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WS 8 - Q3 Vrouwen 2

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 06:59:00 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/15/t1195135032x9w5bfv67c425jw.htm/, Retrieved Thu, 15 Nov 2007 14:57:26 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

8,7 0 8,5 0 8,2 0 8,3 0 8 0 8,1 0 8,7 0 9,3 0 8,9 0 8,8 0 8,4 0 8,4 0 7,3 0 7,2 0 7 0 7 0 6,9 0 6,9 0 7,1 0 7,5 0 7,4 0 8,9 0 8,3 1 8,3 0 9 0 8,9 0 8,8 0 7,8 0 7,8 0 7,8 0 9,2 0 9,3 0 9,2 0 8,6 0 8,5 0 8,5 0 9 0 9 0 8,8 0 8 0 7,9 0 8,1 0 9,3 0 9,4 0 9,4 0 9,3 1 9 0 9,1 0 9,7 0 9,7 0 9,6 0 8,3 0 8,2 0 8,4 0 10,6 0 10,9 0 10,9 0 9,6 0 9,3 0 9,3 0 9,6 0 9,5 0 9,5 0 9 0 8,9 0 9 0 10,1 0 10,2 0 10,2 0 9,5 0 9,3 0 9,3 0 9,4 0 9,3 0 9,1 0 9 0 8,9 0 9 0 9,8 0 10 0 9,8 0 9,4 0 9 1 8,9 0 9,3 0 9,1 0 8,8 0 8,9 1 8,7 0 8,6 0 9,1 0 9,3 0 8,9 0

Text written by user:

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 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 Vrouw[t] = + 8.84494382022472 + 0.0300561797752813x[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) 8.84494382022472 0.089536 98.7861 0 0 x 0.0300561797752813 0.431729 0.0696 0.94465 0.472325 Multiple Linear Regression - Regression Statistics Multiple R 0.00729777799105412 R-squared 5.32575636067139e-05 Adjusted R-squared -0.0109351681774525 F-TEST (value) 0.00484669641145338 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 0.944650292755398 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.84468424895323 Sum Squared Residuals 64.9277247191011 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.84494382022474 -0.144943820224740 2 8.5 8.84494382022472 -0.344943820224718 3 8.2 8.84494382022472 -0.64494382022472 4 8.3 8.84494382022472 -0.544943820224718 5 8 8.84494382022472 -0.844943820224719 6 8.1 8.84494382022472 -0.744943820224719 7 8.7 8.84494382022472 -0.144943820224720 8 9.3 8.84494382022472 0.455056179775282 9 8.9 8.84494382022472 0.0550561797752814 10 8.8 8.84494382022472 -0.0449438202247182 11 8.4 8.84494382022472 -0.444943820224719 12 8.4 8.84494382022472 -0.444943820224719 13 7.3 8.84494382022472 -1.54494382022472 14 7.2 8.84494382022472 -1.64494382022472 15 7 8.84494382022472 -1.84494382022472 16 7 8.84494382022472 -1.84494382022472 17 6.9 8.84494382022472 -1.94494382022472 18 6.9 8.84494382022472 -1.94494382022472 19 7.1 8.84494382022472 -1.74494382022472 20 7.5 8.84494382022472 -1.34494382022472 21 7.4 8.84494382022472 -1.44494382022472 22 8.9 8.84494382022472 0.0550561797752814 23 8.3 8.875 -0.575 24 8.3 8.84494382022472 -0.544943820224718 25 9 8.84494382022472 0.155056179775281 26 8.9 8.84494382022472 0.0550561797752814 27 8.8 8.84494382022472 -0.0449438202247182 28 7.8 8.84494382022472 -1.04494382022472 29 7.8 8.84494382022472 -1.04494382022472 30 7.8 8.84494382022472 -1.04494382022472 31 9.2 8.84494382022472 0.355056179775280 32 9.3 8.84494382022472 0.455056179775282 33 9.2 8.84494382022472 0.355056179775280 34 8.6 8.84494382022472 -0.244943820224719 35 8.5 8.84494382022472 -0.344943820224719 36 8.5 8.84494382022472 -0.344943820224719 37 9 8.84494382022472 0.155056179775281 38 9 8.84494382022472 0.155056179775281 39 8.8 8.84494382022472 -0.0449438202247182 40 8 8.84494382022472 -0.844943820224719 41 7.9 8.84494382022472 -0.944943820224719 42 8.1 8.84494382022472 -0.744943820224719 43 9.3 8.84494382022472 0.455056179775282 44 9.4 8.84494382022472 0.555056179775281 45 9.4 8.84494382022472 0.555056179775281 46 9.3 8.875 0.425 47 9 8.84494382022472 0.155056179775281 48 9.1 8.84494382022472 0.255056179775281 49 9.7 8.84494382022472 0.85505617977528 50 9.7 8.84494382022472 0.85505617977528 51 9.6 8.84494382022472 0.755056179775281 52 8.3 8.84494382022472 -0.544943820224718 53 8.2 8.84494382022472 -0.64494382022472 54 8.4 8.84494382022472 -0.444943820224719 55 10.6 8.84494382022472 1.75505617977528 56 10.9 8.84494382022472 2.05505617977528 57 10.9 8.84494382022472 2.05505617977528 58 9.6 8.84494382022472 0.755056179775281 59 9.3 8.84494382022472 0.455056179775282 60 9.3 8.84494382022472 0.455056179775282 61 9.6 8.84494382022472 0.755056179775281 62 9.5 8.84494382022472 0.655056179775281 63 9.5 8.84494382022472 0.655056179775281 64 9 8.84494382022472 0.155056179775281 65 8.9 8.84494382022472 0.0550561797752814 66 9 8.84494382022472 0.155056179775281 67 10.1 8.84494382022472 1.25505617977528 68 10.2 8.84494382022472 1.35505617977528 69 10.2 8.84494382022472 1.35505617977528 70 9.5 8.84494382022472 0.655056179775281 71 9.3 8.84494382022472 0.455056179775282 72 9.3 8.84494382022472 0.455056179775282 73 9.4 8.84494382022472 0.555056179775281 74 9.3 8.84494382022472 0.455056179775282 75 9.1 8.84494382022472 0.255056179775281 76 9 8.84494382022472 0.155056179775281 77 8.9 8.84494382022472 0.0550561797752814 78 9 8.84494382022472 0.155056179775281 79 9.8 8.84494382022472 0.955056179775282 80 10 8.84494382022472 1.15505617977528 81 9.8 8.84494382022472 0.955056179775282 82 9.4 8.84494382022472 0.555056179775281 83 9 8.875 0.124999999999999 84 8.9 8.84494382022472 0.0550561797752814 85 9.3 8.84494382022472 0.455056179775282 86 9.1 8.84494382022472 0.255056179775281 87 8.8 8.84494382022472 -0.0449438202247182 88 8.9 8.875 0.0249999999999996 89 8.7 8.84494382022472 -0.144943820224720 90 8.6 8.84494382022472 -0.244943820224719 91 9.1 8.84494382022472 0.255056179775281 92 9.3 8.84494382022472 0.455056179775282 93 8.9 8.84494382022472 0.0550561797752814

Charts produced by software:

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Parameters:

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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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