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Workshop 3 Q3

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

Title produced by software: Multiple Regression

Date of computation: Wed, 21 Nov 2007 14:57:39 -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/21/t119568186360sra0o7cs9ihf5.htm/, Retrieved Wed, 21 Nov 2007 22:51:14 +0100

User-defined keywords:

Dummy

Dataseries X:

» Textbox « » Textfile « » CSV «

523 0 519 1 509 1 512 1 519 0 517 0 510 1 509 1 501 0 507 1 569 0 580 0 578 1 565 1 547 0 555 0 562 0 561 0 555 1 544 1 537 1 543 1 594 1 611 0 613 1 611 1 594 1 595 0 591 0 589 0 584 1 573 1 567 0 569 1 621 0 629 0 628 1 612 1 595 1 597 0 593 1 590 0 580 1 574 1 573 1 573 1 620 0 626 0 620 1 588 1 566 1 557 0 561 1 549 1 532 1 526 1 511 1 499 1 555 0 565 1 542 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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 573.130434782609 -12.2620137299771x[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) 573.130434782609 7.557442 75.8366 0 0 x -12.2620137299771 9.575201 -1.2806 0.205345 0.102673 Multiple Linear Regression - Regression Statistics Multiple R 0.164450236155504 R-squared 0.027043880171601 Adjusted R-squared 0.0105530984795943 F-TEST (value) 1.63993925070935 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.205345298596878 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36.2442165581465 Sum Squared Residuals 77504.9508009153 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 523 573.130434782608 -50.1304347826084 2 519 560.868421052632 -41.8684210526316 3 509 560.868421052632 -51.8684210526316 4 512 560.868421052632 -48.8684210526316 5 519 573.130434782609 -54.1304347826087 6 517 573.130434782609 -56.1304347826087 7 510 560.868421052632 -50.8684210526316 8 509 560.868421052632 -51.8684210526316 9 501 573.130434782609 -72.1304347826087 10 507 560.868421052632 -53.8684210526316 11 569 573.130434782609 -4.13043478260871 12 580 573.130434782609 6.86956521739129 13 578 560.868421052632 17.1315789473684 14 565 560.868421052632 4.13157894736843 15 547 573.130434782609 -26.1304347826087 16 555 573.130434782609 -18.1304347826087 17 562 573.130434782609 -11.1304347826087 18 561 573.130434782609 -12.1304347826087 19 555 560.868421052632 -5.86842105263157 20 544 560.868421052632 -16.8684210526316 21 537 560.868421052632 -23.8684210526316 22 543 560.868421052632 -17.8684210526316 23 594 560.868421052632 33.1315789473684 24 611 573.130434782609 37.8695652173913 25 613 560.868421052632 52.1315789473684 26 611 560.868421052632 50.1315789473684 27 594 560.868421052632 33.1315789473684 28 595 573.130434782609 21.8695652173913 29 591 573.130434782609 17.8695652173913 30 589 573.130434782609 15.8695652173913 31 584 560.868421052632 23.1315789473684 32 573 560.868421052632 12.1315789473684 33 567 573.130434782609 -6.13043478260871 34 569 560.868421052632 8.13157894736843 35 621 573.130434782609 47.8695652173913 36 629 573.130434782609 55.8695652173913 37 628 560.868421052632 67.1315789473684 38 612 560.868421052632 51.1315789473684 39 595 560.868421052632 34.1315789473684 40 597 573.130434782609 23.8695652173913 41 593 560.868421052632 32.1315789473684 42 590 573.130434782609 16.8695652173913 43 580 560.868421052632 19.1315789473684 44 574 560.868421052632 13.1315789473684 45 573 560.868421052632 12.1315789473684 46 573 560.868421052632 12.1315789473684 47 620 573.130434782609 46.8695652173913 48 626 573.130434782609 52.8695652173913 49 620 560.868421052632 59.1315789473684 50 588 560.868421052632 27.1315789473684 51 566 560.868421052632 5.13157894736843 52 557 573.130434782609 -16.1304347826087 53 561 560.868421052632 0.131578947368428 54 549 560.868421052632 -11.8684210526316 55 532 560.868421052632 -28.8684210526316 56 526 560.868421052632 -34.8684210526316 57 511 560.868421052632 -49.8684210526316 58 499 560.868421052632 -61.8684210526316 59 555 573.130434782609 -18.1304347826087 60 565 560.868421052632 4.13157894736843 61 542 560.868421052632 -18.8684210526316

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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