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Multiple regression model 3

*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, 21 Dec 2010 17:06:28 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml.htm/, Retrieved Tue, 21 Dec 2010 18:05:31 +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/2010/Dec/21/t12929511203dqzucaq9blrnml.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
1038.00 0 934.00 0 988.00 0 870.00 0 854.00 0 834.00 0 872.00 0 954.00 0 870.00 0 1238.00 0 1082.00 0 1053.00 0 934.00 0 787.00 0 1081.00 0 908.00 0 995.00 0 825.00 0 822.00 0 856.00 0 887.00 0 1094.00 0 990.00 0 936.00 0 1097.00 0 918.00 0 926.00 0 907.00 0 899.00 0 971.00 0 1087.00 0 1000.00 0 1071.00 0 1190.00 0 1116.00 0 1070.00 0 1314.00 0 1068.00 0 1185.00 0 1215.00 0 1145.00 0 1251.00 1 1363.00 1 1368.00 1 1535.00 1 1853.00 1 1866.00 1 2023.00 1 1373.00 1 1968.00 1 1424.00 1 1160.00 1 1243.00 1 1375.00 1 1539.00 1 1773.00 1 1906.00 1 2076.00 1 2004.00 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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Asielaanvragen[t] = + 980.866071428572 + 433.157738095238Verandering[t] -67.4180307539678M1[t] -89.6628472222222M2[t] -109.907663690476M3[t] -224.75248015873M4[t] -215.597296626984M5[t] -284.273660714286M6[t] -204.918477182540M7[t] -157.363293650794M8[t] -99.8081101190475M9[t] + 130.547073412699M10[t] + 45.9022569444446M11[t] + 6.04481646825396t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)980.86607142857295.98455610.21900
Verandering433.15773809523878.7140445.50292e-061e-06
M1-67.4180307539678110.81713-0.60840.5460.273
M2-89.6628472222222110.695264-0.810.4222050.211102
M3-109.907663690476110.613691-0.99360.3257220.162861
M4-224.75248015873110.572502-2.03260.0480160.024008
M5-215.597296626984110.571741-1.94980.0574420.028721
M6-284.273660714286111.170147-2.55710.0139970.006998
M7-204.918477182540111.011432-1.84590.0714880.035744
M8-157.363293650794110.892817-1.41910.1627720.081386
M9-99.8081101190475110.814429-0.90070.3725550.186277
M10130.547073412699110.7763541.17850.2448020.122401
M1145.9022569444446110.7786330.41440.6805790.340289
t6.044816468253962.1144922.85880.0064230.003211


Multiple Linear Regression - Regression Statistics
Multiple R0.91005535453701
R-squared0.828200748321482
Adjusted R-squared0.778569853392133
F-TEST (value)16.6872015807984
F-TEST (DF numerator)13
F-TEST (DF denominator)45
p-value4.51638726417514e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation164.785340947761
Sum Squared Residuals1221939.38660714


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11038919.492857142856118.507142857144
2934903.29285714285730.7071428571429
3988889.09285714285798.9071428571428
4870780.29285714285789.707142857143
5854795.49285714285758.5071428571426
6834732.86130952381101.13869047619
7872818.2613095238153.7386904761904
8954871.8613095238182.1386904761905
9870935.46130952381-65.4613095238097
1012381171.8613095238166.1386904761906
1110821093.26130952381-11.2613095238096
1210531053.40386904762-0.40386904761896
13934992.030654761905-58.0306547619052
14787975.830654761905-188.830654761905
151081961.630654761905119.369345238095
16908852.83065476190555.1693452380951
17995868.030654761905126.969345238095
18825805.39910714285719.6008928571429
19822890.799107142857-68.7991071428571
20856944.399107142857-88.3991071428572
218871007.99910714286-120.999107142857
2210941244.39910714286-150.399107142857
239901165.79910714286-175.799107142857
249361125.94166666667-189.941666666667
2510971064.5684523809532.4315476190473
269181048.36845238095-130.368452380952
279261034.16845238095-108.168452380952
28907925.368452380952-18.3684523809524
29899940.568452380952-41.5684523809524
30971877.93690476190593.0630952380954
311087963.336904761905123.663095238095
3210001016.93690476190-16.9369047619048
3310711080.53690476190-9.53690476190468
3411901316.93690476190-126.936904761905
3511161238.33690476190-122.336904761905
3610701198.47946428571-128.479464285714
3713141137.10625176.893750000000
3810681120.90625-52.90625
3911851106.7062578.2937500000002
401215997.90625217.09375
4111451013.10625131.89375
4212511383.63244047619-132.632440476190
4313631469.03244047619-106.032440476190
4413681522.63244047619-154.632440476190
4515351586.23244047619-51.2324404761905
4618531822.6324404761930.3675595238094
4718661744.03244047619121.967559523809
4820231704.175318.825
4913731642.80178571429-269.801785714286
5019681626.60178571429341.398214285714
5114241612.40178571429-188.401785714286
5211601503.60178571429-343.601785714286
5312431518.80178571429-275.801785714286
5413751456.17023809524-81.1702380952379
5515391541.57023809524-2.57023809523802
5617731595.17023809524177.829761904762
5719061658.77023809524247.229761904762
5820761895.17023809524180.829761904762
5920041816.57023809524187.429761904762


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2121690565909480.4243381131818960.787830943409052
180.1022566601337670.2045133202675350.897743339866233
190.04618999079247280.09237998158494560.953810009207527
200.02364987883431370.04729975766862740.976350121165686
210.009167711308852010.01833542261770400.990832288691148
220.006061945152548520.01212389030509700.993938054847451
230.002574940354757180.005149880709514360.997425059645243
240.001303825175416560.002607650350833110.998696174824584
250.001699135101260150.003398270202520300.99830086489874
260.0009069085491075720.001813817098215140.999093091450892
270.0004749813615473410.0009499627230946820.999525018638453
280.0001992992705898330.0003985985411796660.99980070072941
297.59769774509428e-050.0001519539549018860.99992402302255
300.0001091587165794410.0002183174331588820.99989084128342
310.0004359585848641620.0008719171697283230.999564041415136
320.0001938660567217760.0003877321134435520.999806133943278
330.0001632752114586920.0003265504229173850.999836724788541
347.72650041082006e-050.0001545300082164010.999922734995892
355.89521512398906e-050.0001179043024797810.99994104784876
360.0007065806141003230.001413161228200650.9992934193859
370.00179997069878230.00359994139756460.998200029301218
380.4434253805004930.8868507610009850.556574619499507
390.5278591704874760.9442816590250480.472140829512524
400.5553446628839350.889310674232130.444655337116065
410.4191350940807270.8382701881614530.580864905919273
420.3696012082111530.7392024164223050.630398791788847


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level150.576923076923077NOK
5% type I error level180.692307692307692NOK
10% type I error level190.730769230769231NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/103c491292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/103c491292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/1eb7x1292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/1eb7x1292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/2p2701292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/2p2701292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/3p2701292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/3p2701292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/4p2701292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/4p2701292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/5p2701292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/5p2701292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/60tol1292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/60tol1292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/7a2no1292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/7a2no1292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/8a2no1292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/8a2no1292951181.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/9a2no1292951181.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929511203dqzucaq9blrnml/9a2no1292951181.ps (open in new window)


 
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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