*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, 24 Nov 2008 11:12:25 -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/Nov/24/t1227550549x4bvnc3g0aczfpu.htm/, Retrieved Mon, 24 Nov 2008 18:15:49 +0000

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/Nov/24/t1227550549x4bvnc3g0aczfpu.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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7,4 0 7,2 0 7,1 0 6,9 0 6,8 0 6,8 0 6,8 0 6,9 0 6,7 0 6,6 0 6,5 0 6,4 0 6,3 0 6,3 0 6,3 0 6,5 0 6,6 0 6,5 0 6,4 0 6,5 0 6,7 0 7,1 0 7,1 0 7,2 0 7,2 0 7,3 0 7,3 0 7,3 0 7,3 0 7,4 0 7,6 0 7,6 0 7,6 0 7,7 0 7,8 0 7,9 0 8,1 0 8,1 0 8,1 0 8,2 0 8,2 0 8,2 0 8,2 0 8,2 0 8,2 0 8,3 0 8,3 0 8,4 0 8,4 0 8,4 0 8,3 1 8 1 8 1 8,2 1 8,6 1 8,7 1 8,7 1 8,5 1 8,4 1 8,4 1 8,4 1 8,5 1 8,5 1 8,5 1 8,5 1 8,5 1 8,4 1 8,4 1 8,4 1 8,5 1 8,6 1 8,6 1 8,6 1 8,6 1 8,5 1 8,4 1 8,4 1 8,3 1 8,2 1 8,1 1 8,2 1 8,1 1 8 1 7,9 1 7,8 1 7,7 1 7,7 1 7,9 1 7,8 1 7,6 1 7,4 1 7,3 1 7,1 1 7,1 1 7 1 7 1 7 1 6,9 1 6,8 1 6,7 1 6,6 1 6,6 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 12 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 7.338 + 0.640846153846153x[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) 7.338 0.093834 78.2015 0 0 x 0.640846153846153 0.13142 4.8763 4e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.438298763846614 R-squared 0.192105806389470 Adjusted R-squared 0.184026864453364 F-TEST (value) 23.7785848578682 F-TEST (DF numerator) 1 F-TEST (DF denominator) 100 p-value 4.07781139089014e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.66350983993631 Sum Squared Residuals 44.0245307692308 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.4 7.33799999999998 0.0620000000000203 2 7.2 7.338 -0.138000000000000 3 7.1 7.338 -0.238000000000001 4 6.9 7.338 -0.438 5 6.8 7.338 -0.538 6 6.8 7.338 -0.538 7 6.8 7.338 -0.538 8 6.9 7.338 -0.438 9 6.7 7.338 -0.638 10 6.6 7.338 -0.738 11 6.5 7.338 -0.838 12 6.4 7.338 -0.938 13 6.3 7.338 -1.038 14 6.3 7.338 -1.038 15 6.3 7.338 -1.038 16 6.5 7.338 -0.838 17 6.6 7.338 -0.738 18 6.5 7.338 -0.838 19 6.4 7.338 -0.938 20 6.5 7.338 -0.838 21 6.7 7.338 -0.638 22 7.1 7.338 -0.238000000000001 23 7.1 7.338 -0.238000000000001 24 7.2 7.338 -0.138000000000000 25 7.2 7.338 -0.138000000000000 26 7.3 7.338 -0.0380000000000005 27 7.3 7.338 -0.0380000000000005 28 7.3 7.338 -0.0380000000000005 29 7.3 7.338 -0.0380000000000005 30 7.4 7.338 0.062 31 7.6 7.338 0.261999999999999 32 7.6 7.338 0.261999999999999 33 7.6 7.338 0.261999999999999 34 7.7 7.338 0.362 35 7.8 7.338 0.461999999999999 36 7.9 7.338 0.562 37 8.1 7.338 0.762 38 8.1 7.338 0.762 39 8.1 7.338 0.762 40 8.2 7.338 0.861999999999999 41 8.2 7.338 0.861999999999999 42 8.2 7.338 0.861999999999999 43 8.2 7.338 0.861999999999999 44 8.2 7.338 0.861999999999999 45 8.2 7.338 0.861999999999999 46 8.3 7.338 0.962 47 8.3 7.338 0.962 48 8.4 7.338 1.062 49 8.4 7.338 1.062 50 8.4 7.338 1.062 51 8.3 7.97884615384615 0.321153846153847 52 8 7.97884615384615 0.0211538461538462 53 8 7.97884615384615 0.0211538461538462 54 8.2 7.97884615384615 0.221153846153845 55 8.6 7.97884615384615 0.621153846153846 56 8.7 7.97884615384615 0.721153846153845 57 8.7 7.97884615384615 0.721153846153845 58 8.5 7.97884615384615 0.521153846153846 59 8.4 7.97884615384615 0.421153846153847 60 8.4 7.97884615384615 0.421153846153847 61 8.4 7.97884615384615 0.421153846153847 62 8.5 7.97884615384615 0.521153846153846 63 8.5 7.97884615384615 0.521153846153846 64 8.5 7.97884615384615 0.521153846153846 65 8.5 7.97884615384615 0.521153846153846 66 8.5 7.97884615384615 0.521153846153846 67 8.4 7.97884615384615 0.421153846153847 68 8.4 7.97884615384615 0.421153846153847 69 8.4 7.97884615384615 0.421153846153847 70 8.5 7.97884615384615 0.521153846153846 71 8.6 7.97884615384615 0.621153846153846 72 8.6 7.97884615384615 0.621153846153846 73 8.6 7.97884615384615 0.621153846153846 74 8.6 7.97884615384615 0.621153846153846 75 8.5 7.97884615384615 0.521153846153846 76 8.4 7.97884615384615 0.421153846153847 77 8.4 7.97884615384615 0.421153846153847 78 8.3 7.97884615384615 0.321153846153847 79 8.2 7.97884615384615 0.221153846153845 80 8.1 7.97884615384615 0.121153846153846 81 8.2 7.97884615384615 0.221153846153845 82 8.1 7.97884615384615 0.121153846153846 83 8 7.97884615384615 0.0211538461538462 84 7.9 7.97884615384615 -0.0788461538461535 85 7.8 7.97884615384615 -0.178846153846154 86 7.7 7.97884615384615 -0.278846153846154 87 7.7 7.97884615384615 -0.278846153846154 88 7.9 7.97884615384615 -0.0788461538461535 89 7.8 7.97884615384615 -0.178846153846154 90 7.6 7.97884615384615 -0.378846153846154 91 7.4 7.97884615384615 -0.578846153846153 92 7.3 7.97884615384615 -0.678846153846154 93 7.1 7.97884615384615 -0.878846153846154 94 7.1 7.97884615384615 -0.878846153846154 95 7 7.97884615384615 -0.978846153846154 96 7 7.97884615384615 -0.978846153846154 97 7 7.97884615384615 -0.978846153846154 98 6.9 7.97884615384615 -1.07884615384615 99 6.8 7.97884615384615 -1.17884615384615 100 6.7 7.97884615384615 -1.27884615384615 101 6.6 7.97884615384615 -1.37884615384615 102 6.6 7.97884615384615 -1.37884615384615

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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