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*Unverified author*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 26 Nov 2008 11:19:41 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u.htm/, Retrieved Wed, 26 Nov 2008 18:20:59 +0000
 
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/2008/Nov/26/t1227723650ebu64qh8kxxdj9u.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
147768 0 137507 0 136919 0 136151 1 133001 1 125554 1 119647 0 114158 0 116193 0 152803 0 161761 0 160942 0 149470 0 139208 0 134588 0 130322 1 126611 1 122401 1 117352 0 112135 0 112879 0 148729 0 157230 0 157221 0 146681 0 136524 0 132111 0 125326 1 122716 1 116615 1 113719 0 110737 0 112093 0 143565 0 149946 0 149147 0 134339 0 122683 0 115614 0 116566 1 111272 1 104609 1 101802 0 94542 0 93051 0 124129 0 130374 0 123946 0 114971 0 105531 0 104919 0 104782 1 101281 1 94545 1 93248 0 84031 0 87486 0 115867 0 120327 0 117008 0 108811 0
 
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'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
jonger_dan_25[t] = + 125298.086956522 -7181.28695652175winter[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)125298.0869565222803.34413444.695900
winter-7181.286956521755653.2176-1.27030.2089640.104482


Multiple Linear Regression - Regression Statistics
Multiple R0.163162860071836
R-squared0.0266221189068215
Adjusted R-squared0.0101241887188016
F-TEST (value)1.61366417504623
F-TEST (DF numerator)1
F-TEST (DF denominator)59
p-value0.208964207845363
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation19013.2049750854
Sum Squared Residuals21328615842.0522


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1147768125298.08695652122469.9130434787
2137507125298.08695652212208.9130434782
3136919125298.08695652211620.9130434782
4136151118116.818034.2
5133001118116.814884.2
6125554118116.87437.2
7119647125298.086956522-5651.08695652175
8114158125298.086956522-11140.0869565218
9116193125298.086956522-9105.08695652175
10152803125298.08695652227504.9130434783
11161761125298.08695652236462.9130434782
12160942125298.08695652235643.9130434782
13149470125298.08695652224171.9130434783
14139208125298.08695652213909.9130434782
15134588125298.0869565229289.91304347825
16130322118116.812205.2
17126611118116.88494.2
18122401118116.84284.2
19117352125298.086956522-7946.08695652175
20112135125298.086956522-13163.0869565218
21112879125298.086956522-12419.0869565218
22148729125298.08695652223430.9130434783
23157230125298.08695652231931.9130434783
24157221125298.08695652231922.9130434783
25146681125298.08695652221382.9130434783
26136524125298.08695652211225.9130434782
27132111125298.0869565226812.91304347825
28125326118116.87209.2
29122716118116.84599.2
30116615118116.8-1501.80000000000
31113719125298.086956522-11579.0869565218
32110737125298.086956522-14561.0869565217
33112093125298.086956522-13205.0869565218
34143565125298.08695652218266.9130434782
35149946125298.08695652224647.9130434783
36149147125298.08695652223848.9130434783
37134339125298.0869565229040.91304347825
38122683125298.086956522-2615.08695652175
39115614125298.086956522-9684.08695652175
40116566118116.8-1550.80000000000
41111272118116.8-6844.8
42104609118116.8-13507.8
43101802125298.086956522-23496.0869565217
4494542125298.086956522-30756.0869565218
4593051125298.086956522-32247.0869565218
46124129125298.086956522-1169.08695652175
47130374125298.0869565225075.91304347825
48123946125298.086956522-1352.08695652175
49114971125298.086956522-10327.0869565218
50105531125298.086956522-19767.0869565217
51104919125298.086956522-20379.0869565217
52104782118116.8-13334.8
53101281118116.8-16835.8
5494545118116.8-23571.8
5593248125298.086956522-32050.0869565218
5684031125298.086956522-41267.0869565218
5787486125298.086956522-37812.0869565218
58115867125298.086956522-9431.08695652175
59120327125298.086956522-4971.08695652175
60117008125298.086956522-8290.08695652175
61108811125298.086956522-16487.0869565217


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.02527748682459570.05055497364919140.974722513175404
60.01469422615059280.02938845230118560.985305773849407
70.06013770912702390.1202754182540480.939862290872976
80.09902374528668270.1980474905733650.900976254713317
90.08556506530023790.1711301306004760.914434934699762
100.1463019221838520.2926038443677040.853698077816148
110.2982459368716770.5964918737433540.701754063128323
120.4110359624515860.8220719249031730.588964037548414
130.3790367521370940.7580735042741880.620963247862906
140.30553060312290.61106120624580.6944693968771
150.2407454269189220.4814908538378450.759254573081078
160.1844096026489460.3688192052978920.815590397351054
170.1385990732789130.2771981465578260.861400926721087
180.104582123180890.209164246361780.89541787681911
190.1196761301150150.2393522602300300.880323869884985
200.1541531248853710.3083062497707410.84584687511463
210.1700576180564080.3401152361128170.829942381943592
220.1796075132383820.3592150264767650.820392486761618
230.2716559567517950.5433119135035910.728344043248205
240.3979884429281980.7959768858563960.602011557071802
250.4284353942802290.8568707885604590.571564605719771
260.401208623747560.802417247495120.59879137625244
270.3664178043156490.7328356086312980.633582195684351
280.3249282372376580.6498564744753150.675071762762342
290.2867717431799400.5735434863598810.71322825682006
300.2517720672497330.5035441344994670.748227932750267
310.2662017472438480.5324034944876960.733798252756152
320.2883333996020410.5766667992040830.711666600397959
330.2888825924132860.5777651848265720.711117407586714
340.3367516512072660.6735033024145330.663248348792734
350.5113137363244110.9773725273511790.488686263675589
360.7434881610837630.5130236778324740.256511838916237
370.8045481861631470.3909036276737070.195451813836853
380.8035562483080950.392887503383810.196443751691905
390.790241560429310.4195168791413820.209758439570691
400.7691955236784640.4616089526430720.230804476321536
410.7385314813523530.5229370372952950.261468518647647
420.702108542217720.5957829155645610.297891457782280
430.7223055824522930.5553888350954130.277694417547707
440.7917099363329080.4165801273341840.208290063667092
450.8527617713979390.2944764572041220.147238228602061
460.8404183393859050.3191633212281900.159581660614095
470.887895182334870.2242096353302600.112104817665130
480.9044568759758930.1910862480482150.0955431240241075
490.883719834094090.2325603318118210.116280165905910
500.83892970830510.32214058338980.1610702916949
510.7787244919097420.4425510161805150.221275508090258
520.7015098316049840.5969803367900320.298490168395016
530.605796559594260.788406880811480.39420344040574
540.4922135403089830.9844270806179670.507786459691017
550.4388098743080410.8776197486160820.561190125691959
560.5855446670398530.8289106659202950.414455332960148


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0192307692307692OK
10% type I error level20.0384615384615385OK
 
Charts produced by software:
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/1rs7y1227723576.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/4fthv1227723576.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/54lsp1227723576.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/6dftk1227723576.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/7bswm1227723576.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/8txmh1227723576.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/26/t1227723650ebu64qh8kxxdj9u/99hu21227723576.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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Software written by Ed van Stee & Patrick Wessa


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