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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 08:31:38 -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/t1197559024ebj5pg49vd6rqk0.htm/, Retrieved Thu, 13 Dec 2007 16:17:14 +0100

User-defined keywords:

multiple regression

Dataseries X:

» Textbox « » Textfile « » CSV «

103,1 98,6 98,1 98,6 100,6 98 101,1 98 103,1 106,8 111,1 106,8 95,5 96,6 93,3 96,7 90,5 100,1 100 100,2 90,9 107,7 108 107,7 88,8 91,5 70,4 92 90,7 97,8 75,4 98,4 94,3 107,4 105,5 107,4 104,6 117,5 112,3 117,7 111,1 105,6 102,5 105,7 110,8 97,4 93,5 97,5 107,2 99,5 86,7 99,9 99 98 95,2 98,2 99 104,3 103,8 104,5 91 100,6 97 100,8 96,2 101,1 95,5 101,5 96,9 103,9 101 103,9 96,2 96,9 67,5 99,6 100,1 95,5 64 98,4 99 108,4 106,7 112,7 115,4 117 100,6 118,4 106,9 103,8 101,2 108,1 107,1 100,8 93,1 105,4 99,3 110,6 84,2 114,6 99,2 104 85,8 106,9 108,3 112,6 91,8 115,9 105,6 107,3 92,4 109,8 99,5 98,9 80,3 101,8 107,4 109,8 79,7 114,2 93,1 104,9 62,5 110,8 88,1 102,2 57,1 108,4 110,7 123,9 100,8 127,5 113,1 124,9 100,7 128,6 99,6 112,7 86,2 116,6 93,6 121,9 83,2 127,4 98,6 100,6 71,7 105 99,6 104,3 77,5 108,3 114,3 120,4 89,8 125 107,8 107,5 80,3 111,6 101,2 102,9 78,7 106,5 112,5 125,6 93,8 130,3 100,5 107,5 57,6 115 93,9 108,8 60,6 116,1 116,2 128,4 91 134 112 121,1 85,3 126,5 106,4 119,5 77,4 125,8 95,7 128,7 77,3 136,4 96 108,7 68,3 114,9 95,8 105,5 69,9 110,9 103 119,8 81,7 125,5 102,2 111,3 75,1 116,8 98,4 110,6 69,9 116,8 111,4 120,1 84 125,5 86,6 97,5 54,3 104,2 91,3 107,7 60 115,1 107,9 127,3 89,9 132,8 101,8 117,2 77 123,3 104,4 119,8 85,3 124,8 93,4 116,2 77,6 122 100,1 111 69,2 117,4 98,5 112,4 75,5 117,9 112,9 130,6 85,7 137,4 101,4 109,1 72,2 114,6 107,1 118,8 79,9 124,7 110,8 123,9 85,3 129,6 90,3 101,6 52,2 109,4 95,5 112,8 61,2 120,9 111,4 128 82,4 134,9 113 129,6 85,4 136,3 107,5 125,8 78,2 133,2 95,9 119,5 70,2 127,2 106,3 115,7 70,2 122,7 105,2 113,6 69,3 120,5 117,2 129,7 77,5 137,8 106,9 112 66,1 119,1 108,2 116,8 69 124,3 110 126,3 75,3 134,3 96,1 112,9 58,2 121,7 100,6 115,9 59,7 125

