mpregress
| 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 |
| h[t] = + 47.8203131462657 -0.367047299711292e[t] -21.0384241172281f[t] -0.0112998862209406w[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) | 47.8203131462657 | 34.921373 | 1.3694 | 0.17635 | 0.088175 |
| e | -0.367047299711292 | 0.190277 | -1.929 | 0.058803 | 0.029402 |
| f | -21.0384241172281 | 19.089932 | -1.1021 | 0.275146 | 0.137573 |
| w | -0.0112998862209406 | 0.006886 | -1.6409 | 0.106413 | 0.053207 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.405770367742263 |
| R-squared | 0.164649591337691 |
| Adjusted R-squared | 0.119898676587925 |
| F-TEST (value) | 3.67924526813277 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 56 |
| p-value | 0.0172336407162850 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 261.206416488339 |
| Sum Squared Residuals | 3820812.35282206 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 0 | 47.8203131462658 | -47.8203131462658 |
| 2 | 0 | -57.3718074398748 | 57.3718074398748 |
| 3 | 0 | 110.93558549795 | -110.93558549795 |
| 4 | 0 | 47.8203131462659 | -47.8203131462659 |
| 5 | 0 | 89.8971613807219 | -89.8971613807219 |
| 6 | 0 | 26.7818890290377 | -26.7818890290377 |
| 7 | 0 | 5.74346491180957 | -5.74346491180957 |
| 8 | 0 | 89.8971613807219 | -89.8971613807219 |
| 9 | 0 | 89.8971613807219 | -89.8971613807219 |
| 10 | 0 | 47.8203131462657 | -47.8203131462657 |
| 11 | 0 | 26.7818890290377 | -26.7818890290377 |
| 12 | 0 | 89.8971613807219 | -89.8971613807219 |
| 13 | 173 | -61.426190935357 | 234.426190935357 |
| 14 | 70 | 12.5429508834219 | 57.457049116578 |
| 15 | 215 | 163.155033251901 | 51.8449667480989 |
| 16 | 357 | -52.884817986723 | 409.884817986723 |
| 17 | 424 | 57.3554184711334 | 366.644581528867 |
| 18 | -384 | -147.365970063850 | -236.634029936150 |
| 19 | 123 | -53.7853046997508 | 176.785304699751 |
| 20 | -138 | 37.1803541284053 | -175.180354128405 |
| 21 | 195 | 24.1079605487044 | 170.892039451296 |
| 22 | 135 | 156.429506931631 | -21.4295069316306 |
| 23 | 19 | 190.277096214731 | -171.277096214731 |
| 24 | 162 | -65.2894973901305 | 227.289497390130 |
| 25 | 244 | 159.822544573072 | 84.1774554269282 |
| 26 | 242 | 13.4471925232186 | 228.552807476781 |
| 27 | -227 | -9.51440964223795 | -217.485590357762 |
| 28 | 555 | 125.780304718283 | 429.219695281717 |
| 29 | -59 | 183.246957695382 | -242.246957695382 |
| 30 | -18 | -124.315179929480 | 106.315179929480 |
| 31 | 1155 | 378.907481390538 | 776.092518609462 |
| 32 | -773 | -183.770102289837 | -589.229897710163 |
| 33 | 192 | -6.24035855793616 | 198.240358557936 |
| 34 | 66 | -12.3933627420879 | 78.3933627420879 |
| 35 | 90 | -5.52223601732551 | 95.5222360173255 |
| 36 | 54 | 59.1667831868437 | -5.16678318684367 |
| 37 | -7 | 284.195823649467 | -291.195823649467 |
| 38 | -348 | -52.214101381603 | -295.785898618397 |
| 39 | -35 | 131.411394577060 | -166.411394577060 |
| 40 | -6 | 84.9536601615297 | -90.9536601615297 |
| 41 | -38 | -75.1861211859261 | 37.1861211859261 |
| 42 | -89 | 185.524412537423 | -274.524412537423 |
| 43 | 66 | 17.5908419832035 | 48.4091580167965 |
| 44 | 106 | 214.334709727055 | -108.334709727055 |
| 45 | 336 | 145.814752217547 | 190.185247782453 |
| 46 | -143 | 248.637002497974 | -391.637002497974 |
| 47 | 4 | 45.6228140281741 | -41.6228140281741 |
| 48 | 10 | 57.4172563352942 | -47.4172563352942 |
| 49 | -74 | 6.09776743257379 | -80.0977674325738 |
| 50 | -126 | 128.070037174551 | -254.070037174551 |
| 51 | 289 | 91.1908598610763 | 197.809140138924 |
| 52 | -92 | 148.081322391790 | -240.08132239179 |
| 53 | 8 | 15.1179406670428 | -7.11794066704278 |
| 54 | 700 | 20.4019351194129 | 679.598064880587 |
| 55 | -212 | 258.171467668352 | -470.171467668352 |
| 56 | 197 | 139.341639182114 | 57.6583608178862 |
| 57 | 859 | 251.893108983833 | 607.106891016167 |
| 58 | -52 | 184.976679458315 | -236.976679458315 |
| 59 | -80 | 101.719429278308 | -181.719429278308 |
| 60 | 251 | 308.00260738324 | -57.0026073832402 |
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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')
Copyright
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