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metallurgie

*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 02:20:31 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t1229764889x9o5ejuzalaejln.htm/, Retrieved Sat, 20 Dec 2008 10:21:38 +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/t1229764889x9o5ejuzalaejln.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 «
99,9 11554,5 98,6 13182,1 107,2 14800,1 95,7 12150,7 93,7 14478,2 106,7 13253,9 86,7 12036,8 95,3 12653,2 99,3 14035,4 101,8 14571,4 96 15400,9 91,7 14283,2 95,3 14485,3 96,6 14196,3 107,2 15559,1 108 13767,4 98,4 14634 103,1 14381,1 81,1 12509,9 96,6 12122,3 103,7 13122,3 106,6 13908,7 97,6 13456,5 87,6 12441,6 99,4 12953 98,5 13057,2 105,2 14350,1 104,6 13830,2 97,5 13755,5 108,9 13574,4 86,8 12802,6 88,9 11737,3 110,3 13850,2 114,8 15081,8 94,6 13653,3 92 14019,1 93,8 13962 93,8 13768,7 107,6 14747,1 101 13858,1 95,4 13188 96,5 13693,1 89,2 12970 87,1 11392,8 110,5 13985,2 110,8 14994,7 104,2 13584,7 88,9 14257,8 89,8 13553,4 90 14007,3 93,9 16535,8 91,3 14721,4 87,8 13664,6 99,7 16405,9 73,5 13829,4 79,2 13735,6 96,9 15870,5 95,2 15962,4 95,6 15744,1 89,7 16083,7 92,8 14863,9 88 15533,1 101,1 17473,1 92,7 15925,5 95,8 15573,7 103,8 17495 81,8 14155,8 87,1 14913,9 105,9 17250,4 108,1 15879,8 102,6 17647,8 93,7 17749,9
 
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 time10 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
metallurgie[t] = + 104.813231738284 -0.000959971885384542Invoer[t] + 3.3725896374997M1[t] + 2.83552785337691M2[t] + 13.8407783048884M3[t] + 7.550234803528M4[t] + 3.60007526038129M5[t] + 12.5115628161427M6[t] -9.10154532176792M7[t] -3.53144112448322M8[t] + 13.7179287131787M9[t] + 15.8668193404665M10[t] + 7.93765027821178M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)104.8132317382847.60917813.774600
Invoer-0.0009599718853845420.000495-1.93980.0571940.028597
M13.37258963749972.9663631.13690.2601580.130079
M22.835527853376912.9320080.96710.3374450.168722
M313.84077830488842.9268094.7291.4e-057e-06
M47.5502348035282.9262952.58010.0123850.006193
M53.600075260381292.9164511.23440.2219470.110973
M612.51156281614272.9017894.31176.2e-053.1e-05
M7-9.101545321767923.028999-3.00480.0038970.001948
M8-3.531441124483223.073487-1.1490.2551920.127596
M913.71792871317872.9023974.72641.5e-057e-06
M1015.86681934046652.9046525.46261e-060
M117.937650278211782.9022862.7350.0082260.004113


Multiple Linear Regression - Regression Statistics
Multiple R0.831100331319258
R-squared0.69072776071898
Adjusted R-squared0.627824932390637
F-TEST (value)10.9808696854375
F-TEST (DF numerator)12
F-TEST (DF denominator)59
p-value4.7020498605832e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.02604329013604
Sum Squared Residuals1490.40555810497


