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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: Sat, 21 Nov 2009 07:55:39 -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/21/t1258815426v0be0es7yn92hh4.htm/, Retrieved Sat, 21 Nov 2009 15:57:18 +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/2009/Nov/21/t1258815426v0be0es7yn92hh4.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 «
-22 46 -20 50 -17 49 -21 48 -16 50 -11 47 -19 50 -31 49 -36 51 -33 52 -26 48 -38 55 -27 56 -21 43 -17 44 -14 50 -16 49 -16 47 -15 46 -7 50 -9 49 2 53 -6 54 0 56 7 56 4 58 -5 53 2 51 0 52 3 53 10 56 4 54 5 54 7 56 1 59 -8 62 -3 62 -16 73 -22 76 -32 80 -30 77 -32 81 -38 80 -41 80 -46 81 -58 80 -55 77 -48 71 -58 71 -58 64 -68 64 -75 47 -77 41 -75 35 -71 34 -63 33 -61 23 -53 16 -41 16 -35 8 -33 9
 
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
Econo[t] = -32.6419936980808 + 0.135753843215889Price[t] + 3.18763487061969M1[t] + 2.62257232884560M2[t] -0.923126133868044M3[t] -2.85161844743626M4[t] -2.46156306693402M5[t] -0.698658455074959M6[t] -1.18011076100449M7[t] -2.18011076100449M8[t] -3.76290461185907M9[t] -1.33575384321589M10[t] + 0.345698462713647M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-32.641993698080815.819872-2.06340.044510.022255
Price0.1357538432158890.2061050.65870.513260.25663
M13.1876348706196916.1557160.19730.844420.42221
M22.6225723288456016.9390020.15480.8776090.438804
M3-0.92312613386804416.931979-0.05450.9567470.478374
M4-2.8516184474362616.902852-0.16870.8667370.433368
M5-2.4615630669340216.88842-0.14580.8847260.442363
M6-0.69865845507495916.879967-0.04140.9671570.483578
M7-1.1801107610044916.883741-0.06990.9445670.472283
M8-2.1801107610044916.883741-0.12910.8977980.448899
M9-3.7629046118590716.875688-0.2230.8244990.412249
M10-1.3357538432158916.875134-0.07920.9372380.468619
M110.34569846271364716.8740770.02050.983740.49187


Multiple Linear Regression - Regression Statistics
Multiple R0.127248784179139
R-squared0.0161922530750690
Adjusted R-squared-0.229759683656164
F-TEST (value)0.0658350297634097
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.999993785425542
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation26.6799395968464
Sum Squared Residuals34167.3204907858


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
1-22-23.20968203953021.20968203953021
2-20-23.23172920844083.23172920844077
3-17-26.91318151437039.91318151437029
4-21-28.97742767115447.9774276711544
5-16-28.315864604220412.3158646042204
6-11-26.960221522009015.9602215220090
7-19-27.03441229829088.03441229829085
8-31-28.1701661415067-2.82983385849326
9-36-29.4814523059295-6.51854769407048
10-33-26.9185476940705-6.08145230592953
11-26-25.7801107610045-0.219889238995511
12-38-25.1755323212069-12.8244676787931
13-27-21.8521436073713-5.14785639262866
14-21-24.1820061109523.18200611095198
15-17-27.591950730449710.5919507304497
16-14-28.705919984722614.7059199847226
17-16-28.451618447436312.4516184474363
18-16-26.96022152200910.9602215220090
19-15-27.577427671154412.5774276711544
20-7-28.034412298290821.0344122982908
21-9-29.752959992361320.7529599923613
222-26.782793850854628.7827938508546
23-6-24.965587701709218.9655877017092
240-25.039778477991025.0397784779910
257-21.852143607371428.8521436073714
264-22.145698462713626.1456984627136
27-5-26.370166141506721.3701661415067
282-28.570166141506730.5701661415067
290-28.044356917788628.0443569177886
303-26.145698462713729.1456984627137
3110-26.219889238995536.2198892389955
324-27.491396925427331.4913969254273
335-29.074190776281934.0741907762819
347-26.375532321206933.3755323212069
351-24.286818485629725.2868184856297
36-8-24.225255418695716.2252554186957
37-3-21.03762054807618.037620548076
38-16-20.10939081447534.10939081447532
39-22-23.24782774754131.24782774754130
40-32-24.6333046882460-7.36669531175404
41-30-24.6505108373914-5.34948916260862
42-32-22.3445908526688-9.65540914733123
43-38-22.9617970018142-15.0382029981858
44-41-23.9617970018142-17.0382029981858
45-46-25.4088370094529-20.5911629905471
46-58-23.1174400840256-34.8825599159744
47-55-21.8432493077437-33.1567506922563
48-48-23.0034708297527-24.9965291702473
49-58-19.815835959133-38.184164040867
50-58-21.3311754034183-36.6688245965817
51-68-24.8768738661320-43.123126133868
52-75-29.1131815143703-45.8868184856297
53-77-29.5376491931634-47.4623508068366
54-75-28.5892676405996-46.4107323594004
55-71-29.2064737897451-41.7935262102549
56-63-30.3422276329609-32.6577723670391
57-61-33.2825599159744-27.7174400840256
58-53-31.8056860498425-21.1943139501575
59-41-30.1242337439129-10.8757662560871
60-35-31.5559629523537-3.44403704764632
61-33-28.2325742385181-4.7674257614819


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.001745089005293360.003490178010586710.998254910994707
170.0001524120202824850.0003048240405649700.999847587979718
182.5468519473877e-055.0937038947754e-050.999974531480526
192.88665094621285e-065.77330189242569e-060.999997113349054
200.0001512160283067440.0003024320566134880.999848783971693
210.0004249668325767890.0008499336651535790.999575033167423
220.001590598689074630.003181197378149270.998409401310925
230.0009783755510976030.001956751102195210.999021624448902
240.002048227352507540.004096454705015090.997951772647492
250.002359832475652660.004719664951305310.997640167524347
260.001275581408289510.002551162816579010.99872441859171
270.000646201445112310.001292402890224620.999353798554888
280.0006085652939683050.001217130587936610.999391434706032
290.000499581072188120.000999162144376240.999500418927812
300.0004191536903831160.0008383073807662330.999580846309617
310.0005797888125861090.001159577625172220.999420211187414
320.000808958373381310.001617916746762620.999191041626619
330.001757719575463890.003515439150927790.998242280424536
340.004631867397669730.009263734795339470.99536813260233
350.006319077979917460.01263815595983490.993680922020083
360.004855995265174890.009711990530349770.995144004734825
370.006485095020286010.01297019004057200.993514904979714
380.03131241644184440.06262483288368890.968687583558156
390.08035362785342130.1607072557068430.919646372146579
400.147025679571480.294051359142960.85297432042852
410.2672107639964970.5344215279929930.732789236003504
420.4672138927570920.9344277855141830.532786107242908
430.6683399375525570.6633201248948850.331660062447443
440.7833481948292850.4333036103414310.216651805170715
450.9345247243035590.1309505513928820.0654752756964411


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level200.666666666666667NOK
5% type I error level220.733333333333333NOK
10% type I error level230.766666666666667NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/10ek441258815334.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/10ek441258815334.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/19fg81258815334.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/266y71258815334.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/266y71258815334.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/3f83o1258815334.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/4u4vv1258815334.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/6i8tm1258815334.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/75zlz1258815334.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/75zlz1258815334.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/8ikzn1258815334.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/8ikzn1258815334.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/9tlvv1258815334.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/21/t1258815426v0be0es7yn92hh4/9tlvv1258815334.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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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