Paper - multiple linear regression2

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 20 Dec 2008 08:09:51 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t12297858498cku81x3w8groiz.htm/, Retrieved Sat, 20 Dec 2008 16:10:49 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t12297858498cku81x3w8groiz.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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120.3 0 133.4 0 109.4 0 93.2 0 91.2 0 99.2 0 108.2 0 101.5 0 106.9 0 104.4 0 77.9 0 60 0 99.5 0 95 0 105.6 0 102.5 0 93.3 0 97.3 0 127 0 111.7 0 96.4 0 133 0 72.2 0 95.8 0 124.1 0 127.6 0 110.7 0 104.6 0 112.7 0 115.3 0 139.4 0 119 0 97.4 0 154 0 81.5 0 88.8 0 127.7 1 105.1 1 114.9 1 106.4 1 104.5 1 121.6 1 141.4 1 99 1 126.7 1 134.1 1 81.3 1 88.6 1 132.7 1 132.9 1 134.4 1 103.7 1 119.7 1 115 1 132.9 1 108.5 1 113.9 1 142.9 1 95.2 1 93 1

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 computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 81.305 + 9.8375X[t] + 35.62M1[t] + 33.56M2[t] + 29.76M3[t] + 16.84M4[t] + 19.04M5[t] + 24.44M6[t] + 44.54M7[t] + 22.7M8[t] + 23.02M9[t] + 48.44M10[t] -3.61999999999999M11[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) 81.305 5.305876 15.3236 0 0 X 9.8375 3.043129 3.2327 0.002244 0.001122 M1 35.62 7.303509 4.8771 1.3e-05 6e-06 M2 33.56 7.303509 4.5951 3.3e-05 1.6e-05 M3 29.76 7.303509 4.0748 0.000176 8.8e-05 M4 16.84 7.303509 2.3057 0.025585 0.012792 M5 19.04 7.303509 2.607 0.012202 0.006101 M6 24.44 7.303509 3.3463 0.001618 0.000809 M7 44.54 7.303509 6.0984 0 0 M8 22.7 7.303509 3.1081 0.003193 0.001596 M9 23.02 7.303509 3.1519 0.002823 0.001411 M10 48.44 7.303509 6.6324 0 0 M11 -3.61999999999999 7.303509 -0.4957 0.62245 0.311225 Multiple Linear Regression - Regression Statistics Multiple R 0.838646213721932 R-squared 0.703327471790132 Adjusted R-squared 0.627581294374846 F-TEST (value) 9.28531967935587 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 8.06306976741666e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.5478613199081 Sum Squared Residuals 6267.59575 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 120.3 116.925000000000 3.37499999999987 2 133.4 114.865 18.535 3 109.4 111.065 -1.66500000000000 4 93.2 98.145 -4.945 5 91.2 100.345 -9.14500000000001 6 99.2 105.745 -6.54499999999999 7 108.2 125.845 -17.645 8 101.5 104.005 -2.50500000000000 9 106.9 104.325 2.57500000000001 10 104.4 129.745 -25.345 11 77.9 77.685 0.215 12 60 81.305 -21.305 13 99.5 116.925 -17.4250000000000 14 95 114.865 -19.865 15 105.6 111.065 -5.465 16 102.5 98.145 4.355 17 93.3 100.345 -7.045 18 97.3 105.745 -8.445 19 127 125.845 1.15500000000000 20 111.7 104.005 7.695 21 96.4 104.325 -7.925 22 133 129.745 3.25500000000001 23 72.2 77.685 -5.48499999999999 24 95.8 81.305 14.495 25 124.1 116.925 7.17500000000004 26 127.6 114.865 12.735 27 110.7 111.065 -0.365 28 104.6 98.145 6.455 29 112.7 100.345 12.355 30 115.3 105.745 9.555 31 139.4 125.845 13.5550000000000 32 119 104.005 14.995 33 97.4 104.325 -6.925 34 154 129.745 24.255 35 81.5 77.685 3.815 36 88.8 81.305 7.495 37 127.7 126.7625 0.937500000000037 38 105.1 124.7025 -19.6025 39 114.9 120.9025 -6.00249999999999 40 106.4 107.9825 -1.58250000000000 41 104.5 110.1825 -5.6825 42 121.6 115.5825 6.01749999999999 43 141.4 135.6825 5.71749999999999 44 99 113.8425 -14.8425 45 126.7 114.1625 12.5375 46 134.1 139.5825 -5.48250000000002 47 81.3 87.5225 -6.22250000000001 48 88.6 91.1425 -2.54250000000000 49 132.7 126.7625 5.93750000000002 50 132.9 124.7025 8.1975 51 134.4 120.9025 13.4975 52 103.7 107.9825 -4.2825 53 119.7 110.1825 9.5175 54 115 115.5825 -0.582500000000004 55 132.9 135.6825 -2.78250000000001 56 108.5 113.8425 -5.3425 57 113.9 114.1625 -0.262500000000005 58 142.9 139.5825 3.31750000000000 59 95.2 87.5225 7.6775 60 93 91.1425 1.85750000000000

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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