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
199.997.09382622610752.80617377389250
298.694.9943142013333.60568579866708
3107.2104.4463301422922.75366985770778
495.7100.699136154070-4.99913615406962
593.794.5146420476904-0.81464204769037
6106.7104.6014231827282.09857681727191
786.784.1566968265192.54330317348102
895.389.13507435365276.16492564634733
999.3105.057571051336-5.75757105133607
10101.8106.691916748058-4.8919167480577
119697.9664510068766-1.96645100687657
1291.791.1017613049590.598238695040923
1395.394.28034062442251.01965937557744
1496.694.02071071517592.57928928482409
15107.2103.7177114812853.48228851871466
1610899.14714960696848.85285039303157
1798.494.36507842794754.03492157205254
18103.1103.519342873523-0.419342873522644
1981.183.7025341275436-2.60253412754357
2096.689.64472342760336.95527657239667
21103.7105.934121379881-2.23412137988068
22106.6107.328090116502-0.72809011650205
2397.699.8330203408183-2.23302034081827
2487.692.8696455290833-5.26964552908326
2599.495.75130554439733.64869445560272
2698.595.11421468981743.38578531018257
27105.2104.8783174907150.321682509284746
28104.699.08686337256635.51313662743371
2997.595.20841372925782.29158627074221
30108.9104.2937521934624.60624780653766
3186.883.42155035669153.37844964330849
3288.990.0143126034764-1.11431260347636
33110.3105.2353578445095.06464215549073
34114.8106.2019470977578.59805290224256
3594.699.6440978737746-5.04409787377459
369291.35528987988910.644710120110867
3793.894.7826939120443-0.982693912044286
3893.894.4311946933663-0.631194693366333
39107.6104.4972086522183.10279134778240
4010199.0600801569641.93991984303595
4195.495.7531977742135-0.353197774213514
4296.5104.179803530667-7.6798035306672
4389.283.26085106307815.93914893692187
4487.190.3450229179913-3.24502291799135
45110.5105.1057616399825.39423836001764
46110.8106.2855606489744.51443935102557
47104.299.7099519451124.49004805488804
4888.991.1261445908478-2.22614459084784
4989.895.1749384244124-5.37493842441241
509094.2021454015136-4.20214540151358
5193.9102.780106940830-8.88010694083026
5291.398.2313364283116-6.93133642831158
5387.895.2956751736392-7.49567517363925
5499.7101.575591799996-1.87559179999601
5573.582.4358512247787-8.93585122477866
5679.288.0960007849124-8.89600078491244
5796.9103.295926644467-6.39592664446688
5895.2105.356595855488-10.1565958554878
5995.697.6369886558126-2.03698865581258
6089.789.37333192532420.326668074675799
6192.893.916895268616-1.11689526861597
628892.7374202987938-4.73742029879384
63101.1101.880325292659-0.780325292659332
6492.797.07543428112-4.37543428112004
6595.893.46299284725162.33700715274838
66103.8100.5300864196243.26991358037629
6781.882.1225164013891-0.322516401389145
6887.186.96486591236380.135134087636160
69105.9101.9712614398253.92873856017526
70108.1105.4358895332212.66411046677942
71102.695.8094901776066.79050982239397
7293.787.77382676989655.92617323010352


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.6258062403531450.748387519293710.374193759646855
170.5214075134384340.9571849731231330.478592486561566
180.4073207800526430.8146415601052850.592679219947357
190.3493396245962760.6986792491925530.650660375403724
200.2768077654068740.5536155308137470.723192234593126
210.218212529169230.436425058338460.78178747083077
220.1711796062521770.3423592125043540.828820393747823
230.1113763479077720.2227526958155440.888623652092228
240.0984583341440450.196916668288090.901541665855955
250.06880159692866280.1376031938573260.931198403071337
260.04635815795911280.09271631591822560.953641842040887
270.02949325787399520.05898651574799040.970506742126005
280.02517961107878430.05035922215756850.974820388921216
290.01560401148028850.0312080229605770.984395988519712
300.01455409012205760.02910818024411510.985445909877942
310.01049661962316080.02099323924632160.98950338037684
320.01500072000651320.03000144001302640.984999279993487
330.02958885919172860.05917771838345710.970411140808271
340.08510678551061070.1702135710212210.91489321448939
350.0732558288152870.1465116576305740.926744171184713
360.04932870327765360.09865740655530720.950671296722346
370.04227427224121580.08454854448243170.957725727758784
380.03520865441318160.07041730882636310.964791345586818
390.03579975887604460.07159951775208930.964200241123955
400.03744627943975010.07489255887950010.96255372056025
410.02537136141169320.05074272282338630.974628638588307
420.04671913812114240.09343827624228480.953280861878858
430.08062350342657240.1612470068531450.919376496573428
440.07862189761077560.1572437952215510.921378102389224
450.1491928448719980.2983856897439960.850807155128002
460.2333110237259050.4666220474518110.766688976274095
470.520574871357230.958850257285540.47942512864277
480.5095453824516100.9809092350967790.490454617548390
490.4723343149803170.9446686299606340.527665685019683
500.5657221842537540.8685556314924920.434277815746246
510.6085190978339840.7829618043320320.391480902166016
520.5873356424370630.8253287151258730.412664357562936
530.503837764785410.992324470429180.49616223521459
540.3733362810094000.7466725620187990.6266637189906
550.3982822982389270.7965645964778530.601717701761073
560.3028607541905800.6057215083811590.69713924580942


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.097560975609756NOK
10% type I error level150.365853658536585NOK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229764889x9o5ejuzalaejln/8em191229764819.ps (open in new window)


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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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