Vraag 3 deel 1
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 4 seconds |
| R Server | 'Gwilym Jenkins' @ 72.249.127.135 |
| Multiple Linear Regression - Estimated Regression Equation |
| x[t] = -9.88898916645545 + 0.0939286076487506y[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) | -9.88898916645545 | 0.90438 | -10.9346 | 0 | 0 |
| y | 0.0939286076487506 | 0.008069 | 11.6404 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.826206154961995 |
| R-squared | 0.682616610497085 |
| Adjusted R-squared | 0.677578778917673 |
| F-TEST (value) | 135.498100668313 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 63 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.276161220308293 |
| Sum Squared Residuals | 4.80469623493644 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 0 | -0.153288983662403 | 0.153288983662403 |
| 2 | 0 | -0.132624689979723 | 0.132624689979723 |
| 3 | 0 | -0.126049687444311 | 0.126049687444311 |
| 4 | 0 | 0.00357179111096448 | -0.00357179111096448 |
| 5 | 0 | 0.0242360847936909 | -0.0242360847936909 |
| 6 | 0 | 0.0749575329240155 | -0.0749575329240155 |
| 7 | 0 | 0.0871682519183526 | -0.0871682519183526 |
| 8 | 0 | 0.0232967987172030 | -0.0232967987172030 |
| 9 | 0 | 0.0261146569466655 | -0.0261146569466655 |
| 10 | 0 | -0.0133353582658098 | 0.0133353582658098 |
| 11 | 0 | 0.064625386082653 | -0.064625386082653 |
| 12 | 0 | 0.0157825101053030 | -0.0157825101053030 |
| 13 | 0 | 0.0881075379948406 | -0.0881075379948406 |
| 14 | 0 | 0.0965611126832285 | -0.0965611126832285 |
| 15 | 0 | 0.197064722867391 | -0.197064722867391 |
| 16 | 0 | 0.37834693562948 | -0.37834693562948 |
| 17 | 0 | 0.520179133179093 | -0.520179133179093 |
| 18 | 0 | 0.557750576238593 | -0.557750576238593 |
| 19 | 0 | 0.505150555955293 | -0.505150555955293 |
| 20 | 0 | 0.514543416720169 | -0.514543416720169 |
| 21 | 0 | 0.507968414184756 | -0.507968414184756 |
| 22 | 0 | 0.544600571167768 | -0.544600571167768 |
| 23 | 0 | 0.534268424326406 | -0.534268424326406 |
| 24 | 0 | 0.465700540742818 | -0.465700540742818 |
| 25 | 1 | 0.678918480105482 | 0.321081519894518 |
| 26 | 1 | 0.585929158533218 | 0.414070841466782 |
| 27 | 1 | 0.643225609198956 | 0.356774390801044 |
| 28 | 1 | 0.652618469963832 | 0.347381530036168 |
| 29 | 1 | 0.71742920924147 | 0.28257079075853 |
| 30 | 1 | 0.620682743363257 | 0.379317256636743 |
| 31 | 1 | 0.630075604128131 | 0.369924395871869 |
| 32 | 1 | 0.584989872456732 | 0.415010127543268 |
| 33 | 1 | 0.662011330728707 | 0.337988669271293 |
| 34 | 1 | 0.63477203451057 | 0.36522796548943 |
| 35 | 1 | 0.639468464893007 | 0.360531535106993 |
| 36 | 1 | 0.575597011691856 | 0.424402988308144 |
| 37 | 1 | 0.688311340870357 | 0.311688659129643 |
| 38 | 1 | 0.738093502924195 | 0.261906497075805 |
| 39 | 1 | 0.785997092825058 | 0.214002907174942 |
| 40 | 1 | 0.843293543490796 | 0.156706456509204 |
| 41 | 1 | 0.856443548561621 | 0.143556451438379 |
| 42 | 1 | 0.906225710615459 | 0.093774289384541 |
| 43 | 1 | 0.899650708080046 | 0.100349291919954 |
| 44 | 1 | 0.908104282768434 | 0.0918957172315664 |
| 45 | 1 | 1.02269718409991 | -0.0226971840999092 |
| 46 | 1 | 0.87522927009137 | 0.12477072990863 |
| 47 | 1 | 0.877107842244346 | 0.122892157755654 |
| 48 | 1 | 0.801964956125345 | 0.198035043874655 |
| 49 | 1 | 0.914679285303846 | 0.0853207146961545 |
| 50 | 1 | 0.929707862527647 | 0.0702921374723534 |
| 51 | 1 | 0.968218591663634 | 0.0317814083363660 |
| 52 | 1 | 1.06308648538887 | -0.0630864853888713 |
| 53 | 1 | 1.10723293098378 | -0.107232930983784 |
| 54 | 1 | 1.09690078414242 | -0.0969007841424214 |
| 55 | 1 | 1.06872220184780 | -0.0687222018477966 |
| 56 | 1 | 1.01330432333503 | -0.0133043233350334 |
| 57 | 1 | 1.01048646510557 | -0.0104864651055721 |
| 58 | 1 | 0.98888288534636 | 0.0111171146536409 |
| 59 | 1 | 1.02739361448235 | -0.0273936144823465 |
| 60 | 1 | 0.992640029652308 | 0.00735997034769161 |
| 61 | 1 | 1.04711862208858 | -0.0471186220885849 |
| 62 | 1 | 1.13729008543138 | -0.137290085431385 |
| 63 | 1 | 1.30448300704616 | -0.304483007046161 |
| 64 | 1 | 1.31105800958157 | -0.311058009581573 |
| 65 | 1 | 1.38526160962409 | -0.385261609624086 |
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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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