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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: Wed, 21 Nov 2007 06:35:06 -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/21/t1195651785g67q5xc25ekjylr.htm/, Retrieved Wed, 21 Nov 2007 14:29:56 +0100

User-defined keywords:

Dataseries X:

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1 88.2 1 73.4 1 81.3 1 89.4 1 80.7 1 80.1 1 100.8 1 97.0 1 93.6 1 67.1 1 88.7 1 89.1 1 98.7 1 76.0 1 81.6 1 92.9 1 84.8 1 79.4 1 100.3 1 90.7 1 84.2 1 69.9 1 85.3 1 81.5 1 92.4 1 71.2 1 74.5 1 86.4 1 73.6 1 80.1 1 91.0 1 87.3 1 78.8 1 72.4 1 83.1 1 90.0 1 99.8 1 73.1 1 80.8 1 92.0 1 75.1 1 84.2 1 99.6 1 89.5 1 87.8 1 70.5 1 80.7 1 94.1 1 97.2 1 66.5 1 81.4 1 82.5 1 76.1 1 88.0 1 90.0 1 94.3 1 96.4 1 68.0 1 82.1 1 103.0 1 109.7 1 75.1 1 88.0 1 86.4 1 84.4 1 91.1 1 96.4 1 94.9 1 94.1 0 71.9 0 93.4 0 108.2 0 104.1 0 80.6 0 86.4 0 98.3 0 94.3 0 88.6 0 109.2 0 102.0 0 101.3

