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paper

*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: Wed, 02 Dec 2009 11:07:48 -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/Dec/02/t1259777884qp4g74kkt1g3rr3.htm/, Retrieved Wed, 02 Dec 2009 19:18:16 +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/Dec/02/t1259777884qp4g74kkt1g3rr3.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 «
109 102,86 108,6 102,55 108,8 102,28 108,5 102,26 108,3 102,57 108,2 103,08 108 102,76 107,9 102,51 108 102,87 109,3 103,14 109,6 103,12 109 103,16 108,7 102,48 108,3 102,57 108,4 102,88 107,8 102,63 107,8 102,38 107,6 101,69 107,7 101,96 107,6 102,19 107,6 101,87 108,6 101,6 108,6 101,63 108,2 101,22 107,5 101,21 107,1 101,49 107 101,64 106,9 101,66 106,6 101,77 106,3 101,82 106,1 101,78 105,9 101,28 106 101,29 107,2 101,37 107,2 101,12 106,4 101,51 106,1 102,24 105,9 102,94 106,1 103,09 105,9 103,46 105,8 103,64 105,7 104,39 105,6 104,15 105,3 105,21 105,5 105,8 106,5 105,91 106,5 105,39 106,1 105,46 105,9 104,72 105,8 103,14 106,2 102,63 106,5 102,32 106,6 101,93 106,7 100,62 106,6 100,6 106,5 99,63 106,8 98,9 107,8 98,32 107,9 99,22 107,4 98,81
 
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
Werk[t] = + 123.834438162153 -0.162585407011427Infl[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)123.8344381621539.15813613.521800
Infl-0.1625854070114270.089501-1.81660.0744510.037226


Multiple Linear Regression - Regression Statistics
Multiple R0.232018542744099
R-squared0.0538326041770954
Adjusted R-squared0.0375193732146316
F-TEST (value)3.29993514472775
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.0744510475409212
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.09425369665578
Sum Squared Residuals69.4486868534011


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1109107.1109031969581.88909680304221
2108.6107.1613046731311.43869532686872
3108.8107.2052027330241.59479726697563
4108.5107.2084544411651.29154555883541
5108.3107.1580529649911.14194703500895
6108.2107.0751344074151.12486559258478
7108107.1271617376590.872838262341122
8107.9107.1678080894120.732191910588271
9108107.1092773428880.890722657112379
10109.3107.0653792829952.23462071700546
11109.6107.0686309911352.53136900886523
12109107.0621275748541.93787242514569
13108.7107.1726856516221.52731434837793
14108.3107.1580529649911.14194703500895
15108.4107.1076514888181.29234851118250
16107.8107.1482978405700.651702159429632
17107.8107.1889441923230.611055807676775
18107.6107.3011281231610.298871876838888
19107.7107.2572300632680.442769936731981
20107.6107.2198354196550.380164580344602
21107.6107.2718627498990.328137250100946
22108.6107.3157608097921.28423919020786
23108.6107.3108832475821.28911675241820
24108.2107.3775432644560.822456735543526
25107.5107.3791691185270.120830881473408
26107.1107.333645204563-0.233645204563398
27107107.309257393512-0.309257393511677
28106.9107.306005685371-0.406005685371443
29106.6107.288121290600-0.688121290600198
30106.3107.279992020250-0.979992020249624
31106.1107.28649543653-1.18649543653008
32105.9107.367788140036-1.46778814003579
33106107.366162285966-1.36616228596568
34107.2107.353155453405-0.153155453404759
35107.2107.393801805158-0.193801805157616
36106.4107.330393496423-0.930393496423156
37106.1107.211706149305-1.11170614930483
38105.9107.097896364397-1.19789636439682
39106.1107.073508553345-0.973508553345113
40105.9107.013351952751-1.11335195275087
41105.8106.984086579489-1.18408657948883
42105.7106.862147524230-1.16214752423025
43105.6106.901168021913-1.301168021913
44105.3106.728827490481-1.42882749048089
45105.5106.632902100344-1.13290210034414
46106.5106.615017705573-0.115017705572884
47106.5106.699562117219-0.199562117218825
48106.1106.688181138728-0.588181138728032
49105.9106.808494339916-0.908494339916476
50105.8107.065379282995-1.26537928299454
51106.2107.148297840570-0.948297840570362
52106.5107.198699316744-0.698699316743908
53106.6107.262107625478-0.662107625478368
54106.7107.475094508663-0.77509450866333
55106.6107.478346216804-0.878346216803568
56106.5107.636054061605-1.13605406160465
57106.8107.754741408723-0.95474140872299
58107.8107.849040944790-0.049040944789619
59107.9107.7027140784790.197285921520675
60107.4107.769374095354-0.36937409535401


