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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 18 Nov 2009 13:17:23 -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/18/t1258575549i7m5bsbf3jfxtgn.htm/, Retrieved Wed, 18 Nov 2009 21:19:21 +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/18/t1258575549i7m5bsbf3jfxtgn.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 «
944.2 0 930.9 874 891.9 902.2 935.9 0 944.2 930.9 874 891.9 937.1 0 935.9 944.2 930.9 874 885.1 0 937.1 935.9 944.2 930.9 892.4 0 885.1 937.1 935.9 944.2 987.3 0 892.4 885.1 937.1 935.9 946.3 0 987.3 892.4 885.1 937.1 799.6 0 946.3 987.3 892.4 885.1 875.4 0 799.6 946.3 987.3 892.4 846.2 0 875.4 799.6 946.3 987.3 880.6 0 846.2 875.4 799.6 946.3 885.7 0 880.6 846.2 875.4 799.6 868.9 0 885.7 880.6 846.2 875.4 882.5 0 868.9 885.7 880.6 846.2 789.6 0 882.5 868.9 885.7 880.6 773.3 0 789.6 882.5 868.9 885.7 804.3 0 773.3 789.6 882.5 868.9 817.8 0 804.3 773.3 789.6 882.5 836.7 0 817.8 804.3 773.3 789.6 721.8 0 836.7 817.8 804.3 773.3 760.8 0 721.8 836.7 817.8 804.3 841.4 0 760.8 721.8 836.7 817.8 1045.6 0 841.4 760.8 721.8 836.7 949.2 0 1045.6 841.4 760.8 721.8 850.1 0 949.2 1045.6 841.4 760.8 957.4 0 850.1 949.2 1045.6 841.4 851.8 0 957.4 850.1 949.2 1045.6 913.9 0 851.8 957.4 850.1 949.2 888 0 913.9 851.8 957.4 850.1 973.8 0 888 913.9 851.8 957.4 927.6 1 973.8 888 913.9 851.8 833 1 92 etc...
 
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] = + 216.239700723775 -49.088920369534X[t] + 0.371323296188282Y1[t] + 0.185849885726791Y2[t] + 0.235814478394152Y3[t] -0.129975533253905Y4[t] + 71.868552684524M1[t] + 90.2999304272343M2[t] + 1.57747955706059M3[t] + 52.3107421420012M4[t] + 28.1986325605593M5[t] + 146.712766884783M6[t] + 88.1853992603089M7[t] + 6.55743999523928M8[t] + 34.2452911491028M9[t] + 41.726930355377M10[t] + 173.295912043324M11[t] + 1.22679408189955t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)216.239700723775184.8019711.17010.2492410.12462
X-49.08892036953434.986374-1.40310.1687090.084355
Y10.3713232961882820.1591552.33310.0250370.012518
Y20.1858498857267910.1574211.18060.2451010.12255
Y30.2358144783941520.1645491.43310.1600080.080004
Y4-0.1299755332539050.164839-0.78850.4352950.217648
M171.86855268452448.5139741.48140.1467460.073373
M290.299930427234345.6240211.97920.055070.027535
M31.5774795570605946.5904160.03390.9731670.486584
M452.310742142001250.5450561.03490.3072420.153621
M528.198632560559347.7328370.59080.5581790.27909
M6146.71276688478350.6136122.89870.0061920.003096
M788.185399260308941.6529512.11710.0408510.020425
M86.5574399952392845.616480.14380.8864560.443228
M934.245291149102852.8664880.64780.5210290.260514
M1041.72693035537751.3463850.81270.4214780.210739
M11173.29591204332451.4275963.36970.0017370.000869
t1.226794081899551.1593871.05810.2966720.148336


Multiple Linear Regression - Regression Statistics
Multiple R0.755754198583511
R-squared0.571164408676605
Adjusted R-squared0.379316907295086
F-TEST (value)2.97717929378061
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0.00257148750707459
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation61.6353408099398
Sum Squared Residuals144358.778996782


