Paper

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 16 Dec 2008 12:46:15 -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/16/t1229456934kyb1jf0ojre5de8.htm/, Retrieved Tue, 16 Dec 2008 20:49:02 +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/16/t1229456934kyb1jf0ojre5de8.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:

» Textbox « » Textfile « » CSV «

87.0 0 96.3 0 107.1 0 115.2 0 106.1 0 89.5 0 91.3 0 97.6 0 100.7 0 104.6 0 94.7 0 101.8 0 102.5 0 105.3 0 110.3 1 109.8 1 117.3 1 118.8 1 131.3 1 125.9 1 133.1 1 147.0 1 145.8 1 164.4 1 149.8 1 137.7 1 151.7 1 156.8 1 180.0 1 180.4 1 170.4 1 191.6 1 199.5 1 218.2 1 217.5 1 205.0 1 194.0 1 199.3 1 219.3 1 211.1 1 215.2 1 240.2 1 242.2 1 240.7 1 255.4 1 253.0 1 218.2 1 203.7 1 205.6 1 215.6 1 188.5 1 202.9 1 214.0 1 230.3 1 230.0 1 241.0 1 259.6 1 247.8 1 270.3 1 289.7 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 82.6574825174825 + 3.81678321678324X[t] -11.61831002331M1[t] -11.5363403263403M2[t] -10.7377272727273M3[t] -9.93575757575757M4[t] -5.5537878787879M5[t] -3.21181818181818M6[t] -4.98984848484848M7[t] -1.64787878787879M8[t] + 5.67409090909092M9[t] + 7.1560606060606M10[t] -0.641969696969688M11[t] + 2.97803030303030t + 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) 82.6574825174825 10.678801 7.7403 0 0 X 3.81678321678324 9.248113 0.4127 0.681737 0.340868 M1 -11.61831002331 12.881285 -0.902 0.371781 0.18589 M2 -11.5363403263403 12.86329 -0.8968 0.374473 0.187236 M3 -10.7377272727273 12.932211 -0.8303 0.410653 0.205326 M4 -9.93575757575757 12.898334 -0.7703 0.445052 0.222526 M5 -5.5537878787879 12.868368 -0.4316 0.66806 0.33403 M6 -3.21181818181818 12.842341 -0.2501 0.803627 0.401813 M7 -4.98984848484848 12.820276 -0.3892 0.698913 0.349456 M8 -1.64787878787879 12.802196 -0.1287 0.898142 0.449071 M9 5.67409090909092 12.788115 0.4437 0.659339 0.32967 M10 7.1560606060606 12.778048 0.56 0.578178 0.289089 M11 -0.641969696969688 12.772004 -0.0503 0.96013 0.480065 t 2.97803030303030 0.226881 13.126 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.950628485445134 R-squared 0.90369451733971 Adjusted R-squared 0.876477750500931 F-TEST (value) 33.2035955149583 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.1911251798702 Sum Squared Residuals 18753.3506573427 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 87 74.0172027972028 12.9827972027972 2 96.3 77.0772027972028 19.2227972027972 3 107.1 80.8538461538461 26.2461538461539 4 115.2 84.6338461538461 30.5661538461539 5 106.1 91.9938461538461 14.1061538461539 6 89.5 97.3138461538462 -7.81384615384616 7 91.3 98.5138461538461 -7.21384615384614 8 97.6 104.833846153846 -7.23384615384613 9 100.7 115.133846153846 -14.4338461538462 10 104.6 119.593846153846 -14.9938461538462 11 94.7 114.773846153846 -20.0738461538461 12 101.8 118.393846153846 -16.5938461538462 13 102.5 109.753566433566 -7.25356643356643 14 105.3 112.813566433566 -7.51356643356636 15 110.3 120.406993006993 -10.106993006993 16 109.8 124.186993006993 -14.3869930069930 17 117.3 131.546993006993 -14.246993006993 18 118.8 136.866993006993 -18.0669930069931 19 131.3 138.066993006993 -6.76699300699301 20 125.9 144.386993006993 -18.4869930069930 21 133.1 154.686993006993 -21.5869930069930 22 147 159.146993006993 -12.146993006993 23 145.8 154.326993006993 -8.52699300699299 24 164.4 157.946993006993 6.45300699300698 25 149.8 149.306713286713 0.493286713286695 26 137.7 152.366713286713 -14.6667132867133 27 151.7 156.143356643357 -4.44335664335666 28 156.8 159.923356643357 -3.12335664335662 29 180 167.283356643357 12.7166433566434 30 180.4 172.603356643357 7.79664335664337 31 170.4 173.803356643357 -3.40335664335665 32 191.6 180.123356643357 11.4766433566434 33 199.5 190.423356643357 9.07664335664334 34 218.2 194.883356643357 23.3166433566433 35 217.5 190.063356643357 27.4366433566433 36 205 193.683356643357 11.3166433566433 37 194 185.043076923077 8.95692307692305 38 199.3 188.103076923077 11.1969230769231 39 219.3 191.879720279720 27.4202797202797 40 211.1 195.659720279720 15.4402797202797 41 215.2 203.019720279720 12.1802797202797 42 240.2 208.339720279720 31.8602797202797 43 242.2 209.539720279720 32.6602797202797 44 240.7 215.859720279720 24.8402797202797 45 255.4 226.159720279720 29.2402797202797 46 253 230.619720279720 22.3802797202797 47 218.2 225.799720279720 -7.5997202797203 48 203.7 229.419720279720 -25.7197202797203 49 205.6 220.779440559441 -15.1794405594406 50 215.6 223.839440559441 -8.23944055944058 51 188.5 227.616083916084 -39.1160839160839 52 202.9 231.396083916084 -28.4960839160839 53 214 238.756083916084 -24.7560839160839 54 230.3 244.076083916084 -13.7760839160839 55 230 245.276083916084 -15.2760839160839 56 241 251.596083916084 -10.5960839160839 57 259.6 261.896083916084 -2.29608391608390 58 247.8 266.356083916084 -18.5560839160839 59 270.3 261.536083916084 8.76391608391608 60 289.7 265.156083916084 24.5439160839161

Charts produced by software:

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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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Software written by Ed van Stee & Patrick Wessa

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