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Data X:
8 78 284 9.100000381 109 0.274647887 9.300000191 68 433 8.699999809 144 0.15704388 7.5 70 739 7.199999809 113 0.094722598 8.899999619 96 1792 8.899999619 97 0.053571429 10.19999981 74 477 8.300000191 206 0.155136268 8.300000191 111 362 10.89999962 124 0.306629834 8.800000191 77 671 10 152 0.114754098 8.800000191 168 636 9.100000381 162 0.264150943 10.69999981 82 329 8.699999809 150 0.249240122 11.69999981 89 634 7.599999905 134 0.140378549 8.5 149 631 10.80000019 292 0.236133122 8.300000191 60 257 9.5 108 0.233463035 8.199999809 96 284 8.800000191 111 0.338028169 7.900000095 83 603 9.5 182 0.137645108 10.30000019 130 686 8.699999809 129 0.189504373 7.400000095 145 345 11.19999981 158 0.420289855 9.600000381 112 1357 9.699999809 186 0.082535004 9.300000191 131 544 9.600000381 177 0.240808824 10.60000038 80 205 9.100000381 127 0.390243902 9.699999809 130 1264 9.199999809 179 0.102848101 11.60000038 140 688 8.300000191 80 0.203488372 8.100000381 154 354 8.399999619 103 0.435028249 9.800000191 118 1632 9.399999619 101 0.072303922 7.400000095 94 348 9.800000191 117 0.270114943 9.399999619 119 370 10.39999962 88 0.321621622 11.19999981 153 648 9.899999619 78 0.236111111 9.100000381 116 366 9.199999809 102 0.316939891 10.5 97 540 10.30000019 95 0.17962963 11.89999962 176 680 8.899999619 80 0.258823529 8.399999619 75 345 9.600000381 92 0.217391304 5 134 525 10.30000019 126 0.255238095 9.800000191 161 870 10.39999962 108 0.185057471 9.800000191 111 669 9.699999809 77 0.165919283 10.80000019 114 452 9.600000381 60 0.252212389 10.10000038 142 430 10.69999981 71 0.330232558 10.89999962 238 822 10.30000019 86 0.289537713 9.199999809 78 190 10.69999981 93 0.410526316 8.300000191 196 867 9.600000381 106 0.226066897 7.300000191 125 969 10.5 162 0.128998968 9.399999619 82 499 7.699999809 95 0.164328657 9.399999619 125 925 10.19999981 91 0.135135135 9.800000191 129 353 9.899999619 52 0.365439093 3.599999905 84 288 8.399999619 110 0.291666667 8.399999619 183 718 10.39999962 69 0.254874652 10.80000019 119 540 9.199999809 57 0.22037037 10.10000038 180 668 13 106 0.269461078 9 82 347 8.800000191 40 0.236311239 10 71 345 9.199999809 50 0.205797101 11.30000019 118 463 7.800000191 35 0.254859611 11.30000019 121 728 8.199999809 86 0.166208791 12.80000019 68 383 7.400000095 57 0.177545692 10 112 316 10.39999962 57 0.35443038 6.699999809 109 388 8.899999619 94 0.280927835
Names of X columns:
death_rate Doctor Hospital income Population ratio_d/z
Sample Range:
(leave blank to include all observations)
From:
To:
Column Number of Endogenous Series
(?)
