| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 3 seconds |
| R Server | 'Gwilym Jenkins' @ 72.249.127.135 |
| Multiple Linear Regression - Estimated Regression Equation |
| (1-B)Totaal[t] = -0.00166813856920151 + 0.238045611732930`(1-B)prod_metaal`[t] + 0.205463823682829`(1-B)mach_app`[t] + 0.273686165047863`(1-B)elek_app`[t] + 0.283193162946932`(1-B)Metaalverwerking `[t] + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | -0.00166813856920151 | 0.02431 | -0.0686 | 0.945478 | 0.472739 |
| `(1-B)prod_metaal` | 0.238045611732930 | 0.003341 | 71.2478 | 0 | 0 |
| `(1-B)mach_app` | 0.205463823682829 | 0.002984 | 68.8564 | 0 | 0 |
| `(1-B)elek_app` | 0.273686165047863 | 0.003611 | 75.7834 | 0 | 0 |
| `(1-B)Metaalverwerking ` | 0.283193162946932 | 0.001893 | 149.5786 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.999912016818188 |
| R-squared | 0.999824041377416 |
| Adjusted R-squared | 0.99981453010052 |
| F-TEST (value) | 105119.854280796 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 74 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.214909813310561 |
| Sum Squared Residuals | 3.41778086143133 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 3.5 | 3.35527760222354 | 0.144722397776457 |
| 2 | 15.7 | 15.6116915728785 | 0.0883084271215486 |
| 3 | -25.8 | -25.5290754987697 | -0.270924501230362 |
| 4 | 6.30000000000001 | 6.02581577820199 | 0.274184221798026 |
| 5 | 8.39999999999999 | 8.6633713878864 | -0.263371387886416 |
| 6 | -33.5 | -33.696646497419 | 0.196646497419019 |
| 7 | 5.7 | 6.56712133799643 | -0.867121337996427 |
| 8 | 17.2 | 16.4721870392453 | 0.727812960754678 |
| 9 | 3.8 | 3.78460605632986 | 0.0153939436701421 |
| 10 | -3 | -3.26791821780088 | 0.267918217800883 |
| 11 | -10.5 | -10.0921578321491 | -0.407842167850905 |
| 12 | -2.5 | -2.66132890012864 | 0.161328900128643 |
| 13 | 3.90000000000001 | 4.10513823962471 | -0.205138239624704 |
| 14 | 12.9 | 12.8857223357780 | 0.0142776642220173 |
| 15 | -5.39999999999999 | -5.12331044102201 | -0.276689558977979 |
| 16 | -1.30000000000001 | -1.41081367054091 | 0.110813670540900 |
| 17 | 8 | 8.01427478282186 | -0.0142747828218620 |
| 18 | -26.9 | -27.0438831482924 | 0.143883148292443 |
| 19 | -0.5 | -0.382769897026964 | -0.117230102973036 |
| 20 | 24.1 | 24.033146222692 | 0.0668537773079729 |
| 21 | 6.9 | 6.9375767435345 | -0.037576743534495 |
| 22 | -11.2 | -11.3631129480276 | 0.163112948027624 |
| 23 | -5.9 | -5.95785431745253 | 0.0578543174525227 |
| 24 | -4.5 | -4.43194800626857 | -0.0680519937314348 |
| 25 | 3.5 | 3.53715505850575 | -0.0371550585057534 |
| 26 | 6.7 | 6.70954375966163 | -0.00954375966162266 |
| 27 | -3.7 | -3.6458246478631 | -0.0541753521369029 |
| 28 | -0.399999999999991 | -0.371897024505795 | -0.0281029754941960 |
| 29 | 6.3 | 6.22494858715787 | 0.0750514128421267 |
| 30 | -20.5 | -20.6228403558222 | 0.122840355822167 |
| 31 | -10.2 | -10.3245035275216 | 0.124503527521591 |
