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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: Fri, 21 Dec 2007 06:19:43 -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/21/t11982422859ndxbqiqcekeu6l.htm/, Retrieved Fri, 21 Dec 2007 14:04:56 +0100

User-defined keywords:

Dataseries X:

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8.1 359 8.3 304.6 8.2 297.7 8.1 303.3 7.7 304.7 7.6 331.3 7.7 318.8 8.2 306.8 8.4 331.1 8.4 284.1 8.6 259.7 8.4 335.8 8.5 338.5 8.7 310.3 8.7 322.1 8.6 289.3 7.4 300.8 7.3 360.6 7.4 327.3 9 304.1 9.2 362 9.2 287.8 8.5 286.1 8.3 358.2 8.3 346 8.6 329.9 8.6 334.3 8.5 303.7 8.1 307.6 8.1 351.7 8 324.6 8.6 311.9 8.7 361.5 8.7 271.1 8.6 286.5 8.4 352.8 8.4 322.4 8.7 335 8.7 322.2 8.5 313.6 8.3 323.3 8.3 379.1 8.3 315.6 8.1 353.6 8.2 371.7 8.1 282.9 8.1 298.8 7.9 361.8 7.7 365.9 8.1 357.6 8 335.4 7.7 340.1 7.8 337.8 7.6 389.6 7.4 342.5 7.7 354.6 7.8 391.6 7.5 317.7 7.2 312.8 7 356.2

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 Iprod[t] = + 480.35014392631 -18.6911341393208werkl[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) 480.35014392631 62.434264 7.6937 0 0 werkl -18.6911341393208 7.619376 -2.4531 0.01719 0.008595 Multiple Linear Regression - Regression Statistics Multiple R 0.306595751824479 R-squared 0.0940009550368178 Adjusted R-squared 0.0783802818477976 F-TEST (value) 6.0177275268066 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0171902079089168 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 28.4030054508137 Sum Squared Residuals 46790.3816810592 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 359 328.951957397814 30.0480426021856 2 304.6 325.213730569948 -20.6137305699481 3 297.7 327.08284398388 -29.3828439838802 4 303.3 328.951957397812 -25.6519573978123 5 304.7 336.428411053541 -31.7284110535406 6 331.3 338.297524467473 -6.99752446747267 7 318.8 336.428411053541 -17.6284110535406 8 306.8 327.08284398388 -20.2828439838802 9 331.1 323.344617156016 7.75538284398396 10 284.1 323.344617156016 -39.244617156016 11 259.7 319.606390328152 -59.9063903281519 12 335.8 323.344617156016 12.4553828439840 13 338.5 321.475503742084 17.024496257916 14 310.3 317.73727691422 -7.43727691421984 15 322.1 317.73727691422 4.36272308578017 16 289.3 319.606390328152 -30.3063903281519 17 300.8 342.035751295337 -41.2357512953368 18 360.6 343.904864709269 16.6951352907311 19 327.3 342.035751295337 -14.7357512953368 20 304.1 312.129936672424 -8.02993667242359 21 362 308.391709844559 53.6082901554405 22 287.8 308.391709844559 -20.5917098445595 23 286.1 321.475503742084 -35.375503742084 24 358.2 325.213730569948 32.9862694300519 25 346 325.213730569948 20.7862694300519 26 329.9 319.606390328152 10.2936096718481 27 334.3 319.606390328152 14.6936096718481 28 303.7 321.475503742084 -17.775503742084 29 307.6 328.951957397812 -21.3519573978123 30 351.7 328.951957397812 22.7480426021877 31 324.6 330.821070811744 -6.22107081174435 32 311.9 319.606390328152 -7.70639032815195 33 361.5 317.73727691422 43.7627230857802 34 271.1 317.73727691422 -46.6372769142198 35 286.5 319.606390328152 -33.1063903281519 36 352.8 323.344617156016 29.4553828439839 37 322.4 323.344617156016 -0.944617156016084 38 335 317.73727691422 17.2627230857801 39 322.2 317.73727691422 4.46272308578014 40 313.6 321.475503742084 -7.87550374208397 41 323.3 325.213730569948 -1.91373056994812 42 379.1 325.213730569948 53.8862694300519 43 315.6 325.213730569948 -9.6137305699481 44 353.6 328.951957397812 24.6480426021877 45 371.7 327.08284398388 44.6171560161198 46 282.9 328.951957397812 -46.0519573978123 47 298.8 328.951957397812 -30.1519573978123 48 361.8 332.690184225676 29.1098157743236 49 365.9 336.428411053541 29.4715889464594 50 357.6 328.951957397812 28.6480426021877 51 335.4 330.821070811744 4.57892918825560 52 340.1 336.428411053541 3.67158894645942 53 337.8 334.559297639609 3.24070236039148 54 389.6 338.297524467473 51.3024755325273 55 342.5 342.035751295337 0.464248704663175 56 354.6 336.428411053541 18.1715889464594 57 391.6 334.559297639609 57.0407023603915 58 317.7 340.166637881405 -22.4666378814048 59 312.8 345.773978123201 -32.973978123201 60 356.2 349.512204951065 6.68779504893485

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal 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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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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