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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: Sun, 18 Nov 2007 04:51:00 -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/18/t1195386304snm8bly5iq4ncvs.htm/, Retrieved Sun, 18 Nov 2007 12:45:05 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

7.4 0 7.2 0 7,0 0 6.6 0 6.4 0 6.4 0 6.8 0 7.3 0 7,0 0 7,0 0 6.7 0 6.7 0 6.3 0 6.2 0 6,0 0 6.3 0 6.2 0 6.1 0 6.2 0 6.6 0 6.6 0 7.8 0 7.4 0 7.4 1 7.5 1 7.4 1 7.4 1 7,0 1 6.9 1 6.9 1 7.6 1 7.7 1 7.6 1 8.2 1 8,0 1 8.1 1 8.3 1 8.2 1 8.1 1 7.7 1 7.6 1 7.7 1 8.2 1 8.4 1 8.4 1 8.6 1 8.4 1 8.5 1 8.7 1 8.7 1 8.6 1 7.4 1 7.3 1 7.4 1 9,0 1 9.2 1 9.2 1 8.5 1 8.3 1 8.3 1 8.6 1 8.6 1 8.5 1 8.1 1 8.1 1 8,0 1 8.6 1 8.7 1 8.7 1 8.6 1 8.4 1 8.4 1 8.7 1 8.7 1 8.5 1 8.3 1 8.3 1 8.3 1 8.1 1 8.2 1 8.1 1 8.1 1 7.9 1 7.7 1 8.1 1 8,0 1 7.7 1 7.8 1 7.6 1 7.4 1 7.7 1 7.9 1 7.6 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation x[t] = + 6.70434782608696 + 1.38708074534161y[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) 6.70434782608696 0.10687 62.7339 0 0 y 1.38708074534161 0.123182 11.2604 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.763007246200546 R-squared 0.58218005775454 Adjusted R-squared 0.577588629817777 F-TEST (value) 126.797167629064 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.512528984548903 Sum Squared Residuals 23.9044223602484 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.4 6.70434782608696 0.695652173913044 2 7.2 6.70434782608696 0.495652173913043 3 7 6.70434782608696 0.295652173913044 4 6.6 6.70434782608696 -0.104347826086957 5 6.4 6.70434782608696 -0.304347826086956 6 6.4 6.70434782608696 -0.304347826086956 7 6.8 6.70434782608696 0.0956521739130434 8 7.3 6.70434782608696 0.595652173913043 9 7 6.70434782608696 0.295652173913044 10 7 6.70434782608696 0.295652173913044 11 6.7 6.70434782608696 -0.00434782608695632 12 6.7 6.70434782608696 -0.00434782608695632 13 6.3 6.70434782608696 -0.404347826086957 14 6.2 6.70434782608696 -0.504347826086956 15 6 6.70434782608696 -0.704347826086957 16 6.3 6.70434782608696 -0.404347826086957 17 6.2 6.70434782608696 -0.504347826086956 18 6.1 6.70434782608696 -0.604347826086957 19 6.2 6.70434782608696 -0.504347826086956 20 6.6 6.70434782608696 -0.104347826086957 21 6.6 6.70434782608696 -0.104347826086957 22 7.8 6.70434782608696 1.09565217391304 23 7.4 6.70434782608696 0.695652173913044 24 7.4 8.09142857142857 -0.691428571428571 25 7.5 8.09142857142857 -0.591428571428571 26 7.4 8.09142857142857 -0.691428571428571 27 7.4 8.09142857142857 -0.691428571428571 28 7 8.09142857142857 -1.09142857142857 29 6.9 8.09142857142857 -1.19142857142857 30 6.9 8.09142857142857 -1.19142857142857 31 7.6 8.09142857142857 -0.491428571428572 32 7.7 8.09142857142857 -0.391428571428571 33 7.6 8.09142857142857 -0.491428571428572 34 8.2 8.09142857142857 0.108571428571428 35 8 8.09142857142857 -0.0914285714285714 36 8.1 8.09142857142857 0.00857142857142826 37 8.3 8.09142857142857 0.208571428571429 38 8.2 8.09142857142857 0.108571428571428 39 8.1 8.09142857142857 0.00857142857142826 40 7.7 8.09142857142857 -0.391428571428571 41 7.6 8.09142857142857 -0.491428571428572 42 7.7 8.09142857142857 -0.391428571428571 43 8.2 8.09142857142857 0.108571428571428 44 8.4 8.09142857142857 0.308571428571429 45 8.4 8.09142857142857 0.308571428571429 46 8.6 8.09142857142857 0.508571428571428 47 8.4 8.09142857142857 0.308571428571429 48 8.5 8.09142857142857 0.408571428571429 49 8.7 8.09142857142857 0.608571428571428 50 8.7 8.09142857142857 0.608571428571428 51 8.6 8.09142857142857 0.508571428571428 52 7.4 8.09142857142857 -0.691428571428571 53 7.3 8.09142857142857 -0.791428571428572 54 7.4 8.09142857142857 -0.691428571428571 55 9 8.09142857142857 0.908571428571429 56 9.2 8.09142857142857 1.10857142857143 57 9.2 8.09142857142857 1.10857142857143 58 8.5 8.09142857142857 0.408571428571429 59 8.3 8.09142857142857 0.208571428571429 60 8.3 8.09142857142857 0.208571428571429 61 8.6 8.09142857142857 0.508571428571428 62 8.6 8.09142857142857 0.508571428571428 63 8.5 8.09142857142857 0.408571428571429 64 8.1 8.09142857142857 0.00857142857142826 65 8.1 8.09142857142857 0.00857142857142826 66 8 8.09142857142857 -0.0914285714285714 67 8.6 8.09142857142857 0.508571428571428 68 8.7 8.09142857142857 0.608571428571428 69 8.7 8.09142857142857 0.608571428571428 70 8.6 8.09142857142857 0.508571428571428 71 8.4 8.09142857142857 0.308571428571429 72 8.4 8.09142857142857 0.308571428571429 73 8.7 8.09142857142857 0.608571428571428 74 8.7 8.09142857142857 0.608571428571428 75 8.5 8.09142857142857 0.408571428571429 76 8.3 8.09142857142857 0.208571428571429 77 8.3 8.09142857142857 0.208571428571429 78 8.3 8.09142857142857 0.208571428571429 79 8.1 8.09142857142857 0.00857142857142826 80 8.2 8.09142857142857 0.108571428571428 81 8.1 8.09142857142857 0.00857142857142826 82 8.1 8.09142857142857 0.00857142857142826 83 7.9 8.09142857142857 -0.191428571428571 84 7.7 8.09142857142857 -0.391428571428571 85 8.1 8.09142857142857 0.00857142857142826 86 8 8.09142857142857 -0.0914285714285714 87 7.7 8.09142857142857 -0.391428571428571 88 7.8 8.09142857142857 -0.291428571428572 89 7.6 8.09142857142857 -0.491428571428572 90 7.4 8.09142857142857 -0.691428571428571 91 7.7 8.09142857142857 -0.391428571428571 92 7.9 8.09142857142857 -0.191428571428571 93 7.6 8.09142857142857 -0.491428571428572

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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