WS 7

*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: Thu, 19 Nov 2009 07:34:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri.htm/, Retrieved Thu, 19 Nov 2009 15:38:20 +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/2009/Nov/19/t1258641489rmib54lyj8h6tri.htm/}, year = {2009}, } @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 = {2009}, 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:

WS 7

Dataseries X:

» Textbox « » Textfile « » CSV «

286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 0 280190 0 280408 0 276836 0 275216 0 274352 0 271311 0 289802 0 290726 0 292300 0 278506 0 269826 0 265861 0 269034 0 264176 0 255198 0 253353 0 246057 0 235372 0 258556 0 260993 0 254663 0 250643 0 243422 0 247105 0 248541 0 245039 0 237080 0 237085 0 225554 0 226839 0 247934 0 248333 1 246969 1 245098 1 246263 1 255765 1 264319 1 268347 1 273046 1 273963 1 267430 1 271993 1 292710 1 295881 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation nwwmb[t] = + 301925.215652174 + 27102.0695652174dummy_variable[t] -8235.60492753617M1[t] -12725.675942029M2[t] -17303.9469565217M3[t] -13996.8179710145M4[t] -11033.0889855073M5[t] -10879.1600000000M6[t] -13472.6310144928M7[t] -13976.9020289855M8[t] -18841.9730434783M9[t] -19865.2440579710M10[t] + 2267.08492753623M11[t] -981.728985507247t + 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) 301925.215652174 7126.659374 42.3656 0 0 dummy_variable 27102.0695652174 6092.422991 4.4485 5.4e-05 2.7e-05 M1 -8235.60492753617 8508.262135 -0.968 0.338129 0.169065 M2 -12725.675942029 8496.893764 -1.4977 0.141046 0.070523 M3 -17303.9469565217 8488.041171 -2.0386 0.047259 0.023629 M4 -13996.8179710145 8481.712233 -1.6502 0.105708 0.052854 M5 -11033.0889855073 8477.912602 -1.3014 0.199605 0.099802 M6 -10879.1600000000 8476.64568 -1.2834 0.20577 0.102885 M7 -13472.6310144928 8477.912602 -1.5891 0.118878 0.059439 M8 -13976.9020289855 8481.712233 -1.6479 0.106191 0.053095 M9 -18841.9730434783 8488.041171 -2.2198 0.0314 0.0157 M10 -19865.2440579710 8496.893764 -2.3379 0.023795 0.011897 M11 2267.08492753623 8508.262135 0.2665 0.791078 0.395539 t -981.728985507247 146.560919 -6.6984 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.755624544566562 R-squared 0.570968452351425 Adjusted R-squared 0.449720406276828 F-TEST (value) 4.70909405006114 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.2543697165609e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13336.2383167097 Sum Squared Residuals 8181341612.24347 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 286602 292707.88173913 -6105.88173913017 2 283042 287236.081739130 -4194.08173913043 3 276687 281676.081739130 -4989.08173913046 4 277915 284001.481739130 -6086.48173913043 5 277128 285983.481739130 -8855.48173913047 6 277103 285155.681739130 -8052.68173913045 7 275037 281580.481739130 -6543.48173913046 8 270150 280094.481739130 -9944.48173913043 9 267140 274247.681739130 -7107.68173913044 10 264993 272242.681739130 -7249.68173913046 11 287259 293393.281739130 -6134.28173913044 12 291186 290144.467826087 1041.53217391303 13 292300 280927.133913044 11372.8660869565 14 288186 275455.333913043 12730.6660869565 15 281477 269895.333913043 11581.6660869565 16 282656 272220.733913044 10435.2660869565 17 280190 274202.733913043 5987.26608695652 18 280408 273374.933913043 7033.06608695651 19 276836 269799.733913044 7036.26608695651 20 275216 268313.733913044 6902.26608695651 21 274352 262466.933913043 11885.0660869565 22 271311 260461.933913043 10849.0660869565 23 289802 281612.533913044 8189.46608695652 24 290726 278363.72 12362.28 25 292300 269146.386086957 23153.6139130434 26 278506 263674.586086956 14831.4139130435 27 269826 258114.586086957 11711.4139130435 28 265861 260439.986086957 5421.01391304348 29 269034 262421.986086957 6612.01391304349 30 264176 261594.186086957 2581.81391304349 31 255198 258018.986086957 -2820.98608695652 32 253353 256532.986086957 -3179.98608695652 33 246057 250686.186086957 -4629.18608695652 34 235372 248681.186086957 -13309.1860869565 35 258556 269831.786086957 -11275.7860869565 36 260993 266582.972173913 -5589.97217391304 37 254663 257365.638260870 -2702.63826086963 38 250643 251893.838260870 -1250.83826086955 39 243422 246333.838260870 -2911.83826086955 40 247105 248659.238260870 -1554.23826086955 41 248541 250641.238260870 -2100.23826086954 42 245039 249813.438260870 -4774.43826086955 43 237080 246238.238260870 -9158.23826086955 44 237085 244752.238260870 -7667.23826086955 45 225554 238905.438260870 -13351.4382608696 46 226839 236900.438260870 -10061.4382608696 47 247934 258051.038260870 -10117.0382608696 48 248333 281904.293913043 -33571.2939130435 49 246969 272686.96 -25717.9600000001 50 245098 267215.16 -22117.16 51 246263 261655.16 -15392.16 52 255765 263980.56 -8215.56 53 264319 265962.56 -1643.55999999999 54 268347 265134.76 3212.24000000001 55 273046 261559.56 11486.44 56 273963 260073.56 13889.44 57 267430 254226.76 13203.24 58 271993 252221.76 19771.24 59 292710 273372.36 19337.64 60 295881 270123.546086957 25757.4539130435

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/15axx1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/15axx1258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/2b3on1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/2b3on1258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/3ks8v1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/3ks8v1258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/4or6n1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/4or6n1258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/5egj31258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/5egj31258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/62h8w1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/62h8w1258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/75n0c1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/75n0c1258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/8n0q41258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/8n0q41258641286.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/9uzfw1258641286.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/19/t1258641489rmib54lyj8h6tri/9uzfw1258641286.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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