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Multivariate regressie calculator

*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, 19 Nov 2009 01:22:38 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3.htm/, Retrieved Thu, 19 Nov 2009 09:28:15 +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/2009/Nov/19/t1258619281ury9902malyxgs3.htm/},
    year = {2009},
}
@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 = {2009},
    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 «
121.6 0 118.8 0 114.0 1 111.5 1 97.2 1 102.5 1 113.4 1 109.8 1 104.9 1 126.1 1 80.0 1 96.8 1 117.2 1 112.3 1 117.3 1 111.1 0 102.2 0 104.3 0 122.9 0 107.6 0 121.3 0 131.5 0 89.0 0 104.4 0 128.9 0 135.9 0 133.3 0 121.3 0 120.5 0 120.4 0 137.9 0 126.1 0 133.2 0 151.1 0 105.0 0 119.0 0 140.4 0 156.6 0 137.1 0 122.7 0 125.8 0 139.3 0 134.9 0 149.2 1 132.3 0 149.0 1 117.2 1 119.6 1 152.0 1 149.4 1 127.3 1 114.1 1 102.1 1 107.7 1 104.4 1 102.1 1 96.0 1 109.3 1 90.0 1 83.9 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 time9 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Promet[t] = + 124.4 -11.4241379310345Dummy[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)124.43.01590641.24800
Dummy-11.42413793103454.338049-2.63350.0108170.005408


Multiple Linear Regression - Regression Statistics
Multiple R0.32680517137013
R-squared0.106801620034260
Adjusted R-squared0.0914016479658856
F-TEST (value)6.93518271072625
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.0108165836382075
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation16.7918561457057
Sum Squared Residuals16354.0531034483


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1121.6124.4-2.7999999999999
2118.8124.4-5.59999999999997
3114112.9758620689661.02413793103448
4111.5112.975862068966-1.47586206896552
597.2112.975862068966-15.7758620689655
6102.5112.975862068966-10.4758620689655
7113.4112.9758620689660.42413793103449
8109.8112.975862068966-3.17586206896552
9104.9112.975862068966-8.0758620689655
10126.1112.97586206896613.1241379310345
1180112.975862068966-32.9758620689655
1296.8112.975862068966-16.1758620689655
13117.2112.9758620689664.22413793103449
14112.3112.975862068966-0.675862068965519
15117.3112.9758620689664.32413793103448
16111.1124.4-13.3
17102.2124.4-22.2
18104.3124.4-20.1
19122.9124.4-1.5
20107.6124.4-16.8
21121.3124.4-3.10000000000001
22131.5124.47.1
2389124.4-35.4
24104.4124.4-20
25128.9124.44.5
26135.9124.411.5
27133.3124.48.9
28121.3124.4-3.10000000000001
29120.5124.4-3.90000000000001
30120.4124.4-4
31137.9124.413.5
32126.1124.41.69999999999999
33133.2124.48.79999999999998
34151.1124.426.7
35105124.4-19.4
36119124.4-5.40000000000001
37140.4124.416
38156.6124.432.2
39137.1124.412.7
40122.7124.4-1.70000000000000
41125.8124.41.39999999999999
42139.3124.414.9
43134.9124.410.5
44149.2112.97586206896636.2241379310345
45132.3124.47.9
46149112.97586206896636.0241379310345
47117.2112.9758620689664.22413793103449
48119.6112.9758620689666.62413793103448
49152112.97586206896639.0241379310345
50149.4112.97586206896636.4241379310345
51127.3112.97586206896614.3241379310345
52114.1112.9758620689661.12413793103448
53102.1112.975862068966-10.8758620689655
54107.7112.975862068966-5.27586206896551
55104.4112.975862068966-8.5758620689655
56102.1112.975862068966-10.8758620689655
5796112.975862068966-16.9758620689655
58109.3112.975862068966-3.67586206896552
5990112.975862068966-22.9758620689655
6083.9112.975862068966-29.0758620689655


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.09399023504074770.1879804700814950.906009764959252
60.0392261376321970.0784522752643940.960773862367803
70.01963059450938010.03926118901876030.98036940549062
80.006674142884893430.01334828576978690.993325857115107
90.002312576815646770.004625153631293540.997687423184353
100.01162861471917970.02325722943835930.98837138528082
110.1209582041065330.2419164082130660.879041795893467
120.0959801253534690.1919602507069380.904019874646531
130.07571020563856470.1514204112771290.924289794361435
140.04836900345284770.09673800690569530.951630996547152
150.03523102750672620.07046205501345240.964768972493274
160.0243910176098260.0487820352196520.975608982390174
170.02525115682833390.05050231365666770.974748843171666
180.02033980350279470.04067960700558950.979660196497205
190.0151668490754960.0303336981509920.984833150924504
200.01083200074675890.02166400149351780.98916799925324
210.007253678103435770.01450735620687150.992746321896564
220.008268497962714450.01653699592542890.991731502037286
230.03819845375226670.07639690750453350.961801546247733
240.03807774942084060.07615549884168110.96192225057916
250.03676417107192590.07352834214385170.963235828928074
260.04671822380312970.09343644760625940.95328177619687
270.04554357353068090.09108714706136180.95445642646932
280.03214497765123320.06428995530246640.967855022348767
290.02239295764516140.04478591529032270.977607042354839
300.01547520368531880.03095040737063760.984524796314681
310.0171915358442470.0343830716884940.982808464155753
320.01170123392208970.02340246784417930.98829876607791
330.009252595106317920.01850519021263580.990747404893682
340.02321512340275260.04643024680550510.976784876597247
350.03221369104592260.06442738209184510.967786308954077
360.02499511423293340.04999022846586690.975004885767067
370.0235446766449290.0470893532898580.976455323355071
380.05915363498164250.1183072699632850.940846365018357
390.04646695716578120.09293391433156230.953533042834219
400.03222109814398740.06444219628797480.967778901856013
410.02155536339774880.04311072679549750.978444636602251
420.01631999438137720.03263998876275440.983680005618623
430.01066753013071350.02133506026142690.989332469869286
440.04801177258830370.09602354517660750.951988227411696
450.03129960573567530.06259921147135060.968700394264325
460.1057965865061380.2115931730122760.894203413493862
470.07169860038522370.1433972007704470.928301399614776
480.04825314544578160.09650629089156330.951746854554218
490.2396427224249960.4792854448499920.760357277575004
500.7769723663060140.4460552673879710.223027633693986
510.9124376220403650.1751247559192700.0875623779596351
520.9177282714104070.1645434571791850.0822717285895927
530.8523230283645140.2953539432709720.147676971635486
540.7965870329698060.4068259340603880.203412967030194
550.6903844064507470.6192311870985060.309615593549253


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0196078431372549NOK
5% type I error level210.411764705882353NOK
10% type I error level370.725490196078431NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/10yg0y1258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/10yg0y1258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/1i64j1258618947.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/1i64j1258618947.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/2eegc1258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/2eegc1258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/35lh21258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/35lh21258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/4tfq21258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/4tfq21258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/5m72d1258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/5m72d1258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/6l1651258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/6l1651258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/76v9h1258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/76v9h1258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/8s9rq1258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/8s9rq1258618948.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/9fqgc1258618948.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258619281ury9902malyxgs3/9fqgc1258618948.ps (open in new window)


 
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)
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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