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Consumptiegoederen met seizoenale 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: Tue, 16 Dec 2008 05:43:50 -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/16/t1229431486y9w96rahvlz7p2s.htm/, Retrieved Tue, 16 Dec 2008 13:44:56 +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/16/t1229431486y9w96rahvlz7p2s.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 «
98.5 0 97.0 0 103.3 0 99.6 0 100.1 0 102.9 0 95.9 0 94.5 0 107.4 0 116.0 0 102.8 0 99.8 0 109.6 0 103.0 0 111.6 0 106.3 0 97.9 0 108.8 0 103.9 0 101.2 0 122.9 0 123.9 0 111.7 0 120.9 0 99.6 0 103.3 0 119.4 0 106.5 0 101.9 0 124.6 0 106.5 0 107.8 0 127.4 0 120.1 0 118.5 0 127.7 0 107.7 0 104.5 0 118.8 0 110.3 0 109.6 0 119.1 0 96.5 0 106.7 0 126.3 0 116.2 0 118.8 0 115.2 0 110.0 0 111.4 0 129.6 0 108.1 0 117.8 0 122.9 0 100.6 0 111.8 0 127.0 0 128.6 0 124.8 0 118.5 0 114.7 0 112.6 0 128.7 0 111.0 0 115.8 0 126.0 0 111.1 1 113.2 1 120.1 1 130.6 1 124.0 1 119.4 1 116.7 1 116.5 1 119.6 1 126.5 1 111.3 1 123.5 1 114.2 1 103.7 1 129.5 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] = + 115.674051896208 + 7.4556886227545X[t] -8.62486455660116M1[t] -9.8391502708868M2[t] + 1.97513544339892M3[t] -6.98200741374394M4[t] -8.96772169945823M5[t] + 1.51799258625606M6[t] -13.704248645566M7[t] -12.2471057884231M8[t] + 5.13860849729114M9[t] + 5.65000000000001M10[t] -0.149999999999998M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)115.6740518962082.95917839.089900
X7.45568862275452.0842013.57720.0006450.000323
M1-8.624864556601164.005107-2.15350.0348310.017415
M2-9.83915027088684.005107-2.45670.0165820.008291
M31.975135443398924.0051070.49320.6234930.311746
M4-6.982007413743944.005107-1.74330.0858050.042903
M5-8.967721699458234.005107-2.23910.0284270.014213
M61.517992586256064.0051070.3790.7058580.352929
M7-13.7042486455664.012479-3.41540.0010780.000539
M8-12.24710578842314.012479-3.05230.0032390.00162
M95.138608497291144.0124791.28070.2046650.102333
M105.650000000000014.1559771.35950.1784830.089242
M11-0.1499999999999984.155977-0.03610.9713140.485657


Multiple Linear Regression - Regression Statistics
Multiple R0.734924625676036
R-squared0.540114205425062
Adjusted R-squared0.458957888735367
F-TEST (value)6.65523310391494
F-TEST (DF numerator)12
F-TEST (DF denominator)68
p-value1.01711674527216e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation7.19836379166195
Sum Squared Residuals3523.51800684347


