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Workshop6-Q3a

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 15:14:23 -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/Nov/15/t1195164540cxqilqgn6z2svn8.htm/, Retrieved Thu, 15 Nov 2007 23:09:10 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

36409 0 33163 0 34122 0 35225 0 28249 0 30374 0 26311 0 22069 0 23651 0 28628 0 23187 0 14727 0 43080 0 32519 0 39657 0 33614 0 28671 0 34243 0 27336 0 22916 0 24537 0 26128 0 22602 0 15744 0 41086 0 39690 0 43129 0 37863 0 35953 0 29133 0 24693 0 22205 0 21725 0 27192 0 21790 0 13253 0 37702 0 30364 0 32609 0 30212 0 29965 0 28352 0 25814 0 22414 0 20506 0 28806 0 22228 0 13971 0 36845 0 35338 0 35022 0 34777 0 26887 0 23970 0 22780 0 17351 0 21382 0 24561 0 17409 0 11514 0 31514 0 27071 0 29462 0 26105 0 22397 0 23843 0 21705 0 18089 0 20764 0 25316 0 17704 0 15548 0 28029 0 29383 0 36438 0 32034 0 22679 0 24319 0 18004 0 17537 0 20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 1 26482 1 22405 1 27044 1 17970 1 18730 1 19684 1 19785 1 18479 1 10698 1

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 Inschr_pw[t] = + 26686.6511627907 -5649.3511627907Olieprijzen[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) 26686.6511627907 770.438624 34.6383 0 0 Olieprijzen -5649.3511627907 2387.116768 -2.3666 0.020004 0.010002 Multiple Linear Regression - Regression Statistics Multiple R 0.237133822191584 R-squared 0.0562324496271897 Adjusted R-squared 0.0461923693040746 F-TEST (value) 5.60079678822163 F-TEST (DF numerator) 1 F-TEST (DF denominator) 94 p-value 0.0200037728180864 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7144.75387336817 Sum Squared Residuals 4798465743.63488 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 36409 26686.6511627907 9722.34883720935 2 33163 26686.6511627907 6476.3488372093 3 34122 26686.6511627907 7435.3488372093 4 35225 26686.6511627907 8538.3488372093 5 28249 26686.6511627907 1562.34883720930 6 30374 26686.6511627907 3687.3488372093 7 26311 26686.6511627907 -375.651162790698 8 22069 26686.6511627907 -4617.6511627907 9 23651 26686.6511627907 -3035.6511627907 10 28628 26686.6511627907 1941.34883720930 11 23187 26686.6511627907 -3499.6511627907 12 14727 26686.6511627907 -11959.6511627907 13 43080 26686.6511627907 16393.3488372093 14 32519 26686.6511627907 5832.3488372093 15 39657 26686.6511627907 12970.3488372093 16 33614 26686.6511627907 6927.3488372093 17 28671 26686.6511627907 1984.3488372093 18 34243 26686.6511627907 7556.3488372093 19 27336 26686.6511627907 649.348837209302 20 22916 26686.6511627907 -3770.6511627907 21 24537 26686.6511627907 -2149.65116279070 22 26128 26686.6511627907 -558.651162790698 23 22602 26686.6511627907 -4084.6511627907 24 15744 26686.6511627907 -10942.6511627907 25 41086 26686.6511627907 14399.3488372093 26 39690 26686.6511627907 13003.3488372093 27 43129 26686.6511627907 16442.3488372093 28 37863 26686.6511627907 11176.3488372093 29 35953 26686.6511627907 9266.3488372093 30 29133 26686.6511627907 2446.3488372093 31 24693 26686.6511627907 -1993.6511627907 32 22205 26686.6511627907 -4481.6511627907 33 21725 26686.6511627907 -4961.6511627907 34 27192 26686.6511627907 505.348837209302 35 21790 26686.6511627907 -4896.6511627907 36 13253 26686.6511627907 -13433.6511627907 37 37702 26686.6511627907 11015.3488372093 38 30364 26686.6511627907 3677.3488372093 39 32609 26686.6511627907 5922.3488372093 40 30212 26686.6511627907 3525.3488372093 41 29965 26686.6511627907 3278.3488372093 42 28352 26686.6511627907 1665.34883720930 43 25814 26686.6511627907 -872.651162790698 44 22414 26686.6511627907 -4272.6511627907 45 20506 26686.6511627907 -6180.6511627907 46 28806 26686.6511627907 2119.3488372093 47 22228 26686.6511627907 -4458.6511627907 48 13971 26686.6511627907 -12715.6511627907 49 36845 26686.6511627907 10158.3488372093 50 35338 26686.6511627907 8651.3488372093 51 35022 26686.6511627907 8335.3488372093 52 34777 26686.6511627907 8090.3488372093 53 26887 26686.6511627907 200.348837209302 54 23970 26686.6511627907 -2716.6511627907 55 22780 26686.6511627907 -3906.6511627907 56 17351 26686.6511627907 -9335.6511627907 57 21382 26686.6511627907 -5304.6511627907 58 24561 26686.6511627907 -2125.65116279070 59 17409 26686.6511627907 -9277.6511627907 60 11514 26686.6511627907 -15172.6511627907 61 31514 26686.6511627907 4827.3488372093 62 27071 26686.6511627907 384.348837209302 63 29462 26686.6511627907 2775.3488372093 64 26105 26686.6511627907 -581.651162790698 65 22397 26686.6511627907 -4289.6511627907 66 23843 26686.6511627907 -2843.6511627907 67 21705 26686.6511627907 -4981.6511627907 68 18089 26686.6511627907 -8597.6511627907 69 20764 26686.6511627907 -5922.6511627907 70 25316 26686.6511627907 -1370.65116279070 71 17704 26686.6511627907 -8982.6511627907 72 15548 26686.6511627907 -11138.6511627907 73 28029 26686.6511627907 1342.34883720930 74 29383 26686.6511627907 2696.3488372093 75 36438 26686.6511627907 9751.3488372093 76 32034 26686.6511627907 5347.3488372093 77 22679 26686.6511627907 -4007.6511627907 78 24319 26686.6511627907 -2367.6511627907 79 18004 26686.6511627907 -8682.6511627907 80 17537 26686.6511627907 -9149.6511627907 81 20366 26686.6511627907 -6320.6511627907 82 22782 26686.6511627907 -3904.6511627907 83 19169 26686.6511627907 -7517.6511627907 84 13807 26686.6511627907 -12879.6511627907 85 29743 26686.6511627907 3056.3488372093 86 25591 26686.6511627907 -1095.65116279070 87 29096 21037.3 8058.7 88 26482 21037.3 5444.7 89 22405 21037.3 1367.7 90 27044 21037.3 6006.7 91 17970 21037.3 -3067.3 92 18730 21037.3 -2307.3 93 19684 21037.3 -1353.3 94 19785 21037.3 -1252.3 95 18479 21037.3 -2558.3 96 10698 21037.3 -10339.3

Charts produced by software:

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Parameters:

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')

Copyright

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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