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*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, 02 Dec 2010 22:23:09 +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/02/t1291328480engv4la2tdvizg6.htm/, Retrieved Thu, 02 Dec 2010 23:21:30 +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/02/t1291328480engv4la2tdvizg6.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 «
-820.8 0 993.3 0 741.7 0 603.6 0 -145.8 0 -35.1 0 395.1 0 523.1 0 462.3 0 183.4 0 791.5 0 344.8 0 -217.0 0 406.7 0 228.6 0 -580.1 0 -1550.4 0 -1447.5 0 -40.1 0 -1033.5 0 -925.6 0 -347.8 0 -447.7 0 -102.6 0 -2062.2 0 -929.7 1 -720.7 1 -1541.8 1 -1432.3 1 -1216.2 1 -212.8 1 -378.2 1 76.9 1 -101.3 1 220.4 1 495.6 1 -1035.2 1 61.8 1 -734.8 1 -6.9 1 -1061.1 1 -854.6 1 -186.5 1 244.0 1 -992.6 1 -335.2 1 316.8 1 477.6 1 -572.1 1 1115.2 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 time11 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Totaal[t] = + 752.928125 + 197.798958333334Dummy[t] -1316.85970486111M1[t] -67.2335763888896M2[t] -589.543281250001M3[t] -831.277361111111M4[t] -1479.11144097222M5[t] -1301.79552083333M6[t] -406.254600694444M7[t] -538.063680555555M8[t] -703.397760416667M9[t] -490.606840277778M10[t] -101.865920138889M11[t] -18.2659201388889t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)752.928125397.4390331.89440.0662210.03311
Dummy197.798958333334376.5062910.52540.6025580.301279
M1-1316.85970486111419.950077-3.13580.0034060.001703
M2-67.2335763888896427.418418-0.15730.8758860.437943
M3-589.543281250001456.655946-1.2910.2049320.102466
M4-831.277361111111453.398425-1.83340.0750160.037508
M5-1479.11144097222450.504582-3.28320.0022890.001144
M6-1301.79552083333447.981463-2.90590.0062280.003114
M7-406.254600694444445.835364-0.91120.368240.18412
M8-538.063680555555444.07175-1.21170.2335360.116768
M9-703.397760416667442.695193-1.58890.1208280.060414
M10-490.606840277778441.709312-1.11070.2740610.13703
M11-101.865920138889441.116725-0.23090.8186790.409339
t-18.265920138888913.205438-1.38320.1751190.087559


Multiple Linear Regression - Regression Statistics
Multiple R0.68542514570994
R-squared0.469807630371493
Adjusted R-squared0.27834927467231
F-TEST (value)2.45383717339372
F-TEST (DF numerator)13
F-TEST (DF denominator)36
p-value0.0167757306492929
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation623.553657493665
Sum Squared Residuals13997489.8958542


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1-820.8-582.1975-238.602500000001
2993.3649.162708333334344.137291666666
3741.7108.587083333333633.112916666667
4603.6-151.412916666667755.012916666667
5-145.8-817.512916666667671.712916666667
6-35.1-658.462916666668623.362916666668
7395.1218.812083333333176.287916666667
8523.168.737083333333454.362916666667
9462.3-114.862916666666577.162916666666
10183.479.6620833333334103.737916666667
11791.5450.137083333334341.362916666666
12344.8533.737083333333-188.937083333333
13-217-801.388541666666584.388541666666
14406.7429.971666666667-23.2716666666672
15228.6-110.603958333334339.203958333334
16-580.1-370.603958333333-209.496041666668
17-1550.4-1036.70395833333-513.696041666667
18-1447.5-877.653958333333-569.846041666667
19-40.1-0.378958333333365-39.7210416666666
20-1033.5-150.453958333334-883.046041666666
21-925.6-334.053958333334-591.546041666666
22-347.8-139.528958333333-208.271041666667
23-447.7230.946041666667-678.646041666667
24-102.6314.546041666666-417.146041666666
25-2062.2-1020.57958333333-1041.62041666667
26-929.7408.579583333332-1338.27958333333
27-720.7-131.996041666667-588.703958333333
28-1541.8-391.996041666666-1149.80395833333
29-1432.3-1058.09604166667-374.203958333334
30-1216.2-899.046041666666-317.153958333334
31-212.8-21.7710416666668-191.028958333333
32-378.2-171.846041666667-206.353958333333
3376.9-355.446041666667432.346041666667
34-101.3-160.92104166666759.6210416666668
35220.4209.55395833333310.8460416666666
36495.6293.153958333333202.446041666667
37-1035.2-1041.971666666676.77166666666657
3861.8189.388541666666-127.588541666666
39-734.8-351.187083333334-383.612916666666
40-6.9-611.187083333333604.287083333333
41-1061.1-1277.28708333333216.187083333333
42-854.6-1118.23708333333263.637083333333
43-186.5-240.96208333333354.4620833333332
44244-391.037083333333635.037083333333
45-992.6-574.637083333333-417.962916666667
46-335.2-380.11208333333344.9120833333333
47316.8-9.63708333333312326.437083333333
48477.673.9629166666666403.637083333333
49-572.1-1261.16270833333689.062708333333
501115.2-29.80250000000051145.0025


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.8451413981052360.3097172037895280.154858601894764
180.8052504873832540.3894990252334920.194749512616746
190.7493778142892330.5012443714215330.250622185710767
200.732375060798060.535249878403880.26762493920194
210.6579720067582430.6840559864835150.342027993241757
220.5956408807207740.8087182385584510.404359119279226
230.4937429380557310.9874858761114630.506257061944269
240.423457165115320.846914330230640.57654283488468
250.3167062062427250.633412412485450.683293793757275
260.349987904642720.699975809285440.65001209535728
270.2650270048007650.530054009601530.734972995199235
280.4180177058658570.8360354117317130.581982294134143
290.3923392875806770.7846785751613540.607660712419323
300.336593781624980.673187563249960.66340621837502
310.2577672338929130.5155344677858260.742232766107087
320.2353073399562560.4706146799125130.764692660043744
330.5529790631537840.8940418736924310.447020936846216


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/10mrrq1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/10mrrq1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/1qhth1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/1qhth1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/2qhth1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/2qhth1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/3qhth1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/3qhth1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/4j8ak1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/4j8ak1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/5j8ak1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/5j8ak1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/6j8ak1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/6j8ak1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/7uzr51291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/7uzr51291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/8mrrq1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/8mrrq1291328577.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/9mrrq1291328577.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291328480engv4la2tdvizg6/9mrrq1291328577.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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