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Q3_WS8_LisStrat_9/11

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

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 12:30:31 -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/19/t1195500318ti8x8y3jeqoiy8f.htm/, Retrieved Mon, 19 Nov 2007 20:25:28 +0100

User-defined keywords:

Q3, workshop 8, rik, tim, giel, Lissabon

Dataseries X:

» Textbox « » Textfile « » CSV «

513 0 2 503 0 2 471 0 2 471 0 2 476 0 2 475 0 2 470 0 2 461 0 2 455 0 2 456 0 2 517 0 2 525 0 1 523 0 1 519 0 1 509 0 1 512 0 1 519 0 1 517 0 1 510 0 1 509 0 1 501 0 1 507 0 1 569 0 1 580 0 1 578 0 1 565 0 1 547 0 1 555 0 1 562 0 0 561 0 0 555 0 0 544 0 0 537 0 0 543 0 0 594 0 0 611 0 0 613 0 0 611 0 0 594 0 0 595 0 0 591 0 0 589 0 0 584 0 0 573 0 0 567 0 0 569 0 0 621 0 0 629 0 0 628 0 0 612 0 0 595 1 0 597 1 0 593 1 0 590 1 0 580 1 0 574 1 0 573 1 0 573 1 0 620 1 0 626 1 0 620 1 0 588 1 0 566 1 0 557 1 0 561 1 0 549 1 0 532 1 0 526 1 0 511 1 0 499 1 0 555 1 0 565 1 0 542 1 0

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 Werklh[t] = + 585.544146500981 -16.3267551966331LisStrat[t] -53.364290385873`9/11`[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) 585.544146500981 5.745951 101.9055 0 0 LisStrat -16.3267551966331 8.306443 -1.9656 0.053318 0.026659 `9/11` -53.364290385873 5.20214 -10.2581 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.791511639049646 R-squared 0.626490674751057 Adjusted R-squared 0.615818979743945 F-TEST (value) 58.7058264252777 F-TEST (DF numerator) 2 F-TEST (DF denominator) 70 p-value 1.11022302462516e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 28.7674108394948 Sum Squared Residuals 57929.4748485797 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 513 478.815565729234 34.1844342707661 2 503 478.815565729235 24.1844342707650 3 471 478.815565729234 -7.81556572923448 4 471 478.815565729235 -7.81556572923487 5 476 478.815565729235 -2.81556572923487 6 475 478.815565729235 -3.81556572923487 7 470 478.815565729235 -8.81556572923487 8 461 478.815565729235 -17.8155657292349 9 455 478.815565729235 -23.8155657292349 10 456 478.815565729235 -22.8155657292349 11 517 478.815565729235 38.1844342707651 12 525 532.179856115108 -7.17985611510794 13 523 532.179856115108 -9.17985611510795 14 519 532.179856115108 -13.1798561151079 15 509 532.179856115108 -23.1798561151079 16 512 532.179856115108 -20.1798561151079 17 519 532.179856115108 -13.1798561151079 18 517 532.179856115108 -15.1798561151079 19 510 532.179856115108 -22.1798561151079 20 509 532.179856115108 -23.1798561151079 21 501 532.179856115108 -31.1798561151079 22 507 532.179856115108 -25.1798561151079 23 569 532.179856115108 36.8201438848921 24 580 532.179856115108 47.820143884892 25 578 532.179856115108 45.8201438848921 26 565 532.179856115108 32.8201438848921 27 547 532.179856115108 14.8201438848921 28 555 532.179856115108 22.8201438848921 29 562 585.544146500981 -23.5441465009810 30 561 585.544146500981 -24.544146500981 31 555 585.544146500981 -30.544146500981 32 544 585.544146500981 -41.544146500981 33 537 585.544146500981 -48.544146500981 34 543 585.544146500981 -42.544146500981 35 594 585.544146500981 8.45585349901897 36 611 585.544146500981 25.4558534990190 37 613 585.544146500981 27.455853499019 38 611 585.544146500981 25.4558534990190 39 594 585.544146500981 8.45585349901897 40 595 585.544146500981 9.45585349901897 41 591 585.544146500981 5.45585349901897 42 589 585.544146500981 3.45585349901897 43 584 585.544146500981 -1.54414650098103 44 573 585.544146500981 -12.5441465009810 45 567 585.544146500981 -18.5441465009810 46 569 585.544146500981 -16.5441465009810 47 621 585.544146500981 35.455853499019 48 629 585.544146500981 43.455853499019 49 628 585.544146500981 42.455853499019 50 612 585.544146500981 26.455853499019 51 595 569.217391304348 25.7826086956522 52 597 569.217391304348 27.7826086956522 53 593 569.217391304348 23.7826086956522 54 590 569.217391304348 20.7826086956522 55 580 569.217391304348 10.7826086956522 56 574 569.217391304348 4.78260869565217 57 573 569.217391304348 3.78260869565217 58 573 569.217391304348 3.78260869565217 59 620 569.217391304348 50.7826086956522 60 626 569.217391304348 56.7826086956522 61 620 569.217391304348 50.7826086956522 62 588 569.217391304348 18.7826086956522 63 566 569.217391304348 -3.21739130434783 64 557 569.217391304348 -12.2173913043478 65 561 569.217391304348 -8.21739130434783 66 549 569.217391304348 -20.2173913043478 67 532 569.217391304348 -37.2173913043478 68 526 569.217391304348 -43.2173913043478 69 511 569.217391304348 -58.2173913043478 70 499 569.217391304348 -70.2173913043478 71 555 569.217391304348 -14.2173913043478 72 565 569.217391304348 -4.21739130434783 73 542 569.217391304348 -27.2173913043478

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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