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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 07:06:33 -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/t1258726023gf5a21uwupalve5.htm/, Retrieved Fri, 20 Nov 2009 15:07:16 +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/Nov/20/t1258726023gf5a21uwupalve5.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 «
89.1 0 100 88 82.6 0 89.1 100 102.7 0 82.6 89.1 91.8 0 102.7 82.6 94.1 0 91.8 102.7 103.1 0 94.1 91.8 93.2 0 103.1 94.1 91 0 93.2 103.1 94.3 0 91 93.2 99.4 0 94.3 91 115.7 0 99.4 94.3 116.8 0 115.7 99.4 99.8 0 116.8 115.7 96 0 99.8 116.8 115.9 0 96 99.8 109.1 0 115.9 96 117.3 0 109.1 115.9 109.8 0 117.3 109.1 112.8 0 109.8 117.3 110.7 0 112.8 109.8 100 0 110.7 112.8 113.3 0 100 110.7 122.4 0 113.3 100 112.5 0 122.4 113.3 104.2 0 112.5 122.4 92.5 0 104.2 112.5 117.2 0 92.5 104.2 109.3 0 117.2 92.5 106.1 0 109.3 117.2 118.8 0 106.1 109.3 105.3 0 118.8 106.1 106 0 105.3 118.8 102 0 106 105.3 112.9 0 102 106 116.5 0 112.9 102 114.8 0 116.5 112.9 100.5 0 114.8 116.5 85.4 0 100.5 114.8 114.6 0 85.4 100.5 109.9 0 114.6 85.4 100.7 0 109.9 114.6 115.5 0 100.7 109.9 100.7 1 115.5 100.7 99 1 100.7 115.5 102.3 1 99 100.7 108.8 1 102.3 99 105.9 1 108.8 102.3 113.2 1 105.9 108.8 95.7 1 113.2 105.9 80.9 1 95.7 113.2 113.9 1 80.9 95.7 98.1 1 113.9 80.9 102.8 1 98.1 113.9 1 etc...
 
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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
TotaleIndustrieleProductie[t] = + 48.7719098176646 -3.92815091693391X[t] + 0.229632225851288Y1[t] + 0.35939013498551Y2[t] -16.6549309698687M1[t] -24.6048091612375M2[t] + 7.98612935353004M3[t] -3.39181676279789M4[t] -9.8962790917531M5[t] -0.591645919035228M6[t] -10.2867511923731M7[t] -11.8673684644641M8[t] -8.68197056383971M9[t] -0.597406321343375M10[t] + 4.17151212199479M11[t] + 0.0603498253718281t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)48.771909817664614.3222413.40530.0014210.00071
X-3.928150916933912.800057-1.40290.1676690.083835
Y10.2296322258512880.1347011.70480.0952930.047646
Y20.359390134985510.1269882.83010.0069860.003493
M1-16.65493096986873.091986-5.38653e-061e-06
M2-24.60480916123753.912985-6.28800
M37.986129353530044.3884981.81980.0755990.037799
M4-3.391816762797893.893557-0.87110.3884080.194204
M5-9.89627909175313.544963-2.79160.0077290.003865
M6-0.5916459190352283.2706-0.18090.8572780.428639
M7-10.28675119237313.035381-3.38890.001490.000745
M8-11.86736846446413.544847-3.34780.0016770.000838
M9-8.681970563839713.393313-2.55860.0140280.007014
M10-0.5974063213433753.411245-0.17510.8617820.430891
M114.171512121994793.1397651.32860.1908280.095414
t0.06034982537182810.073210.82430.4141910.207096


Multiple Linear Regression - Regression Statistics
Multiple R0.904468438807846
R-squared0.818063156799503
Adjusted R-squared0.756039232981151
F-TEST (value)13.1894776472923
F-TEST (DF numerator)15
F-TEST (DF denominator)44
p-value1.17428289314603e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.75429381103554
Sum Squared Residuals994.545624232637