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1944.2890.49171121515553.7082887848453
2935.9922.78101020618513.1189897938154
3937.1850.41957940558686.6804205944141
4885.1897.023394696815-11.9233946968148
5892.4851.36635289540541.0336471045945
6987.3965.5155216059921.7844783940093
7946.3932.39190952108913.9080904789111
8799.6862.883816771152-63.283816771152
9875.4851.13546174814724.2645382518527
10846.2838.7229509313177.47704906868335
11880.6945.498520673544-64.8985206735445
12885.7817.71825562839967.981744371601
13868.9882.362659084629-13.4626590846292
14882.5908.637737578255-26.1377375782554
15789.6819.801295033808-30.2012950338076
16773.3835.168417474024-61.868417474024
17804.3794.355743727429.94425627258015
18817.8898.903508882963-81.1035088829636
19836.7860.608097337924-23.9080973379241
20721.8799.162765932282-77.3627659322818
21760.8788.079181203698-27.2791812036976
22841.4792.61729511592848.7827048840723
231045.6933.038252955908112.561747044092
24949.2875.90380629395573.2961937060446
25850.1965.091735134906-114.991735134906
26957.4967.713127831015-10.3131278310154
27851.8852.369217440575-0.569217440575073
28913.9874.21965336523339.6803466347666
29888892.951235503389-4.95123550338862
30973.8975.767784805303-1.96778480530282
31927.6924.7938130857142.80618691428599
32833829.0043562085283.99564379147196
33879.5837.80480146179641.6951985382037
34797.3824.151839177976-26.8518391779758
35834.5918.763679667685-84.2636796676853
36735.1768.49198640887-33.3919864088699
37835786.1636008629148.8363991370910
38892.8843.89977876521948.9002212347813
39697.2768.15796309131-70.9579630913096
40821.1794.70674081574426.3932591842557
41732.7782.121665144887-49.4216651448865
42797.6838.426517213543-40.8265172135434
43866.3843.4363238728422.8636761271608
44826.3763.6567582612762.6432417387291
45778.6817.280555586359-38.6805555863589
46779.2808.60791477478-29.4079147747798
47951914.39954670286236.6004532971378
48692.3800.185951668776-107.885951668776
49841.4815.49029370240125.9097062975988
50857.3882.868345619326-25.568345619326
51760.7745.65194502872215.0480549712781
52841.2833.4817936481837.71820635181659
53810.3806.90500272893.39499727110049
541007.4905.2866674922102.113332507801
55931.3946.969856182434-15.6698561824337
56931.2857.19230282676774.0076971732328


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.04794355209054020.09588710418108050.95205644790946
220.01761473219377110.03522946438754220.982385267806229
230.1366975869895480.2733951739790960.863302413010452
240.4640688925258010.9281377850516020.535931107474199
250.4450856481662930.8901712963325860.554914351833707
260.3462658077089440.6925316154178880.653734192291056
270.3448529646768080.6897059293536150.655147035323193
280.7123644986644750.5752710026710510.287635501335525
290.648731181000730.7025376379985420.351268818999271
300.5621009104228110.8757981791543770.437899089577189
310.4476595256492630.8953190512985260.552340474350737
320.3604562690603780.7209125381207550.639543730939622
330.2507764200272990.5015528400545970.749223579972701
340.1771992284046270.3543984568092530.822800771595373
350.1805073019173740.3610146038347480.819492698082626


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0666666666666667NOK
10% type I error level20.133333333333333NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/10fpwj1258575439.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/1et441258575439.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/1et441258575439.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/2e1mw1258575439.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/4sqfk1258575439.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/6cowb1258575439.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/7ue981258575439.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/8q1mv1258575439.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/8q1mv1258575439.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/91e6v1258575439.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258575549i7m5bsbf3jfxtgn/91e6v1258575439.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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