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 Y[t] = + 98.3519097222222 -7.36510416666666X[t] + 4.69468625992064M1[t] -20.2410838293651M2[t] -11.9911396329365M3[t] -4.34119543650794M4[t] -12.8055369543651M5[t] -9.6413070436508M6[t] + 3.99435143849206M7[t] -0.569990079365075M8[t] -3.4057601686508M9[t] -24.2498883928571M10[t] -8.71661086309524M11[t] + 0.0500558035714289t + 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) 98.3519097222222 3.219354 30.5502 0 0 X -7.36510416666666 1.918055 -3.8399 0.000276 0.000138 M1 4.69468625992064 2.682411 1.7502 0.084666 0.042333 M2 -20.2410838293651 2.681282 -7.549 0 0 M3 -11.9911396329365 2.680471 -4.4735 3.1e-05 1.5e-05 M4 -4.34119543650794 2.67998 -1.6199 0.10996 0.05498 M5 -12.8055369543651 2.679809 -4.7785 1e-05 5e-06 M6 -9.6413070436508 2.679958 -3.5976 0.00061 0.000305 M7 3.99435143849206 2.680427 1.4902 0.140867 0.070433 M8 -0.569990079365075 2.681215 -0.2126 0.832295 0.416147 M9 -3.4057601686508 2.682322 -1.2697 0.208582 0.104291 M10 -24.2498883928571 2.781336 -8.7188 0 0 M11 -8.71661086309524 2.780874 -3.1345 0.002555 0.001278 t 0.0500558035714289 0.029275 1.7099 0.091917 0.045958 Multiple Linear Regression - Regression Statistics Multiple R 0.904758360115568 R-squared 0.818587690199012 Adjusted R-squared 0.78338828680479 F-TEST (value) 23.2557262698775 F-TEST (DF numerator) 13 F-TEST (DF denominator) 67 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.81634859434812 Sum Squared Residuals 1554.2133234127 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 88.2 95.7315476190477 -7.53154761904765 2 73.4 70.8458333333334 2.55416666666663 3 81.3 79.1458333333334 2.15416666666664 4 89.4 86.8458333333333 2.55416666666666 5 80.7 78.4315476190476 2.26845238095237 6 80.1 81.6458333333333 -1.54583333333332 7 100.8 95.3315476190476 5.4684523809524 8 97 90.8172619047619 6.18273809523812 9 93.6 88.0315476190476 5.56845238095239 10 67.1 67.2374751984127 -0.137475198412703 11 88.7 82.820808531746 5.87919146825399 12 89.1 91.5874751984127 -2.48747519841271 13 98.7 96.3322172619047 2.36778273809525 14 76 71.4465029761905 4.55349702380954 15 81.6 79.7465029761905 1.85349702380953 16 92.9 87.4465029761905 5.45349702380954 17 84.8 79.0322172619047 5.76778273809524 18 79.4 82.2465029761905 -2.84650297619047 19 100.3 95.9322172619048 4.36778273809524 20 90.7 91.417931547619 -0.717931547619043 21 84.2 88.6322172619048 -4.43221726190476 22 69.9 67.8381448412698 2.06185515873017 23 85.3 83.4214781746032 1.87852182539682 24 81.5 92.1881448412698 -10.6881448412698 25 92.4 96.9328869047619 -4.53288690476189 26 71.2 72.0471726190476 -0.847172619047602 27 74.5 80.3471726190476 -5.84717261904761 28 86.4 88.0471726190476 -1.64717261904761 29 73.6 79.6328869047619 -6.0328869047619 30 80.1 82.8471726190476 -2.74717261904762 31 91 96.5328869047619 -5.53288690476191 32 87.3 92.0186011904762 -4.7186011904762 33 78.8 89.2328869047619 -10.4328869047619 34 72.4 68.438814484127 3.96118551587302 35 83.1 84.0221478174603 -0.922147817460325 36 90 92.788814484127 -2.78881448412699 37 99.8 97.533556547619 2.26644345238095 38 73.1 72.6478422619048 0.452157738095243 39 80.8 80.9478422619048 -0.147842261904760 40 92 88.6478422619048 3.35215773809524 41 75.1 80.233556547619 -5.13355654761905 42 84.2 83.4478422619048 0.752157738095237 43 99.6 97.133556547619 2.46644345238094 44 89.5 92.6192708333333 -3.11927083333334 45 87.8 89.833556547619 -2.03355654761905 46 70.5 69.0394841269841 1.46051587301587 47 80.7 84.6228174603175 -3.92281746031746 48 94.1 93.3894841269841 0.710515873015865 49 97.2 98.1342261904762 -0.934226190476187 50 66.5 73.2485119047619 -6.7485119047619 51 81.4 81.5485119047619 -0.148511904761898 52 82.5 89.2485119047619 -6.74851190476191 53 76.1 80.8342261904762 -4.7342261904762 54 88 84.0485119047619 3.95148809523809 55 90 97.7342261904762 -7.7342261904762 56 94.3 93.2199404761905 1.08005952380951 57 96.4 90.4342261904762 5.96577380952381 58 68 69.6401537698413 -1.64015376984128 59 82.1 85.2234871031746 -3.12348710317462 60 103 93.9901537698413 9.00984623015872 61 109.7 98.7348958333333 10.9651041666667 62 75.1 73.849181547619 1.25081845238095 63 88 82.149181547619 5.85081845238095 64 86.4 89.849181547619 -3.44918154761905 65 84.4 81.4348958333333 2.96510416666666 66 91.1 84.649181547619 6.45081845238094 67 96.4 98.3348958333333 -1.93489583333334 68 94.9 93.8206101190476 1.07938988095237 69 94.1 91.0348958333333 3.06510416666665 70 71.9 77.605927579365 -5.70592757936507 71 93.4 93.1892609126984 0.210739087301597 72 108.2 101.955927579365 6.24407242063493 73 104.1 106.700669642857 -2.60066964285713 74 80.6 81.8149553571428 -1.21495535714285 75 86.4 90.1149553571428 -3.71495535714284 76 98.3 97.8149553571428 0.485044642857148 77 94.3 89.400669642857 4.89933035714287 78 88.6 92.6149553571428 -4.01495535714286 79 109.2 106.300669642857 2.89933035714287 80 102 101.786383928571 0.213616071428576 81 101.3 99.0006696428571 2.29933035714286

Charts produced by software:

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Parameters:

par1 = 2 ; 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')

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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