Q3 geen seasonal dummies en geen lineaire trend

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 19 Nov 2008 11:53:58 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/19/t1227120898ddz90vdb060w41j.htm/, Retrieved Wed, 19 Nov 2008 18:55:07 +0000

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/2008/Nov/19/t1227120898ddz90vdb060w41j.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1332.7 0 1343.8 0 1421.6 0 1329.8 0 1306.8 0 1412.8 0 1358.1 0 1163.9 0 1467.9 0 1433.7 0 1362.2 0 1299 0 1291.5 0 1452.7 0 1555.4 0 1402.5 0 1242.9 0 1514.6 0 1308.6 0 1239.3 0 1519.9 0 1659.4 0 1597.6 0 1340.6 0 1427.2 0 1438.1 0 1616.2 0 1392.8 0 1318.7 0 1420.9 0 1221 0 1310 0 1466.7 0 1299.3 0 1640 0 1506.3 0 1530.2 0 1661.9 0 1880.3 1 1230.8 0 1406.5 0 1523.5 0 1323.2 0 1319.2 0 1500.7 0 1483 0 1497 0 1219.8 0 1472.9 0 1423.9 0 1629.6 0 1353.4 0 1366.8 0 1527.1 0 1487.6 0 1478.6 0 1536.7 0 1682.1 0 1576.5 0 1280.5 0

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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 1422.47457627119 + 457.825423728813x[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) 1422.47457627119 16.378677 86.8492 0 0 x 457.825423728813 126.868687 3.6087 0.000642 0.000321 Multiple Linear Regression - Regression Statistics Multiple R 0.428201120612388 R-squared 0.183356199693705 Adjusted R-squared 0.169276134171182 F-TEST (value) 13.0223967637374 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.000642403807251335 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 125.807005442272 Sum Squared Residuals 917989.351864407 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1332.7 1422.47457627119 -89.7745762711878 2 1343.8 1422.47457627119 -78.6745762711863 3 1421.6 1422.47457627119 -0.874576271186511 4 1329.8 1422.47457627119 -92.6745762711865 5 1306.8 1422.47457627119 -115.674576271186 6 1412.8 1422.47457627119 -9.67457627118647 7 1358.1 1422.47457627119 -64.3745762711865 8 1163.9 1422.47457627119 -258.574576271186 9 1467.9 1422.47457627119 45.4254237288137 10 1433.7 1422.47457627119 11.2254237288136 11 1362.2 1422.47457627119 -60.2745762711864 12 1299 1422.47457627119 -123.474576271186 13 1291.5 1422.47457627119 -130.974576271186 14 1452.7 1422.47457627119 30.2254237288136 15 1555.4 1422.47457627119 132.925423728814 16 1402.5 1422.47457627119 -19.9745762711864 17 1242.9 1422.47457627119 -179.574576271186 18 1514.6 1422.47457627119 92.1254237288135 19 1308.6 1422.47457627119 -113.874576271187 20 1239.3 1422.47457627119 -183.174576271186 21 1519.9 1422.47457627119 97.4254237288137 22 1659.4 1422.47457627119 236.925423728814 23 1597.6 1422.47457627119 175.125423728814 24 1340.6 1422.47457627119 -81.8745762711865 25 1427.2 1422.47457627119 4.72542372881363 26 1438.1 1422.47457627119 15.6254237288135 27 1616.2 1422.47457627119 193.725423728814 28 1392.8 1422.47457627119 -29.6745762711865 29 1318.7 1422.47457627119 -103.774576271186 30 1420.9 1422.47457627119 -1.57457627118633 31 1221 1422.47457627119 -201.474576271186 32 1310 1422.47457627119 -112.474576271186 33 1466.7 1422.47457627119 44.2254237288136 34 1299.3 1422.47457627119 -123.174576271186 35 1640 1422.47457627119 217.525423728814 36 1506.3 1422.47457627119 83.8254237288135 37 1530.2 1422.47457627119 107.725423728814 38 1661.9 1422.47457627119 239.425423728814 39 1880.3 1880.3 -1.77635683940025e-15 40 1230.8 1422.47457627119 -191.674576271186 41 1406.5 1422.47457627119 -15.9745762711864 42 1523.5 1422.47457627119 101.025423728814 43 1323.2 1422.47457627119 -99.2745762711864 44 1319.2 1422.47457627119 -103.274576271186 45 1500.7 1422.47457627119 78.2254237288136 46 1483 1422.47457627119 60.5254237288136 47 1497 1422.47457627119 74.5254237288136 48 1219.8 1422.47457627119 -202.674576271186 49 1472.9 1422.47457627119 50.4254237288137 50 1423.9 1422.47457627119 1.42542372881367 51 1629.6 1422.47457627119 207.125423728814 52 1353.4 1422.47457627119 -69.0745762711863 53 1366.8 1422.47457627119 -55.6745762711865 54 1527.1 1422.47457627119 104.625423728813 55 1487.6 1422.47457627119 65.1254237288135 56 1478.6 1422.47457627119 56.1254237288135 57 1536.7 1422.47457627119 114.225423728814 58 1682.1 1422.47457627119 259.625423728813 59 1576.5 1422.47457627119 154.025423728814 60 1280.5 1422.47457627119 -141.974576271186

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) 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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