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multiple regression PS

*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, 14 Dec 2010 21:01:56 +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/14/t1292360418n9g7qlwqsn7vfve.htm/, Retrieved Tue, 14 Dec 2010 22:00:18 +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/14/t1292360418n9g7qlwqsn7vfve.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 «
0,301029996 3 162324929 0,255272505 4 279518459 -0,15490196 4 2255272505 0,591064607 1 1544068044 0 4 2593286067 0,556302501 1 1799340549 0,146128036 1 2361727836 0,176091259 4 2049218023 -0,15490196 5 244870632 0,322219295 1 162324929 0,612783857 2 162324929 0,079181246 2 2079181246 -0,301029996 5 2170261715 0,531478917 2 1204119983 0,176091259 1 2491361694 0,531478917 3 1447158031 -0,096910013 4 1832508913 -0,096910013 5 2526339277 0,301029996 1 1698970004 0,278753601 1 2426511261 0,113943352 3 1278753601 0,748188027 1 1079181246 0,491361694 1 2079181246 0,255272505 2 2146128036 -0,045757491 4 2230448921 0,255272505 2 1230448921 0,278753601 4 206069784 -0,045757491 5 1491361694 0,414973348 3 1322219295 0,380211242 1 1716003344 0,079181246 2 2214843848 -0,045757491 2 2352182518 -0,301029996 3 2352182518 -0,22184875 5 2178976947 0,361727836 2 177815125 -0,301029996 3 2301029996 0,414973348 2 1662757832 -0,22184875 4 2322219295 0,819543936 1 1146128036
 
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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Ps[t] = + 0.835834783520968 -0.141292771986980D[t] -1.65428892255176e-10Tg[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.8358347835209680.0850839.823800
D-0.1412927719869800.020716-6.820500
Tg-1.65428892255176e-100-4.44188.2e-054.1e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.810328521823468
R-squared0.656632313280607
Adjusted R-squared0.637556330685086
F-TEST (value)34.4219392103427
F-TEST (DF numerator)2
F-TEST (DF denominator)36
p-value4.40219838360179e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.181236178233053
Sum Squared Residuals1.18247588281883


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
10.3010299960.385103234370157-0.0840732383701566
20.2552725050.2244232665358020.0308492384641977
3-0.15490196-0.102423536662660-0.0524784233373403
40.5910646070.4391085454484510.151956061551549
50-0.1583407457915460.158340745791546
60.5563025010.3968790977230970.159423403276903
70.1461280360.303843991816293-0.157715955816293
80.176091259-0.06833617196118570.244427430961186
9-0.154901960.0888622461884808-0.243764206188481
100.3222192950.667688778344117-0.345469483344117
110.6127838570.5263960063571370.0863878506428631
120.0791812460.209292589223490-0.130111343223490
13-0.301029996-0.229653067830203-0.0713769281697972
140.5314789170.3540530046169960.177425912383004
150.1760912590.282398806288589-0.106307547288589
160.5314789170.1725547175735150.358924199426485
17-0.096910013-0.0324862239522806-0.0644237890477194
18-0.096910013-0.2885585844687870.191648571468787
190.3010299960.413483285797495-0.112453289797495
200.2787536010.293126941582047-0.0143733405820471
210.1139433520.200413675879279-0.0864703238792792
220.7481880270.5160142534656470.232173773534353
230.4913616940.3505853612104710.140776332789529
240.2552725050.1982176559137510.0570548490862495
25-0.045757491-0.09831699865973650.0525595076597365
260.2552725050.349697437569400-0.0944249325694004
270.2787536010.2365737994786630.0421798015213373
28-0.045757491-0.1173433894041570.0715858984041571
290.4149733480.1932231942697570.221750153730243
300.3802112420.41066547922989-0.0304542372298897
310.0791812460.186850075254176-0.107668829254176
32-0.0457574910.164130291212276-0.209887782212276
33-0.3010299960.0228375192252960-0.323867515225296
34-0.22184875-0.2310948190057100.00924606900570972
350.3617278360.523833480392041-0.162105644392041
36-0.3010299960.0312996242758145-0.332329620275815
370.4149733480.2781810533106290.136792294689371
38-0.22184875-0.113498469972400-0.108350280027600
390.8195439360.5049393201559070.314604615844093


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.158640194038340.317280388076680.84135980596166
70.3900411270478680.7800822540957370.609958872952132
80.4040796533295340.8081593066590680.595920346670466
90.4730061732838320.9460123465676640.526993826716168
100.6290796757648990.7418406484702020.370920324235101
110.6357012176165230.7285975647669550.364298782383477
120.6080441185178210.7839117629643590.391955881482179
130.5377601550573910.9244796898852170.462239844942609
140.5334829439339090.9330341121321810.466517056066091
150.4778424627237180.9556849254474370.522157537276282
160.7210277204561860.5579445590876270.278972279543814
170.6470448785345560.7059102429308890.352955121465444
180.6728408963943580.6543182072112830.327159103605642
190.6204910624895210.7590178750209570.379508937510479
200.5240633659607370.9518732680785270.475936634039263
210.4504915107546470.9009830215092940.549508489245353
220.4900209250591640.9800418501183270.509979074940836
230.4622979645323190.9245959290646390.537702035467681
240.3932290228809440.7864580457618880.606770977119056
250.3329417965900370.6658835931800750.667058203409963
260.2664463907696890.5328927815393780.733553609230311
270.2035327353582250.4070654707164510.796467264641775
280.1424109394625780.2848218789251550.857589060537422
290.1791342004759360.3582684009518730.820865799524064
300.1112634253617210.2225268507234430.888736574638279
310.06849295708500510.1369859141700100.931507042914995
320.05451386187002770.1090277237400550.945486138129972
330.09206185454257550.1841237090851510.907938145457424


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/14/t1292360418n9g7qlwqsn7vfve/104wjz1292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/104wjz1292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/1xv351292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/1xv351292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/2xv351292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/2xv351292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/3q4l81292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/3q4l81292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/4q4l81292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/4q4l81292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/5q4l81292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/5q4l81292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/6iw2t1292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/6iw2t1292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/7bn1e1292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/7bn1e1292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/8bn1e1292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/8bn1e1292360507.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/9bn1e1292360507.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/14/t1292360418n9g7qlwqsn7vfve/9bn1e1292360507.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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