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
198.5107.049187339607-8.54918733960694
297105.834901625321-8.8349016253208
3103.3117.649187339606-14.3491873396065
499.6108.692044482464-9.09204448246365
5100.1106.706330196749-6.60633019674938
6102.9117.192044482464-14.2920444824636
795.9101.969803250642-6.06980325064156
894.5103.426946107784-8.9269461077844
9107.4120.812660393499-13.4126603934987
10116121.324051896208-5.32405189620757
11102.8115.524051896208-12.7240518962076
1299.8115.674051896208-15.8740518962076
13109.6107.0491873396062.55081266039357
14103105.834901625321-2.83490162532078
15111.6117.649187339606-6.04918733960651
16106.3108.692044482464-2.39204448246365
1797.9106.706330196749-8.80633019674935
18108.8117.192044482464-8.39204448246365
19103.9101.9698032506421.93019674935843
20101.2103.426946107784-2.22694610778443
21122.9120.8126603934992.08733960650129
22123.9121.3240518962082.57594810379243
23111.7115.524051896208-3.82405189620758
24120.9115.6740518962085.22594810379243
2599.6107.049187339606-7.44918733960643
26103.3105.834901625321-2.53490162532078
27119.4117.6491873396061.75081266039351
28106.5108.692044482464-2.19204448246364
29101.9106.706330196749-4.80633019674935
30124.6117.1920444824647.40795551753635
31106.5101.9698032506424.53019674935842
32107.8103.4269461077844.37305389221556
33127.4120.8126603934996.58733960650129
34120.1121.324051896208-1.22405189620759
35118.5115.5240518962082.97594810379242
36127.7115.67405189620812.0259481037924
37107.7107.0491873396060.650812660393578
38104.5105.834901625321-1.33490162532078
39118.8117.6491873396061.15081266039350
40110.3108.6920444824641.60795551753635
41109.6106.7063301967492.89366980325064
42119.1117.1920444824641.90795551753635
4396.5101.969803250642-5.46980325064157
44106.7103.4269461077843.27305389221557
45126.3120.8126603934995.48733960650128
46116.2121.324051896208-5.12405189620758
47118.8115.5240518962083.27594810379242
48115.2115.674051896208-0.474051896207581
49110107.0491873396062.95081266039357
50111.4105.8349016253215.56509837467923
51129.6117.64918733960611.9508126603935
52108.1108.692044482464-0.592044482463647
53117.8106.70633019674911.0936698032506
54122.9117.1920444824645.70795551753636
55100.6101.969803250642-1.36980325064158
56111.8103.4269461077848.37305389221557
57127120.8126603934996.18733960650128
58128.6121.3240518962087.27594810379242
59124.8115.5240518962089.27594810379241
60118.5115.6740518962082.82594810379242
61114.7107.0491873396067.65081266039358
62112.6105.8349016253216.76509837467921
63128.7117.64918733960611.0508126603935
64111108.6920444824642.30795551753636
65115.8106.7063301967499.09366980325064
66126117.1920444824648.80795551753635
67111.1109.4254918733961.67450812660392
68113.2110.8826347305392.31736526946107
69120.1128.268349016253-8.16834901625322
70130.6128.7797405189621.82025948103792
71124122.9797405189621.02025948103792
72119.4123.129740518962-3.72974051896207
73116.7114.5048759623612.19512403763908
74116.5113.2905902480753.20940975192472
75119.6125.104875962361-5.504875962361
76126.5116.14773310521810.3522668947819
77111.3114.162018819504-2.86201881950385
78123.5124.647733105218-1.14773310521814
79114.2109.4254918733964.77450812660393
80103.7110.882634730539-7.18263473053893
81129.5128.2683490162531.23165098374679


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.7592013454682350.481597309063530.240798654531765
170.6661291176289150.6677417647421710.333870882371085
180.6536457610725490.6927084778549020.346354238927451
190.642183766945430.715632466109140.35781623305457
200.612803795822260.7743924083554790.387196204177740
210.8033665513597570.3932668972804860.196633448640243
220.780954299951890.438091400096220.21904570004811
230.8004043205528610.3991913588942780.199595679447139
240.9451321428528640.1097357142942730.0548678571471364
250.9490284552161350.1019430895677300.0509715447838651
260.9363487432202730.1273025135594540.063651256779727
270.952720739749810.09455852050038180.0472792602501909
280.9414878839022850.1170242321954290.0585121160977147
290.946285138182470.1074297236350590.0537148618175294
300.9825236132280220.03495277354395540.0174763867719777
310.9770914962613080.04581700747738420.0229085037386921
320.975064553538180.04987089292364170.0249354464618208
330.9781956082966490.04360878340670280.0218043917033514
340.9679483767548610.06410324649027710.0320516232451385
350.9679227298453140.06415454030937280.0320772701546864
360.9895119144941340.02097617101173220.0104880855058661
370.9861785752332410.02764284953351700.0138214247667585
380.9849226946879980.03015461062400370.0150773053120018
390.983489427739240.03302114452151960.0165105722607598
400.9782972606182180.04340547876356460.0217027393817823
410.976182035118840.04763592976231860.0238179648811593
420.970013411134950.05997317773010090.0299865888650504
430.9778007424812350.04439851503753010.0221992575187651
440.9677043543153030.06459129136939420.0322956456846971
450.9567954101301180.08640917973976320.0432045898698816
460.9738289097004370.05234218059912540.0261710902995627
470.9684239042406140.06315219151877280.0315760957593864
480.9530978766094730.09380424678105480.0469021233905274
490.9425306551346150.1149386897307700.0574693448653851
500.9286691621549330.1426616756901350.0713308378450674
510.9444600883814280.1110798232371430.0555399116185717
520.9555275010544480.08894499789110480.0444724989455524
530.9577266784236750.08454664315265040.0422733215763252
540.9391911872803190.1216176254393620.060808812719681
550.9638148060997240.07237038780055120.0361851939002756
560.950151276763170.09969744647365860.0498487232368293
570.9247674914343440.1504650171313130.0752325085656564
580.8891271503915620.2217456992168770.110872849608438
590.846344327158030.3073113456839390.153655672841970
600.7680479627752520.4639040744494950.231952037224748
610.6834264125412160.6331471749175690.316573587458784
620.5902996031889340.8194007936221320.409700396811066
630.6025155027926660.7949689944146680.397484497207334
640.800910797299350.3981784054012980.199089202700649
650.6604506883790710.6790986232418580.339549311620929


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level110.22NOK
10% type I error level240.48NOK
 
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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