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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 03:50:21 -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/t1195469005n5npvtzq49us2dr.htm/, Retrieved Mon, 19 Nov 2007 11:43:35 +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 0 113.3 0 113.1 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] = + 74.2583333333333 -3.73888888888889ramp[t] + 27.1565277777778M1[t] + 27.5202777777778M2[t] + 22.73625M3[t] + 21.2322222222222M4[t] + 12.1281944444444M5[t] + 14.6241666666666M6[t] + 30.8401388888889M7[t] + 17.3361111111111M8[t] + 17.7720833333333M9[t] + 33.8280555555556M10[t] -0.335972222222222M11[t] + 0.504027777777778t + 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) 74.2583333333333 2.768867 26.819 0 0 ramp -3.73888888888889 2.664344 -1.4033 0.16724 0.08362 M1 27.1565277777778 3.231261 8.4043 0 0 M2 27.5202777777778 3.288423 8.3688 0 0 M3 22.73625 3.271289 6.9502 0 0 M4 21.2322222222222 3.255882 6.5212 0 0 M5 12.1281944444444 3.242226 3.7407 0.000508 0.000254 M6 14.6241666666666 3.230345 4.5271 4.2e-05 2.1e-05 M7 30.8401388888889 3.220257 9.5769 0 0 M8 17.3361111111111 3.21198 5.3973 2e-06 1e-06 M9 17.7720833333333 3.205528 5.5442 1e-06 1e-06 M10 33.8280555555556 3.200911 10.5683 0 0 M11 -0.335972222222222 3.198137 -0.1051 0.916791 0.458395 t 0.504027777777778 0.076913 6.5532 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.938281557051727 R-squared 0.880372280303414 Adjusted R-squared 0.846564446476118 F-TEST (value) 26.0404817652827 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.05523667837582 Sum Squared Residuals 1175.54922222222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.8 101.918888888889 4.88111111111118 2 113.7 102.786666666667 10.9133333333333 3 102.5 98.5066666666667 3.9933333333333 4 96.6 97.5066666666666 -0.906666666666637 5 92.1 88.9066666666667 3.19333333333331 6 95.6 91.9066666666667 3.69333333333333 7 102.3 108.626666666667 -6.32666666666669 8 98.6 95.6266666666666 2.97333333333338 9 98.2 96.5666666666667 1.63333333333331 10 104.5 113.126666666667 -8.62666666666666 11 84 79.4666666666667 4.53333333333333 12 73.8 80.3066666666667 -6.50666666666669 13 103.9 107.967222222222 -4.06722222222223 14 106 108.835 -2.835 15 97.2 104.555 -7.35499999999999 16 102.6 103.555 -0.955000000000015 17 89 94.955 -5.955 18 93.8 97.955 -4.155 19 116.7 114.675 2.025 20 106.8 101.675 5.12499999999999 21 98.5 102.615 -4.11499999999999 22 118.7 119.175 -0.475000000000011 23 90 85.515 4.485 24 91.9 86.355 5.545 25 113.3 114.015555555556 -0.715555555555573 26 113.1 111.144444444444 1.95555555555555 27 104.1 106.864444444444 -2.76444444444444 28 108.7 105.864444444444 2.83555555555555 29 96.7 97.2644444444444 -0.564444444444436 30 101 100.264444444444 0.73555555555556 31 116.9 116.984444444444 -0.0844444444444379 32 105.8 103.984444444444 1.81555555555554 33 99 104.924444444444 -5.92444444444444 34 129.4 121.484444444444 7.91555555555555 35 83 87.8244444444444 -4.82444444444444 36 88.9 88.6644444444444 0.235555555555560 37 115.9 116.325 -0.425000000000014 38 104.2 117.192777777778 -12.9927777777778 39 113.4 112.912777777778 0.487222222222234 40 112.2 111.912777777778 0.287222222222215 41 100.8 103.312777777778 -2.51277777777777 42 107.3 106.312777777778 0.987222222222225 43 126.6 123.032777777778 3.56722222222222 44 102.9 110.032777777778 -7.13277777777778 45 117.9 110.972777777778 6.92722222222223 46 128.8 127.532777777778 1.26722222222222 47 87.5 93.8727777777778 -6.37277777777778 48 93.8 94.7127777777778 -0.912777777777781 49 122.7 122.373333333333 0.326666666666651 50 126.2 123.241111111111 2.95888888888890 51 124.6 118.961111111111 5.63888888888889 52 116.7 117.961111111111 -1.26111111111112 53 115.2 109.361111111111 5.8388888888889 54 111.1 112.361111111111 -1.26111111111111 55 129.9 129.081111111111 0.8188888888889 56 113.3 116.081111111111 -2.78111111111112 57 118.5 117.021111111111 1.47888888888889 58 133.5 133.581111111111 -0.0811111111111192 59 102.1 99.9211111111111 2.17888888888888 60 102.4 100.761111111111 1.63888888888890

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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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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