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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: Thu, 13 Dec 2007 13:27:28 -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/Dec/13/t1197576759aookedi49hmk6sh.htm/, Retrieved Thu, 13 Dec 2007 21:12:39 +0100

User-defined keywords:

inval in irak

Dataseries X:

» Textbox « » Textfile « » CSV «

98,6 0 98 0 106,8 0 96,6 0 100,1 0 107,7 0 91,5 0 97,8 0 107,4 0 117,5 0 105,6 0 97,4 0 99,5 0 98 0 104,3 0 100,6 0 101,1 0 103,9 0 96,9 0 95,5 0 108,4 0 117 0 103,8 0 100,8 0 110,6 0 104 0 112,6 0 107,3 0 98,9 1 109,8 1 104,9 1 102,2 1 123,9 1 124,9 1 112,7 1 121,9 1 100,6 1 104,3 1 120,4 1 107,5 1 102,9 1 125,6 1 107,5 1 108,8 1 128,4 1 121,1 1 119,5 1 128,7 1 108,7 1 105,5 1 119,8 1 111,3 1 110,6 1 120,1 1 97,5 1 107,7 1 127,3 1 117,2 1 119,8 1 116,2 1 111 1 112,4 1 130,6 1 109,1 1 118,8 1 123,9 1 101,6 1 112,8 1 128 1 129,6 1 125,8 1 119,5 1 115,7 1 113,6 1 129,7 1 112 1 116,8 1 126,3 1 112,9 1 115,9 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Totaal[t] = + 102.601121794872 + 3.74855769230769`Inval-Irak`[t] -6.2711881868132M1[t] -7.75650183150183M2[t] + 4.65818452380952M3[t] -6.95570054945055M4[t] -7.01937957875458M5[t] + 2.49530677655677M6[t] -12.6471497252747M7[t] -8.87532051282051M8[t] + 7.12498855311356M9[t] + 7.56110347985348M10[t] + 0.663885073260072M11[t] + 0.213885073260073t + 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) 102.601121794872 2.079233 49.3457 0 0 `Inval-Irak` 3.74855769230769 1.91295 1.9596 0.054272 0.027136 M1 -6.2711881868132 2.534431 -2.4744 0.015924 0.007962 M2 -7.75650183150183 2.534021 -3.0609 0.003189 0.001595 M3 4.65818452380952 2.534223 1.8381 0.070547 0.035273 M4 -6.95570054945055 2.535035 -2.7438 0.007812 0.003906 M5 -7.01937957875458 2.535054 -2.7689 0.007294 0.003647 M6 2.49530677655677 2.533579 0.9849 0.328273 0.164137 M7 -12.6471497252747 2.532715 -4.9935 5e-06 2e-06 M8 -8.87532051282051 2.532461 -3.5046 0.000827 0.000413 M9 7.12498855311356 2.630169 2.7089 0.008589 0.004295 M10 7.56110347985348 2.628697 2.8764 0.005412 0.002706 M11 0.663885073260072 2.627814 0.2526 0.801333 0.400667 t 0.213885073260073 0.03934 5.4369 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.910525771130682 R-squared 0.829057179893123 Adjusted R-squared 0.795386624417526 F-TEST (value) 24.6226166507408 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.55099762610676 Sum Squared Residuals 1366.96423992674 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 96.5438186813188 2.05618131868122 2 98 95.2723901098901 2.72760989010990 3 106.8 107.900961538462 -1.10096153846154 4 96.6 96.5009615384615 0.0990384615384617 5 100.1 96.6511675824176 3.44883241758242 6 107.7 106.379739010989 1.32026098901100 7 91.5 91.4511675824176 0.0488324175824218 8 97.8 95.4368818681319 2.36311813186813 9 107.4 111.651076007326 -4.251076007326 10 117.5 112.301076007326 5.198923992674 11 105.6 105.617742673993 -0.0177426739926767 12 97.4 105.167742673993 -7.76774267399266 13 99.5 99.1104395604395 0.38956043956046 14 98 97.839010989011 0.160989010989013 15 104.3 110.467582417582 -6.16758241758241 16 100.6 99.0675824175824 1.53241758241758 17 101.1 99.2177884615385 1.88221153846154 18 103.9 108.946359890110 -5.04635989010988 19 96.9 94.0177884615385 2.88221153846154 20 95.5 98.0035027472528 -2.50350274725275 21 108.4 114.217696886447 -5.81769688644688 22 117 114.867696886447 2.13230311355312 23 103.8 108.184363553114 -4.38436355311355 24 100.8 107.734363553114 -6.93436355311355 25 110.6 101.677060439560 8.92293956043958 26 104 100.405631868132 3.59436813186813 27 112.6 113.034203296703 -0.434203296703296 28 107.3 101.634203296703 5.6657967032967 29 98.9 105.532967032967 -6.63296703296703 30 109.8 115.261538461538 -5.46153846153846 31 104.9 100.332967032967 4.56703296703297 32 102.2 104.318681318681 -2.11868131868132 33 123.9 120.532875457875 3.36712454212454 34 124.9 121.182875457875 3.71712454212455 35 112.7 114.499542124542 -1.79954212454212 36 121.9 114.049542124542 7.85045787545788 37 100.6 107.992239010989 -7.392239010989 38 104.3 106.720810439560 -2.42081043956044 39 120.4 119.349381868132 1.05061813186814 40 107.5 107.949381868132 -0.449381868131864 41 102.9 108.099587912088 -5.19958791208791 42 125.6 117.828159340659 7.77184065934065 43 107.5 102.899587912088 4.60041208791209 44 108.8 106.885302197802 1.9146978021978 45 128.4 123.099496336996 5.30050366300367 46 121.1 123.749496336996 -2.64949633699634 47 119.5 117.066163003663 2.43383699633700 48 128.7 116.616163003663 12.083836996337 49 108.7 110.558859890110 -1.85885989010987 50 105.5 109.287431318681 -3.78743131868132 51 119.8 121.916002747253 -2.11600274725275 52 111.3 110.516002747253 0.783997252747252 53 110.6 110.666208791209 -0.0662087912087955 54 120.1 120.394780219780 -0.294780219780225 55 97.5 105.466208791209 -7.9662087912088 56 107.7 109.451923076923 -1.75192307692307 57 127.3 125.666117216117 1.63388278388278 58 117.2 126.316117216117 -9.11611721611721 59 119.8 119.632783882784 0.167216117216115 60 116.2 119.182783882784 -2.98278388278388 61 111 113.125480769231 -2.12548076923075 62 112.4 111.854052197802 0.545947802197805 63 130.6 124.482623626374 6.11737637362637 64 109.1 113.082623626374 -3.98262362637363 65 118.8 113.232829670330 5.56717032967033 66 123.9 122.961401098901 0.938598901098903 67 101.6 108.032829670330 -6.43282967032968 68 112.8 112.018543956044 0.78145604395604 69 128 128.232738095238 -0.232738095238099 70 129.6 128.882738095238 0.717261904761897 71 125.8 122.199404761905 3.60059523809523 72 119.5 121.749404761905 -2.24940476190477 73 115.7 115.692101648352 0.00789835164836982 74 113.6 114.420673076923 -0.820673076923087 75 129.7 127.049244505494 2.65075549450548 76 112 115.649244505495 -3.64924450549450 77 116.8 115.799450549451 1.00054945054945 78 126.3 125.528021978022 0.771978021978018 79 112.9 110.599450549451 2.30054945054945 80 115.9 114.585164835165 1.31483516483517

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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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