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SHWWS7model1c

*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 09:11:14 -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/t12586471341bo6ws0mn443swp.htm/, Retrieved Thu, 19 Nov 2009 17:12:26 +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/t12586471341bo6ws0mn443swp.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 «
161 0 149 0 139 0 135 0 130 0 127 0 122 0 117 0 112 0 113 0 149 0 157 0 157 0 147 0 137 0 132 0 125 0 123 0 117 0 114 0 111 0 112 0 144 0 150 0 149 0 134 0 123 0 116 0 117 0 111 0 105 0 102 0 95 0 93 0 124 0 130 0 124 0 115 0 106 0 105 0 105 0 101 0 95 0 93 0 84 0 87 0 116 0 120 0 117 0 109 0 105 0 107 0 109 1 109 1 108 1 107 1 99 1 103 1 131 1 137 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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 120.538461538462 -7.66346153846155X[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)120.5384615384622.54897647.28900
X-7.663461538461556.980659-1.09780.2768230.138411


Multiple Linear Regression - Regression Statistics
Multiple R0.142675247853586
R-squared0.0203562263500823
Adjusted R-squared0.00346581645956656
F-TEST (value)1.20519433702509
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.276822685864108
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation18.3809299964163
Sum Squared Residuals19595.7980769231


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1161120.53846153846140.4615384615387
2149120.53846153846228.4615384615385
3139120.53846153846218.4615384615385
4135120.53846153846214.4615384615385
5130120.5384615384629.46153846153845
6127120.5384615384626.46153846153845
7122120.5384615384621.46153846153845
8117120.538461538462-3.53846153846155
9112120.538461538462-8.53846153846155
10113120.538461538462-7.53846153846155
11149120.53846153846228.4615384615385
12157120.53846153846236.4615384615385
13157120.53846153846236.4615384615385
14147120.53846153846226.4615384615385
15137120.53846153846216.4615384615385
16132120.53846153846211.4615384615385
17125120.5384615384624.46153846153845
18123120.5384615384622.46153846153845
19117120.538461538462-3.53846153846155
20114120.538461538462-6.53846153846155
21111120.538461538462-9.53846153846155
22112120.538461538462-8.53846153846155
23144120.53846153846223.4615384615385
24150120.53846153846229.4615384615385
25149120.53846153846228.4615384615385
26134120.53846153846213.4615384615385
27123120.5384615384622.46153846153845
28116120.538461538462-4.53846153846155
29117120.538461538462-3.53846153846155
30111120.538461538462-9.53846153846155
31105120.538461538462-15.5384615384615
32102120.538461538462-18.5384615384615
3395120.538461538462-25.5384615384615
3493120.538461538462-27.5384615384615
35124120.5384615384623.46153846153845
36130120.5384615384629.46153846153845
37124120.5384615384623.46153846153845
38115120.538461538462-5.53846153846155
39106120.538461538462-14.5384615384615
40105120.538461538462-15.5384615384615
41105120.538461538462-15.5384615384615
42101120.538461538462-19.5384615384615
4395120.538461538462-25.5384615384615
4493120.538461538462-27.5384615384615
4584120.538461538462-36.5384615384615
4687120.538461538462-33.5384615384615
47116120.538461538462-4.53846153846155
48120120.538461538462-0.538461538461546
49117120.538461538462-3.53846153846155
50109120.538461538462-11.5384615384615
51105120.538461538462-15.5384615384615
52107120.538461538462-13.5384615384615
53109112.875-3.875
54109112.875-3.875
55108112.875-4.875
56107112.875-5.875
5799112.875-13.875
58103112.875-9.875
59131112.87518.125
60137112.87524.125


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.4209369662679540.8418739325359080.579063033732046
60.3752784718134650.7505569436269290.624721528186535
70.3700909717681820.7401819435363640.629909028231818
80.3942407443118860.7884814886237710.605759255688114
90.4424741403000470.8849482806000950.557525859699953
100.4362083180245510.8724166360491030.563791681975448
110.4633737214173590.9267474428347180.536626278582641
120.5996138490233010.8007723019533980.400386150976699
130.7206945409617360.5586109180765280.279305459038264
140.7317570392323950.5364859215352090.268242960767605
150.6919638468916380.6160723062167250.308036153108362
160.6435437958314060.7129124083371880.356456204168594
170.6016872499253910.7966255001492190.398312750074609
180.5636259211141360.8727481577717270.436374078885864
190.552291825222440.895416349555120.44770817477756
200.5523774882838870.8952450234322250.447622511716113
210.5639489628443080.8721020743113840.436051037155692
220.5551854306557620.8896291386884750.444814569344238
230.6143500691404830.7712998617190330.385649930859517
240.7681114333060850.4637771333878310.231888566693915
250.9013440146223040.1973119707553930.0986559853776963
260.9227411673426440.1545176653147110.0772588326573555
270.9194407734503510.1611184530992980.0805592265496492
280.9133504336136520.1732991327726950.0866495663863475
290.9057597496637910.1884805006724170.0942402503362085
300.9006042522486760.1987914955026480.0993957477513242
310.9053216568929390.1893566862141230.0946783431070615
320.9136751094550690.1726497810898630.0863248905449314
330.9401906091152690.1196187817694620.0598093908847312
340.9612993806558780.0774012386882440.038700619344122
350.9585953827870780.08280923442584480.0414046172129224
360.9719230502912140.05615389941757270.0280769497087863
370.9760111925827590.04797761483448260.0239888074172413
380.9709213037888350.05815739242233010.0290786962111650
390.9616208753448410.0767582493103170.0383791246551585
400.949368266662610.1012634666747820.0506317333373911
410.9327986421304140.1344027157391720.0672013578695859
420.9153018943521350.169396211295730.084698105647865
430.9096702405831880.1806595188336240.0903297594168118
440.9110464833829580.1779070332340830.0889535166170417
450.9590535713549480.08189285729010330.0409464286450517
460.9848231053981620.03035378920367660.0151768946018383
470.9723455718121920.05530885637561480.0276544281878074
480.9588820510707130.08223589785857490.0411179489292874
490.9378154668432130.1243690663135740.0621845331567871
500.895008357412330.2099832851753400.104991642587670
510.8314743018995390.3370513962009230.168525698100462
520.7392610078000390.5214779843999210.260738992199961
530.619728585094270.7605428298114590.380271414905730
540.4784099265912220.9568198531824440.521590073408778
550.3332991480509060.6665982961018130.666700851949094


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0392156862745098OK
10% type I error level100.196078431372549NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/1065l41258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/1065l41258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/1cb9g1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/1cb9g1258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/22nil1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/22nil1258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/37eam1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/37eam1258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/4n8k91258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/4n8k91258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/5hqee1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/5hqee1258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/6s7l11258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/6s7l11258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/7payw1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/7payw1258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/8d4so1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/8d4so1258647070.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/9yxty1258647070.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t12586471341bo6ws0mn443swp/9yxty1258647070.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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