| 32 | 30.1 | 30.162976007156 | -0.0629760071560093 |
| 33 | 2.09999999999999 | 1.96170233669637 | 0.138297663303627 |
| 34 | -8.8 | -8.50054974362191 | -0.299450256378085 |
| 35 | 5.39999999999999 | 5.25614424804834 | 0.143855751951654 |
| 36 | -13.6 | -13.5895661037538 | -0.0104338962461703 |
| 37 | 4.8 | 4.8412912826344 | -0.0412912826344004 |
| 38 | 22.9 | 22.7656611323118 | 0.134338867688250 |
| 39 | -9.9 | -9.77207201338476 | -0.12792798661524 |
| 40 | -8.3 | -8.28227673664311 | -0.0177232633568864 |
| 41 | 20.2 | 20.0688942404120 | 0.131105759588031 |
| 42 | -28.7 | -28.6930518896990 | -0.00694811030095195 |
| 43 | 1.90000000000001 | 2.10952181896409 | -0.209521818964082 |
| 44 | 21.4 | 21.2602982366382 | 0.139701763361758 |
| 45 | -0.200000000000003 | -0.321178268454279 | 0.121178268454277 |
| 46 | -9 | -8.87345348239838 | -0.126546517601619 |
| 47 | 4.60000000000001 | 4.54178660495549 | 0.058213395044515 |
| 48 | -12 | -11.8176062574602 | -0.182393742539791 |
| 49 | 4.3 | 4.32428150931842 | -0.0242815093184189 |
| 50 | 15.9 | 15.8597779273705 | 0.0402220726294566 |
| 51 | -11.1 | -11.0714010577111 | -0.0285989422889114 |
| 52 | -6.8 | -7.046524800813 | 0.246524800813001 |
| 53 | 30.4 | 30.5476352413126 | -0.147635241312614 |
| 54 | -46.4 | -46.4979662860791 | 0.0979662860791294 |
| 55 | 5.9 | 5.9820649388721 | -0.0820649388720955 |
| 56 | 27 | 26.8635981438018 | 0.136401856198163 |
| 57 | -11.7 | -11.6336520290242 | -0.0663479709757988 |
| 58 | 9.2 | 9.19476458757557 | 0.00523541242443354 |
| 59 | -1.20000000000000 | -1.24214724441312 | 0.0421472444131195 |
| 60 | -11.4 | -11.3319120481223 | -0.0680879518777552 |
| 61 | 6.5 | 6.6685671927591 | -0.168567192759104 |
| 62 | 19.3 | 19.2543871915154 | 0.0456128084845846 |
| 63 | -23.7 | -23.9341864376488 | 0.234186437648859 |
| 64 | 15 | 15.3009370337691 | -0.300937033769051 |
| 65 | 10.9 | 10.7441541262765 | 0.155845873723524 |
| 66 | -41.3 | -41.3282737669366 | 0.0282737669365489 |
| 67 | 6.3 | 6.14786001387479 | 0.152139986125209 |
| 68 | 28.9 | 28.9904290753924 | -0.0904290753924138 |
| 69 | 3.5 | 3.57736610339144 | -0.0773661033914409 |
| 70 | -1.60000000000001 | -1.54423918723686 | -0.0557608127631475 |
| 71 | -7.89999999999999 | -8.127981320386 | 0.227981320386011 |
| 72 | -1.5 | -1.0553405908458 | -0.444659409154201 |
| 73 | -4.10000000000001 | -4.0259166742944 | -0.0740833257056105 |
| 74 | 18.8 | 18.9754298821062 | -0.175429882106217 |
| 75 | -16.6 | -16.7653789265632 | 0.165378926563235 |
| 76 | 5.2 | 5.20315852060602 | -0.00315852060602154 |
| 77 | 15 | 15.0014309736061 | -0.00143097360611348 |
| 78 | -31.4 | -31.206095355383 | -0.193904644616997 |
| 79 | 0.300000000000011 | -0.245039722419085 | 0.545039722419096 |
| 80 | 3.7 | NA | NA |
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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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')
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