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Workshop 3 Q3 assessment part 1

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

Title produced by software: Multiple Regression

Date of computation: Sun, 25 Nov 2007 07:01:10 -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/25/t11959987516nmheary2el29v3.htm/, Retrieved Sun, 25 Nov 2007 14:52:32 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15761.3 0 16943.0 0 15070.3 0 13659.6 0 14768.9 0 14725.1 0 15998.1 0 15370.6 0 14956.9 0 15469.7 0 15101.8 0 11703.7 0 16283.6 0 16726.5 0 14968.9 0 14861.0 1 14583.3 1 15305.8 1 17903.9 1 16379.4 0 15420.3 0 17870.5 1 15912.8 1 13866.5 1 17823.2 1 17872.0 1 17420.4 1 16704.4 1 15991.2 1 16583.6 1 19123.5 1 17838.7 1 17209.4 1 18586.5 1 16258.1 1 15141.6 1 19202.1 1 17746.5 1 19090.1 0 18040.3 0 17515.5 1 17751.8 0 21072.4 0 17170.0 1 19439.5 1 19795.4 1 17574.9 1 16165.4 1 19464.6 1 19932.1 1 19961.2 1 17343.4 1 18924.2 1 18574.1 1 21350.6 1 18840.1 1 20304.8 1 21132.4 1 19753.9 1 18009.9 1 20390.4 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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 11592.6852004111 -182.921377183966x[t] + 3642.81713600548M1[t] + 3810.86903048989M2[t] + 3134.35942446043M3[t] + 1892.41836930456M4[t] + 2065.79731414868M5[t] + 2162.58770811922M6[t] + 4566.12237752655M7[t] + 2498.09704693388M8[t] + 2746.43171634121M9[t] + 3789.65066118534M10[t] + 2040.96533059267M11[t] + 98.0853305926687t + 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) 11592.6852004111 336.134037 34.4883 0 0 x -182.921377183966 231.932867 -0.7887 0.434258 0.217129 M1 3642.81713600548 388.852624 9.3681 0 0 M2 3810.86903048989 408.031693 9.3396 0 0 M3 3134.35942446043 411.460601 7.6176 0 0 M4 1892.41836930456 407.255455 4.6468 2.7e-05 1.4e-05 M5 2065.79731414868 407.507175 5.0694 7e-06 3e-06 M6 2162.58770811922 406.850457 5.3154 3e-06 1e-06 M7 4566.12237752655 406.78756 11.2248 0 0 M8 2498.09704693388 406.81781 6.1406 0 0 M9 2746.43171634121 406.941185 6.749 0 0 M10 3789.65066118534 405.409546 9.3477 0 0 M11 2040.96533059267 405.269318 5.0361 7e-06 4e-06 t 98.0853305926687 6.155753 15.9339 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.961683359108548 R-squared 0.9248348831863 Adjusted R-squared 0.904044531727191 F-TEST (value) 44.4838503574751 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 640.713130962519 Sum Squared Residuals 19294125.8608263 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15761.3 15333.5876670093 427.712332990746 2 16943 15599.7248920863 1343.27510791367 3 15070.3 15021.3006166495 48.9993833504616 4 13659.6 13877.4448920863 -217.844892086332 5 14768.9 14148.9091675231 619.990832476877 6 14725.1 14343.7848920863 381.315107913671 7 15998.1 16845.4048920863 -847.304892086332 8 15370.6 14875.4648920863 495.13510791367 9 14956.9 15221.8848920863 -264.984892086331 10 15469.7 16363.1891675231 -893.489167523125 11 15101.8 14712.5891675231 389.210832476875 12 11703.7 12769.7091675231 -1066.00916752312 13 16283.6 16510.6116341213 -227.011634121272 14 16726.5 16776.7488591984 -50.2488591983559 15 14968.9 16198.3245837616 -1229.42458376156 16 14861 14871.5474820144 -10.5474820143891 17 14583.3 15143.0117574512 -559.711757451184 18 15305.8 15337.8874820144 -32.0874820143884 19 17903.9 17839.5074820144 64.3925179856128 20 16379.4 16052.4888591984 326.911140801645 21 15420.3 16398.9088591984 -978.608859198355 22 17870.5 17357.2917574512 513.208242548818 23 15912.8 15706.6917574512 206.108242548818 24 13866.5 13763.8117574512 102.688242548817 25 17823.2 17504.7142240493 318.48577595067 26 17872 17770.8514491264 101.148550873587 27 17420.4 17192.4271736896 227.972826310382 28 16704.4 16048.5714491264 655.828550873588 29 15991.2 16320.0357245632 -328.835724563206 30 16583.6 16514.9114491264 68.6885508735854 31 19123.5 19016.5314491264 106.968550873586 32 17838.7 17046.5914491264 792.108550873588 33 17209.4 17393.0114491264 -183.611449126411 34 18586.5 18534.3157245632 52.1842754367934 35 16258.1 16883.7157245632 -625.615724563206 36 15141.6 14940.8357245632 200.764275436793 37 19202.1 18681.7381911614 520.361808838642 38 17746.5 18947.8754162384 -1201.37541623844 39 19090.1 18552.3725179856 537.727482014388 40 18040.3 17408.5167934224 631.783206577595 41 17515.5 17497.0596916752 18.4403083247685 42 17751.8 17874.8567934224 -123.056793422405 43 21072.4 20376.4767934224 695.923206577597 44 17170 18223.6154162384 -1053.61541623844 45 19439.5 18570.0354162384 869.464583761562 46 19795.4 19711.3396916752 84.0603083247689 47 17574.9 18060.7396916752 -485.83969167523 48 16165.4 16117.8596916752 47.5403083247679 49 19464.6 19858.7621582734 -394.162158273382 50 19932.1 20124.8993833505 -192.799383350464 51 19961.2 19546.4751079137 414.724892086332 52 17343.4 18402.6193833505 -1059.21938335046 53 18924.2 18674.0836587873 250.116341212744 54 18574.1 18868.9593833505 -294.859383350464 55 21350.6 21370.5793833505 -19.9793833504646 56 18840.1 19400.6393833505 -560.539383350464 57 20304.8 19747.0593833505 557.740616649536 58 21132.4 20888.3636587873 244.036341212745 59 19753.9 19237.7636587873 516.136341212744 60 18009.9 17294.8836587873 715.016341212745 61 20390.4 21035.7861253854 -645.386125385404

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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Software written by Ed van Stee & Patrick Wessa

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