Fixed Seasonal Effects
Do not include Seasonal Dummies
Do not include Seasonal Dummies
Include Seasonal Dummies
Type of Equation
No Linear Trend
No Linear Trend
Linear Trend
First Differences
Seasonal Differences (s)
First and Seasonal Differences (s)
Degree of Predetermination (lagged endogenous variables)
Degree of Seasonal Predetermination
Seasonality
12
1
2
3
4
5
6
7
8
9
10
11
12
Chart options
R Code
library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test mywarning <- '' par1 <- as.numeric(par1) if(is.na(par1)) { par1 <- 1 mywarning = 'Warning: you did not specify the column number of the endogenous series! The first column was selected by default.' } if (par4=='') par4 <- 0 par4 <- as.numeric(par4) if (par5=='') par5 <- 0 par5 <- as.numeric(par5) x <- na.omit(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'){ (n <- n -1) x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep=''))) for (i in 1:n) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par3 == 'Seasonal Differences (s=12)'){ (n <- n - 12) x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep=''))) for (i in 1:n) { for (j in 1:k) { x2[i,j] <- x[i+12,j] - x[i,j] } } x <- x2 } if (par3 == 'First and Seasonal Differences (s=12)'){ (n <- n -1) x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B)',colnames(x),sep=''))) for (i in 1:n) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 (n <- n - 12) x2 <- array(0, dim=c(n,k), dimnames=list(1:n, paste('(1-B12)',colnames(x),sep=''))) for (i in 1:n) { for (j in 1:k) { x2[i,j] <- x[i+12,j] - x[i,j] } } x <- x2 } if(par4 > 0) { x2 <- array(0, dim=c(n-par4,par4), dimnames=list(1:(n-par4), paste(colnames(x)[par1],'(t-',1:par4,')',sep=''))) for (i in 1:(n-par4)) { for (j in 1:par4) { x2[i,j] <- x[i+par4-j,par1] } } x <- cbind(x[(par4+1):n,], x2) n <- n - par4 } if(par5 > 0) { x2 <- array(0, dim=c(n-par5*12,par5), dimnames=list(1:(n-par5*12), paste(colnames(x)[par1],'(t-',1:par5,'s)',sep=''))) for (i in 1:(n-par5*12)) { for (j in 1:par5) { x2[i,j] <- x[i+par5*12-j*12,par1] } } x <- cbind(x[(par5*12+1):n,], x2) n <- n - par5*12 } 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[n,])) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x (k <- length(x[n,])) head(x) 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, mywarning) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,formatC(signif(mysum$coefficients[i,1],5),format='g',flag='+')) a<-table.element(a,formatC(signif(mysum$coefficients[i,2],5),format='g',flag=' ')) a<-table.element(a,formatC(signif(mysum$coefficients[i,3],4),format='e',flag='+')) a<-table.element(a,formatC(signif(mysum$coefficients[i,4],4),format='g',flag=' ')) a<-table.element(a,formatC(signif(mysum$coefficients[i,4]/2,4),format='g',flag=' ')) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a,formatC(signif(sqrt(mysum$r.squared),6),format='g',flag=' ')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a,formatC(signif(mysum$r.squared,6),format='g',flag=' ')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a,formatC(signif(mysum$adj.r.squared,6),format='g',flag=' ')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a,formatC(signif(mysum$fstatistic[1],6),format='g',flag=' ')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, signif(mysum$fstatistic[2],6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, signif(mysum$fstatistic[3],6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a,formatC(signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6),format='g',flag=' ')) 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,formatC(signif(mysum$sigma,6),format='g',flag=' ')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a,formatC(signif(sum(myerror*myerror),6),format='g',flag=' ')) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') if(n < 200) { a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,formatC(signif(x[i],6),format='g',flag=' ')) a<-table.element(a,formatC(signif(x[i]-mysum$resid[i],6),format='g',flag=' ')) a<-table.element(a,formatC(signif(mysum$resid[i],6),format='g',flag=' ')) 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,formatC(signif(gqarr[mypoint-kp3+1,1],6),format='g',flag=' ')) a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,2],6),format='g',flag=' ')) a<-table.element(a,formatC(signif(gqarr[mypoint-kp3+1,3],6),format='g',flag=' ')) 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,signif(numsignificant1,6)) a<-table.element(a,formatC(signif(numsignificant1/numgqtests,6),format='g',flag=' ')) 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,signif(numsignificant5,6)) a<-table.element(a,signif(numsignificant5/numgqtests,6)) 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,signif(numsignificant10,6)) a<-table.element(a,signif(numsignificant10/numgqtests,6)) 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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Big Analytics Cloud Computing Center
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