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

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 04:10:26 -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/19/t1195470235wokjjq2c6f1l39m.htm/, Retrieved Mon, 19 Nov 2007 12:04:18 +0100

User-defined keywords:

Dataseries X:

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106.8 0 113.7 0 102.5 0 96.6 0 92.1 0 95.6 0 102.3 0 98.6 0 98.2 0 104.5 0 84 0 73.8 0 103.9 0 106 0 97.2 0 102.6 0 89 0 93.8 0 116.7 0 106.8 0 98.5 0 118.7 0 90 0 91.9 1 113.3 1 113.1 1 104.1 1 108.7 1 96.7 1 101 1 116.9 1 105.8 1 99 1 129.4 1 83 1 88.9 1 115.9 1 104.2 1 113.4 1 112.2 1 100.8 1 107.3 1 126.6 1 102.9 1 117.9 1 128.8 1 87.5 1 93.8 1 122.7 1 126.2 1 124.6 1 116.7 1 115.2 1 111.1 1 129.9 1 113.3 1 118.5 1 133.5 1 102.1 1 102.4 1

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 Totmetaal[t] = + 99.6478260869565 + 10.6035252643948Ramp[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) 99.6478260869565 2.484137 40.1137 0 0 Ramp 10.6035252643948 3.163372 3.352 0.001417 0.000709 Multiple Linear Regression - Regression Statistics Multiple R 0.402842176110845 R-squared 0.162281818853721 Adjusted R-squared 0.147838401937406 F-TEST (value) 11.2356944200932 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00141709187417027 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.9135027882280 Sum Squared Residuals 8232.02982373678 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.8 99.6478260869565 7.15217391304348 2 113.7 99.6478260869565 14.0521739130435 3 102.5 99.6478260869565 2.85217391304348 4 96.6 99.6478260869565 -3.04782608695653 5 92.1 99.6478260869565 -7.54782608695653 6 95.6 99.6478260869565 -4.04782608695653 7 102.3 99.6478260869565 2.65217391304347 8 98.6 99.6478260869565 -1.04782608695653 9 98.2 99.6478260869565 -1.44782608695652 10 104.5 99.6478260869565 4.85217391304348 11 84 99.6478260869565 -15.6478260869565 12 73.8 99.6478260869565 -25.8478260869565 13 103.9 99.6478260869565 4.25217391304348 14 106 99.6478260869565 6.35217391304348 15 97.2 99.6478260869565 -2.44782608695652 16 102.6 99.6478260869565 2.95217391304347 17 89 99.6478260869565 -10.6478260869565 18 93.8 99.6478260869565 -5.84782608695653 19 116.7 99.6478260869565 17.0521739130435 20 106.8 99.6478260869565 7.15217391304347 21 98.5 99.6478260869565 -1.14782608695652 22 118.7 99.6478260869565 19.0521739130435 23 90 99.6478260869565 -9.64782608695652 24 91.9 110.251351351351 -18.3513513513513 25 113.3 110.251351351351 3.04864864864865 26 113.1 110.251351351351 2.84864864864864 27 104.1 110.251351351351 -6.15135135135136 28 108.7 110.251351351351 -1.55135135135135 29 96.7 110.251351351351 -13.5513513513513 30 101 110.251351351351 -9.25135135135135 31 116.9 110.251351351351 6.64864864864865 32 105.8 110.251351351351 -4.45135135135135 33 99 110.251351351351 -11.2513513513514 34 129.4 110.251351351351 19.1486486486487 35 83 110.251351351351 -27.2513513513513 36 88.9 110.251351351351 -21.3513513513513 37 115.9 110.251351351351 5.64864864864865 38 104.2 110.251351351351 -6.05135135135135 39 113.4 110.251351351351 3.14864864864865 40 112.2 110.251351351351 1.94864864864865 41 100.8 110.251351351351 -9.45135135135135 42 107.3 110.251351351351 -2.95135135135135 43 126.6 110.251351351351 16.3486486486486 44 102.9 110.251351351351 -7.35135135135135 45 117.9 110.251351351351 7.64864864864865 46 128.8 110.251351351351 18.5486486486487 47 87.5 110.251351351351 -22.7513513513513 48 93.8 110.251351351351 -16.4513513513514 49 122.7 110.251351351351 12.4486486486487 50 126.2 110.251351351351 15.9486486486487 51 124.6 110.251351351351 14.3486486486486 52 116.7 110.251351351351 6.44864864864865 53 115.2 110.251351351351 4.94864864864865 54 111.1 110.251351351351 0.848648648648642 55 129.9 110.251351351351 19.6486486486487 56 113.3 110.251351351351 3.04864864864865 57 118.5 110.251351351351 8.24864864864865 58 133.5 110.251351351351 23.2486486486487 59 102.1 110.251351351351 -8.15135135135136 60 102.4 110.251351351351 -7.85135135135135

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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