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 intermediair-goederen[t] = + 40.2461048789932 + 0.241619248015509`totale-consumptie`[t] + 0.181476139543005`Duurzame-consumptiegoederen`[t] + 0.17331501498115`Niet-duurzame-consumptiegoederen`[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) 40.2461048789932 7.911237 5.0872 3e-06 1e-06 `totale-consumptie` 0.241619248015509 0.792198 0.305 0.761201 0.3806 `Duurzame-consumptiegoederen` 0.181476139543005 0.103482 1.7537 0.083513 0.041756 `Niet-duurzame-consumptiegoederen` 0.17331501498115 0.678748 0.2553 0.799146 0.399573 Multiple Linear Regression - Regression Statistics Multiple R 0.679250303354806 R-squared 0.461380974607596 Adjusted R-squared 0.440119697289475 F-TEST (value) 21.7005294509919 F-TEST (DF numerator) 3 F-TEST (DF denominator) 76 p-value 2.97640134760968e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.63774009051499 Sum Squared Residuals 2415.59261294320 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.1 98.9614324996327 4.1385675003673 2 100.6 99.2569003604635 1.34309963953647 3 103.1 104.723083270264 -1.62308327026415 4 95.5 97.2778100053309 -1.77781000533088 5 90.5 99.9459700607573 -9.4459700607573 6 90.9 104.533948074378 -13.6339480743778 7 88.8 91.0751676745056 -2.27516767450558 8 90.7 94.6139657305977 -3.91396573059766 9 94.3 103.955777446621 -9.65577744662134 10 104.6 109.415314254776 -4.81531425477625 11 111.1 102.681798856096 8.41820114390355 12 110.8 97.6460526436368 13.1539473563632 13 107.2 97.3353713515317 9.8646286484683 14 99 98.220854140156 0.779145859843976 15 99 102.395634797105 -3.39563479710481 16 91 99.6263402751247 -8.62634027512474 17 96.2 99.5962562003048 -3.39625620030479 18 96.9 101.686864898190 -4.7868648981895 19 96.2 93.1708249229713 3.02917507702866 20 100.1 91.9894134693717 8.11058653062825 21 99 105.333737641489 -6.33373764148854 22 115.4 107.292554308602 8.10744569139786 23 106.9 102.426921264217 4.47307873578262 24 107.1 99.7641562494234 7.33584375057658 25 99.3 102.111385375869 -2.81138537586924 26 99.2 99.4725345468808 -0.272534546880835 27 108.3 104.199152051903 4.10084794809741 28 105.6 101.970234129761 3.62976587023881 29 99.5 96.3582510381113 3.14174896188865 30 107.4 101.032121343521 6.36787865647915 31 93.1 96.1375263771693 -3.03752637716928 32 88.1 94.0892272180404 -5.98922721804042 33 110.7 110.573188984146 0.126811015853781 34 113.1 110.987307134687 2.1126928653133 35 99.6 103.328368105750 -3.72836810575013 36 93.6 106.878638930660 -13.2786389306602 37 98.6 95.7629170076076 2.83708299239244 38 99.6 98.2814093840522 1.31859061594783 39 114.3 107.297996543666 7.00200345633398 40 107.8 100.13466371786 7.66533628214 41 101.2 97.848946777316 3.35105322268402 42 112.5 110.198890770919 2.30110922908123 43 100.5 96.6044264011697 3.89557359883030 44 93.9 97.6536063586981 -3.75360635869814 45 116.2 111.008557030072 5.19144296992796 46 112 106.910459911805 5.08954008819493 47 106.4 104.968887102104 1.43111289789628 48 95.7 109.010775728692 -13.3107757286923 49 96 98.8188326904004 -2.81883269040035 50 95.8 97.642752860095 -1.84275286009493 51 103 105.769725772049 -2.76972577204895 52 102.2 101.010379012597 1.18962098740272 53 98.4 99.8975696133628 -1.49756961336280 54 111.4 106.259606667403 5.1403933325975 55 86.6 91.7175604987263 -5.11756049872629 56 91.3 97.1056244871741 -5.80562448717414 57 107.9 110.335174085780 -2.43517408578029 58 101.8 103.907284838398 -2.10728483839798 59 104.4 106.301719363917 -1.90171936391695 60 93.4 103.549241754633 -10.1492417546328 61 100.1 99.9711730238776 0.128826976122394 62 98.5 101.539397157711 -3.03939715771082 63 112.9 111.167566887064 1.73243311293586 64 101.4 99.57124282933 1.82875717067008 65 107.1 105.062797460871 2.03720253912888 66 110.8 108.12427035269 2.67572964730993 67 90.3 93.2283376004515 -2.92833760045154 68 95.5 99.5608811063955 -4.0608811063955 69 111.4 109.507198044279 1.89280195572097 70 113 110.680858280706 2.31914171929353 71 107.5 107.918800387096 -0.418800387096338 72 95.9 103.904899918368 -8.00489991836769 73 106.3 102.206829208494 4.09317079150641 74 105.2 101.154807229114 4.04519277088622 75 117.2 109.53133122559 7.66866877440999 76 106.9 99.9448517647778 6.95514823522226 77 108.2 102.532143037829 5.66785696217112 78 110 107.703975722909 2.29602427709135 79 96.1 99.179266624553 -3.07926662455297 80 100.6 100.748278127352 -0.148278127351796

Charts produced by software:

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Parameters:

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;

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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