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.02773504135959330.05547008271918670.972264958640407
60.01820958733572240.03641917467144480.981790412664278
70.01366296096529230.02732592193058470.986337039034708
80.01283577926745160.02567155853490310.987164220732548
90.006299769627374720.01259953925474940.993700230372625
100.02129156056224420.04258312112448840.978708439437756
110.05922454934371490.1184490986874300.940775450656285
120.05564123709743840.1112824741948770.944358762902562
130.0528598352076750.105719670415350.947140164792325
140.04485229773723530.08970459547447050.955147702262765
150.04860720523309650.0972144104661930.951392794766904
160.06690500533979910.1338100106795980.9330949946602
170.06826428441933150.1365285688386630.931735715580668
180.04944714991747940.0988942998349590.95055285008252
190.03965282483938270.07930564967876550.960347175160617
200.03853573515521270.07707147031042540.961464264844787
210.03050242184861130.06100484369722260.969497578151389
220.1672181219180780.3344362438361570.832781878081922
230.4885669959005920.9771339918011850.511433004099408
240.7183589574204880.5632820851590250.281641042579512
250.7530872564993450.4938254870013090.246912743500655
260.796901567304960.4061968653900820.203098432695041
270.8420802988197160.3158394023605690.157919701180284
280.874072417637550.2518551647249020.125927582362451
290.9168899513232170.1662200973535650.0831100486767825
300.9578826376102480.08423472477950370.0421173623897518
310.9809290475387420.03814190492251510.0190709524612575
320.9906809240283770.01863815194324640.00931907597162318
330.99387947003160.01224105993679870.00612052996839937
340.993481551507070.01303689698586010.00651844849293004
350.9932671073530730.01346578529385460.00673289264692732
360.9909619829924510.01807603401509740.00903801700754871
370.9953773063189040.009245387362192680.00462269368109634
380.9989696063770.002060787246000670.00103039362300034
390.9994129835925820.001174032814835600.000587016407417801
400.9996752212592370.0006495574815253370.000324778740762668
410.9997650889565860.0004698220868282050.000234911043414103
420.9997749495692050.0004501008615903320.000225050430795166
430.999778698172080.0004426036558417770.000221301827920888
440.9998279081018250.0003441837963500670.000172091898175034
450.999718912646970.0005621747060601390.000281087353030069
460.999653151144440.0006936977111188010.000346848855559401
470.9996929788676460.0006140422647080390.000307021132354019
480.9995626524257610.0008746951484769130.000437347574238456
490.998999442366840.00200111526631850.00100055763315925
500.9976683307211280.0046633385577430.0023316692788715
510.9935813252855670.01283734942886710.00641867471443355
520.984268673741130.03146265251774050.0157313262588703
530.9699372487504620.06012550249907690.0300627512495384
540.9286992035142630.1426015929714750.0713007964857373
550.8459507903516750.308098419296650.154049209648325


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.274509803921569NOK
5% type I error level270.529411764705882NOK
10% type I error level360.705882352941177NOK
 
Charts produced by software:
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http://www.freestatistics.org/blog/date/2009/Dec/02/t1259777884qp4g74kkt1g3rr3/91ze81259777264.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/02/t1259777884qp4g74kkt1g3rr3/91ze81259777264.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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