925394076291730.01492118474165460.0074605923708273
490.988377461456440.02324507708712050.0116225385435603
500.981255605838880.03748878832223870.0187443941611193
510.9769725965323170.04605480693536580.0230274034676829
520.9927621832933760.01447563341324710.00723781670662353
530.9969841468885070.00603170622298520.0030158531114926
540.9959465553791890.008106889241622160.00405344462081108
550.9966204073838570.006759185232285120.00337959261614256
560.9925441261136880.01491174777262500.00745587388631249
570.9867920930320.02641581393600090.0132079069680004
580.976696553037880.04660689392423920.0233034469621196
590.9633393059307440.0733213881385110.0366606940692555
600.9453162702010810.1093674595978380.0546837297989192
610.9605502751009450.07889944979810920.0394497248990546
620.969607659961470.06078468007706020.0303923400385301
630.9530221179646580.09395576407068480.0469778820353424
640.988161334176820.02367733164636030.0118386658231801


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.291666666666667NOK
5% type I error level370.770833333333333NOK
10% type I error level420.875NOK
 
Charts produced by software:
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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)
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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