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
189.186.76688313702172.33311686297828
282.680.68704512907171.91295487092829
3102.7107.928371529836-5.22837152983556
491.898.8903471010845-7.09034710108453
594.197.1669850489309-3.06698504893088
6103.1103.142769695136-0.042769695136433
793.296.4013015902987-3.20130159029867
89195.8421863225214-4.84218632252139
994.395.0247808152882-0.72478081528819
1099.4103.136822931497-3.73682293149747
11115.7110.3232029975015.37679700249879
12116.8111.7879356706805.01206432931964
1399.8101.304009174884-1.50400917488376
149689.9060621178996.09393788210103
15115.9115.5751157050500.324884294950293
16109.1107.4615181955891.63848180441069
17117.3106.60777024242910.6922297575712
18109.8115.411884574598-5.61188457459761
19112.8107.0018865396285.79811346037193
20110.7103.4750897580717.22491024192851
21100107.316780214736-7.3167802147365
22113.3112.2499101825261.05008981747369
23122.4116.2878126107136.11218738928652
24112.5119.046192364645-6.54619236464452
25104.2103.4487024125880.751297587411934
2692.590.09526423566892.40473576433112
27117.2117.0769174129680.123082587031616
28109.3107.2263725212092.07362747879137
29106.1107.845101767542-1.74510176754219
30118.8113.6360795765225.16392042347777
31105.3105.767604964914-0.467604964913886
32106105.7115571835180.288442816481648
33102104.266280645306-2.26628064530606
34112.9111.7442389042591.15576109574108
35116.5117.638937894806-1.13893789480592
36114.8118.271804082590-3.47180408258966
37100.5102.580652640093-2.08065264009346
3885.490.7964202149477-5.39642021494772
39114.6114.840983014440-0.240983014439798
40109.9104.8018566800605.09814331993991
41100.7107.772664656553-7.07266465655256
42115.5113.3358975423792.16410245762148
43100.799.8651588782110.834841121789101
4499100.265308486678-1.26530848667826
45102.397.80170743094174.49829256905829
46108.8106.0934446146442.70655538535624
47105.9113.601309796839-7.7013097968393
48113.2111.1602499226532.03975007734658
4995.795.1997526354130.500247364586997
5080.985.9152083024127-5.01520830241273
51113.9108.8786123377075.02138766229344
5298.199.8199055020574-1.71990550205743
53102.8101.6074782845461.19252171545447
54104.7106.373368611365-1.67336861136521
5595.998.8640480269485-2.96404802694849
5694.696.0058582492105-1.40585824921052
57101.695.79045089372755.80954910627246
58103.9105.075583367074-1.17558336707354
59110.3112.94873670014-2.64873670014008
60114.1111.1338179594322.96618204056796


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.8857443546620360.2285112906759290.114255645337964
200.8496768909810940.3006462180378110.150323109018906
210.8491034520711770.3017930958576460.150896547928823
220.8432428957364020.3135142085271960.156757104263598
230.9440685990060530.1118628019878950.0559314009939474
240.9982941362682170.003411727463565110.00170586373178255
250.9968477674476840.006304465104631060.00315223255231553
260.9970335437145080.005932912570984070.00296645628549204
270.9933172121019770.01336557579604560.0066827878980228
280.9861818287662040.02763634246759110.0138181712337956
290.982826612706710.03434677458658170.0171733872932908
300.9808189828598550.03836203428029060.0191810171401453
310.9706990077476680.0586019845046640.029300992252332
320.9640073544314020.07198529113719530.0359926455685977
330.9490335046424360.1019329907151280.0509664953575642
340.9113060627241480.1773878745517030.0886939372758516
350.9146890688866840.1706218622266330.0853109311133163
360.8810941838475170.2378116323049670.118905816152483
370.819925314409630.3601493711807390.180074685590370
380.754690517594350.49061896481130.24530948240565
390.7009930854125010.5980138291749980.299006914587499
400.7251935280418640.5496129439162730.274806471958136
410.790978181075250.4180436378494990.209021818924750


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.130434782608696NOK
5% type I error level70.304347826086957NOK
10% type I error level90.391304347826087NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726023gf5a21uwupalve5/100bth1258725989.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726023gf5a21uwupalve5/962nt1258725989.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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Software written by Ed van Stee & Patrick Wessa


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