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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: Fri, 20 Nov 2009 06:10:25 -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/20/t1258723036q9eqtvv62p8ffu6.htm/, Retrieved Fri, 20 Nov 2009 14:17:28 +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/20/t1258723036q9eqtvv62p8ffu6.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 «
10144 112 10751 304 11752 794 13808 901 16203 1232 17432 1240 18014 1032 16956 1145 17982 1588 19435 2264 19990 2209 20154 2917 10327 243 9807 558 10862 1238 13743 1502 16458 2000 18466 2146 18810 2066 17361 2046 17411 1952 18517 2771 18525 3278 17859 4000 9499 410 9490 1107 9255 1622 10758 1986 12375 2036 14617 2400 15427 2736 14136 2901 14308 2883 15293 3747 15679 4075 16319 4996 11196 575 11169 999 12158 1411 14251 1493 16237 1846 19706 2899 18960 2372 18537 2856 19103 3468 19691 4193 19464 4440 17264 4186 8957 655 9703 1453 9166 1989 9519 2209 10535 2667 11526 3005 9630 2195 7061 2236 6021 2489 4728 2651 2657 2636 1264 2819
 
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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 7378.28355988144 + 3.95381014494266X[t] + 6461.74593137428M1[t] + 4918.47723861162M2[t] + 3506.72080584833M3[t] + 4679.62057135073M4[t] + 5504.75273192363M5[t] + 6198.70800814803M6[t] + 7252.52025307776M7[t] + 5491.07357394325M8[t] + 4915.84217683649M9[t] + 3132.54862030323M10[t] + 2278.21743653034M11[t] -215.719989563514t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)7378.283559881442945.7522562.50470.0158610.00793
X3.953810144942660.8122624.86771.4e-057e-06
M16461.745931374283219.3062322.00720.0506270.025313
M24918.477238611622925.3442671.68130.0994770.049738
M33506.720805848332629.9657051.33340.1889760.094488
M44679.620571350732527.9997251.85110.0705790.03529
M55504.752731923632368.6590552.3240.0245970.012299
M66198.708008148032210.590782.80410.0073660.003683
M77252.520253077762327.5742033.11590.0031560.001578
M85491.073573943252266.5800542.42260.0194050.009702
M94915.842176836492177.6976952.25740.0287770.014389
M103132.548620303231991.6303361.57290.1226060.061303
M112278.217436530341959.2300551.16280.2509030.125451
t-215.71998956351428.521856-7.563300


Multiple Linear Regression - Regression Statistics
Multiple R0.813060614890317
R-squared0.661067563485821
Adjusted R-squared0.565282309688335
F-TEST (value)6.90155882327656
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value3.96688436321568e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3046.67568215229
Sum Squared Residuals426982704.762034


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11014414067.1362379258-3923.13623792581
21075113067.2791034286-2316.2791034286
31175213377.1696521237-1625.16965212370
41380814757.4071135715-949.407113571461
51620316675.5304425569-472.530442556864
61743217185.3962103773246.603789622711
71801417201.0959555954812.904044404558
81695615670.70983327591285.29016672406
91798216631.29634081531350.70365918475
101943517305.05845269972129.94154730029
111999016017.54772139153972.45227860853
122015416322.90787791703831.09212208298
131032711996.4454921511-1669.44549215111
14980711482.9070054819-1675.90700548187
151086212544.0214817161-1682.02148171608
161374314545.0071359198-802.00713591983
171645817123.4167591107-665.416759110656
181846618178.9083269332287.091673066823
191881018700.6957707040109.304229296019
201736116644.4528991071716.547100892892
211741115481.84335881221929.15664118778
221851716721.00032142351795.99967857652
231852517655.530891573869.469108426989
241785918016.2443901278-157.244390127759
25949910068.0919115944-569.091911594363
26949011064.9089002932-1574.90890029323
27925511473.6447026119-2218.64470261189
281075813870.0113713099-3112.01137130991
291237514677.1140495664-2302.11404956642
301461716594.5362289864-1977.53622898645
311542718761.1086930534-3334.1086930534
321413617436.3206982709-3300.32069827092
331430816574.2007289917-2266.20072899166
341529317991.2791481253-2698.27914812535
351567918218.0777023301-2539.07770233015
361631919365.5994197285-3046.59941972848
37111968131.830710747733064.16928925227
38111698049.257529877253119.74247012275
39121588050.750887266824107.24911273318
40142519332.143095091014918.85690490899
411623711337.25024726514899.74975273485
421970615978.84761655073727.15238344933
431896014733.28192553214226.7180744679
441853714669.75936698633867.24063301367
451910316298.53978902102804.46021097905
461969117166.03859800762524.96140199239
471946417072.57853047202391.42146952795
481726413574.37332756283689.62667243724
4989575859.495647580983097.50435241902
5097037255.647460919052447.35253908095
5191667747.413276281511418.58672371849
5295199574.43128410779-55.4312841077877
531053511994.6885015009-1459.68850150091
541152613809.3116171524-2283.31161715242
55963011444.8176551151-1814.81765511508
5670619629.75720235971-2568.75720235971
5760219839.11978235992-3818.11978235992
5847288480.62347974385-3752.62347974385
5926577351.26515423332-4694.26515423332
6012645580.87498466397-4316.87498466397


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.003568091536812260.007136183073624520.996431908463188
180.000750224310472290.001500448620944580.999249775689528
198.56748506512946e-050.0001713497013025890.999914325149349
209.2675548917958e-061.85351097835916e-050.999990732445108
211.12815764249729e-062.25631528499459e-060.999998871842358
223.74303397903608e-077.48606795807215e-070.999999625696602
232.74098465785763e-065.48196931571526e-060.999997259015342
247.34818240664762e-061.46963648132952e-050.999992651817593
251.48352498926296e-062.96704997852593e-060.99999851647501
263.11337802941747e-076.22675605883494e-070.999999688662197
272.25773476370176e-074.51546952740352e-070.999999774226524
287.62023095888406e-071.52404619177681e-060.999999237976904
292.7765244417018e-065.5530488834036e-060.999997223475558
302.22377507220397e-064.44755014440795e-060.999997776224928
313.16853245085323e-066.33706490170646e-060.99999683146755
324.59469066445211e-069.18938132890421e-060.999995405309336
334.51110223721642e-069.02220447443284e-060.999995488897763
349.63390611245494e-061.92678122249099e-050.999990366093888
353.00676300578268e-056.01352601156536e-050.999969932369942
360.03836778137742910.07673556275485820.96163221862257
370.3351519647863860.6703039295727730.664848035213614
380.8617727857465880.2764544285068250.138227214253412
390.99295691693240.01408616613519980.00704308306759989
400.9915179767822840.01696404643543220.00848202321771608
410.982560334622060.03487933075587880.0174396653779394
420.9717263727608080.0565472544783840.028273627239192
430.9188654412945730.1622691174108540.081134558705427


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.703703703703704NOK
5% type I error level220.814814814814815NOK
10% type I error level240.888888888888889NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/108tw81258722619.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/1kvuu1258722619.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/2gywb1258722619.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/2gywb1258722619.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/3clu81258722619.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/6pdu21258722619.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/6pdu21258722619.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/7napx1258722619.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/8k3ib1258722619.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/8k3ib1258722619.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/9cu391258722619.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723036q9eqtvv62p8ffu6/9cu391258722619.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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