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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 04:36:49 -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/t11975450856v46i5w0uuvpad0.htm/, Retrieved Thu, 13 Dec 2007 12:24:56 +0100

User-defined keywords:

Dataseries X:

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106.5 112.3 102.8 96,5 101.0 98.9 105.1 103.0 99.0 104.3 94.6 90.4 108.9 111.4 100.8 102.5 98.2 98.7 113.3 104.6 99.3 111.8 97.3 97.7 115.6 111.9 107.0 107.1 100.6 99.2 108.4 103.0 99.8 115.0 90.8 95.9 114.4 108.2 112.6 109.1 105.0 105.0 118.5 103.7 112.5 116.6 96.6 101.9 116.5 119.3 115.4 108.5 111.5 108.8 121.8 109.6 112.2 119.6 103.4 105.3 113.5

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 industriële_productie[t] = + 90.3011764705882 + 15.4292810457517M1[t] + 16.5852287581699M2[t] + 11.4647058823530M3[t] + 8.26418300653594M4[t] + 6.56366013071895M5[t] + 5.20313725490195M6[t] + 16.2826143790850M7[t] + 7.42209150326796M8[t] + 6.98156862745097M9[t] + 15.661045751634M10[t] -1.47947712418301M11[t] + 0.220522875816993t + 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) 90.3011764705882 1.657133 54.4924 0 0 M1 15.4292810457517 1.932607 7.9837 0 0 M2 16.5852287581699 2.028475 8.1762 0 0 M3 11.4647058823530 2.025885 5.6591 1e-06 0 M4 8.26418300653594 2.023564 4.084 0.000167 8.3e-05 M5 6.56366013071895 2.021515 3.2469 0.002131 0.001065 M6 5.20313725490195 2.019736 2.5761 0.013124 0.006562 M7 16.2826143790850 2.018231 8.0678 0 0 M8 7.42209150326796 2.016998 3.6798 0.00059 0.000295 M9 6.98156862745097 2.016038 3.463 0.001133 0.000567 M10 15.661045751634 2.015353 7.7709 0 0 M11 -1.47947712418301 2.014941 -0.7343 0.466366 0.233183 t 0.220522875816993 0.023511 9.3797 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.923456661459081 R-squared 0.852772205593152 Adjusted R-squared 0.81596525699144 F-TEST (value) 23.1687830148867 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 6.66133814775094e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.1856851491133 Sum Squared Residuals 487.13231372549 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.5 105.950980392157 0.549019607843207 2 112.3 107.327450980392 4.97254901960782 3 102.8 102.427450980392 0.37254901960783 4 96.5 99.4474509803922 -2.94745098039219 5 101 97.9674509803922 3.03254901960782 6 98.9 96.8274509803922 2.07254901960784 7 105.1 108.127450980392 -3.02745098039216 8 103 99.4874509803922 3.51254901960784 9 99 99.2674509803921 -0.267450980392144 10 104.3 108.167450980392 -3.86745098039215 11 94.6 91.2474509803922 3.35254901960783 12 90.4 92.9474509803922 -2.54745098039216 13 108.9 108.597254901961 0.302745098039209 14 111.4 109.973725490196 1.42627450980393 15 100.8 105.073725490196 -4.27372549019608 16 102.5 102.093725490196 0.406274509803932 17 98.2 100.613725490196 -2.41372549019607 18 98.7 99.473725490196 -0.773725490196077 19 113.3 110.773725490196 2.52627450980392 20 104.6 102.133725490196 2.46627450980392 21 99.3 101.913725490196 -2.61372549019609 22 111.8 110.813725490196 0.986274509803915 23 97.3 93.893725490196 3.40627450980392 24 97.7 95.593725490196 2.10627450980392 25 115.6 111.243529411765 4.35647058823527 26 111.9 112.62 -0.719999999999992 27 107 107.72 -0.719999999999996 28 107.1 104.74 2.36000000000000 29 100.6 103.26 -2.66000000000000 30 99.2 102.12 -2.92 31 108.4 113.42 -5.01999999999999 32 103 104.78 -1.78000000000000 33 99.8 104.56 -4.76000000000001 34 115 113.46 1.54000000000000 35 90.8 96.54 -5.74 36 95.9 98.24 -2.33999999999999 37 114.4 113.889803921569 0.510196078431359 38 108.2 115.266274509804 -7.06627450980391 39 112.6 110.366274509804 2.23372549019608 40 109.1 107.386274509804 1.71372549019609 41 105 105.906274509804 -0.906274509803916 42 105 104.766274509804 0.233725490196078 43 118.5 116.066274509804 2.43372549019608 44 103.7 107.426274509804 -3.72627450980392 45 112.5 107.206274509804 5.29372549019608 46 116.6 116.106274509804 0.493725490196069 47 96.6 99.186274509804 -2.58627450980392 48 101.9 100.886274509804 1.01372549019608 49 116.5 116.536078431373 -0.0360784313725666 50 119.3 117.912549019608 1.38745098039216 51 115.4 113.012549019608 2.38745098039217 52 108.5 110.032549019608 -1.53254901960783 53 111.5 108.552549019608 2.94745098039216 54 108.8 107.412549019608 1.38745098039216 55 121.8 118.712549019608 3.08745098039215 56 109.6 110.072549019608 -0.472549019607844 57 112.2 109.852549019608 2.34745098039216 58 119.6 118.752549019608 0.847450980392155 59 103.4 101.832549019608 1.56745098039217 60 105.3 103.532549019608 1.76745098039216 61 113.5 119.182352941176 -5.68235294117648

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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