WS 8, Multiple Regression

*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: Mon, 29 Nov 2010 23:45:10 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr.htm/, Retrieved Tue, 30 Nov 2010 00:44:15 +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/2010/Nov/30/t1291074246mwgy9ysn53so9xr.htm/}, year = {2010}, } @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 = {2010}, 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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9 911 8 915 9 452 9 112 8 472 8 230 8 384 8 625 8 221 8 649 8 625 10 443 10 357 8 586 8 892 8 329 8 101 7 922 8 120 7 838 7 735 8 406 8 209 9 451 10 041 9 411 10 405 8 467 8 464 8 102 7 627 7 513 7 510 8 291 8 064 9 383 9 706 8 579 9 474 8 318 8 213 8 059 9 111 7 708 7 680 8 014 8 007 8 718 9 486 9 113 9 025 8 476 7 952 7 759 7 835 7 600 7 651 8 319 8 812 8 630

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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 9.81564665770551 -0.00130798098140336V2[t] + 0.467047542017969M1[t] -0.496870365252102M2[t] + 0.0191390733849997M3[t] -0.914554765271227M4[t] -1.17461898261787M5[t] -1.39948880362134M6[t] -1.18904313812691M7[t] -1.46415884470312M8[t] -1.58241850777879M9[t] -1.06574537070756M10[t] -1.04666703073587M11[t] -0.0091376845130207t + 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) 9.81564665770551 0.223663 43.8858 0 0 V2 -0.00130798098140336 0.000196 -6.6898 0 0 M1 0.467047542017969 0.241431 1.9345 0.059216 0.029608 M2 -0.496870365252102 0.24102 -2.0615 0.044929 0.022465 M3 0.0191390733849997 0.241151 0.0794 0.937086 0.468543 M4 -0.914554765271227 0.243112 -3.7619 0.000476 0.000238 M5 -1.17461898261787 0.240717 -4.8797 1.3e-05 7e-06 M6 -1.39948880362134 0.240897 -5.8095 1e-06 0 M7 -1.18904313812691 0.240689 -4.9402 1.1e-05 5e-06 M8 -1.46415884470312 0.240945 -6.0767 0 0 M9 -1.58241850777879 0.239542 -6.606 0 0 M10 -1.06574537070756 0.242209 -4.4001 6.4e-05 3.2e-05 M11 -1.04666703073587 0.241932 -4.3263 8.1e-05 4e-05 t -0.0091376845130207 0.002878 -3.1747 0.002676 0.001338 Multiple Linear Regression - Regression Statistics Multiple R 0.914398840553984 R-squared 0.83612523960647 Adjusted R-squared 0.789812807321342 F-TEST (value) 18.0540126776060 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 7.37188088351104e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.378355541378205 Sum Squared Residuals 6.58503412181335 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9 9.081985841152 -0.0819858411519943 2 8 8.1036983254433 -0.103698325443292 3 9 9.21616527395713 -0.216165273957128 4 9 8.71804728446502 0.281952715534975 5 8 7.97797222930015 0.0220277706998493 6 8 8.06049612128328 -0.0604961212832768 7 8 8.06037503112856 -0.0603750311285617 8 8 7.46089822352112 0.539101776478877 9 8 7.8619251924194 0.138074807580605 10 8 7.80964478493696 0.190355215063036 11 8 7.85097698394931 0.149023016050689 12 10 9.12655886878757 0.873441131212428 13 10 9.69695509069321 0.30304490930679 14 8 8.42437185416875 -0.424371854168749 15 8 8.5310014279834 -0.531001427983402 16 8 8.32456319734425 -0.324563197344247 17 8 8.35358095924455 -0.353580959244549 18 7 7.0457210679959 -0.0457210679959024 19 8 8.2960297960628 -0.296029796062801 20 7 7.07264606032596 -0.07264606032596 21 7 7.07997075382182 -0.0799707538218178 22 8 8.01783194926173 -0.0178319492617327 23 8 8.28544485805686 -0.28544485805686 24 9 9.0064428067801 -0.00644280678009763 25 10 10.0006248666604 -0.000624866660424087 26 9 8.54361631175809 0.456383688241911 27 10 9.05833595177059 0.94166404822941 28 8 8.03440960775433 -0.0344096077543344 29 8 7.76913164883888 0.230868351161119 30 8 8.00861325859041 -0.00861325859040978 31 7 7.52323122433505 -0.523231224335049 32 7 7.3880876651258 -0.388087665125803 33 7 7.26461426048133 -0.264614260481326 34 8 8.05859754796687 -0.0585975479668706 35 8 8.3654498862041 -0.365449886204099 36 9 8.98573329935928 0.0142667006407225 37 9 9.02116529987094 -0.0211652998709404 38 8 8.21422329272608 -0.214223292726076 39 9 8.85843304989751 0.141566950102490 40 8 8.11964655982719 -0.119646559827187 41 8 7.98778266101488 0.0122173389851243 42 8 7.9552042266345 0.044795773365494 43 9 8.08849719658294 0.911502803417065 44 7 7.0233791595959 -0.0233791595958998 45 7 6.93260527948651 0.0673947205134941 46 8 8.31125606565935 -0.311256065659353 47 8 8.33035258798784 -0.330352587987842 48 8 8.4379074564329 -0.437907456432903 49 9 9.19926890162343 -0.199268901623431 50 9 8.7140902159038 0.285909784096206 51 9 9.33606429639137 -0.33606429639137 52 8 7.8033333506092 0.196666649390793 53 7 6.91153250160154 0.0884674983984564 54 7 6.9299653254959 0.0700346745040952 55 7 7.03186675189065 -0.0318667518906529 56 7 7.05498889143121 -0.054988891431214 57 7 6.86088451379096 0.139115486209045 58 8 7.80266965217508 0.197330347824921 59 8 7.16777568380189 0.832224316198112 60 8 8.44335756864015 -0.44335756864015

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/1lshp1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/1lshp1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/2lshp1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/2lshp1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/3lshp1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/3lshp1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/4vjya1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/4vjya1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/5vjya1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/5vjya1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/6vjya1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/6vjya1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/76sxv1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/76sxv1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/8hkfy1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/8hkfy1291074300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/9hkfy1291074300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291074246mwgy9ysn53so9xr/9hkfy1291074300.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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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