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Stat Opdr3 Q3-1

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 06:30:04 -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/t1195651442skts8apthnhemoo.htm/, Retrieved Wed, 21 Nov 2007 14:24:12 +0100

User-defined keywords:

Dataseries X:

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3 804 0 3 491 0 4 151 0 4 254 0 4 717 0 4 866 0 4 001 0 3 758 0 4 780 0 5 016 0 4 296 0 4 467 0 3 891 0 3 872 0 3 867 0 3 973 0 4 640 0 4 538 0 3 836 0 3 770 0 4 374 0 4 497 0 3 945 0 3 862 0 3 608 0 3 301 0 3 882 0 3 605 0 4 305 0 4 216 0 3 971 0 3 988 0 4 317 0 4 484 0 4 247 0 3 520 0 3 686 0 3 403 0 3 990 0 4 053 0 4 548 0 4 559 0 3 922 0 4 209 0 4 517 0 4 386 0 3 221 0 3 127 0 3 777 0 3 322 0 3 899 1 4 033 1 4 463 1 4 819 1 4 246 1 4 255 1 4 760 1 4 581 1 4 309 1 4 016 1 3 601 1 3 257 1 3 823 1 3 940 1 4 534 1 4 575 1 3 953 1 4 206 1 4 649 1 4 353 1 3 835 1 3 944 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation s[t] = + 4.08121751504731 -0.00104422837773501d[t] + 0.127145947683812V3[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) 4.08121751504731 0.115651 35.2891 0 0 d -0.00104422837773501 0.000176 -5.9281 0 0 V3 0.127145947683812 0.110975 1.1457 0.255872 0.127936 Multiple Linear Regression - Regression Statistics Multiple R 0.588993850917756 R-squared 0.346913756418928 Adjusted R-squared 0.3279837203731 F-TEST (value) 18.3261012065205 F-TEST (DF numerator) 2 F-TEST (DF denominator) 69 p-value 4.13507596386253e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.433724835818076 Sum Squared Residuals 12.9800890911738 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 3.24165789934834 -0.241657899348343 2 3 3.56850138157942 -0.568501381579417 3 4 3.92353903000932 0.0764609699906813 4 4 3.81598350710261 0.184016492897387 5 4 3.33250576821131 0.667494231788694 6 4 3.17691573992879 0.82308426007121 7 4 4.08017328666957 -0.0801732866695696 8 3 3.28969240472417 -0.28969240472417 9 4 3.266719380414 0.733280619586 10 5 4.06450986100354 0.935490138996456 11 4 3.77212591523774 0.227874084762257 12 4 3.59356286264506 0.406437137354943 13 3 3.15081003048541 -0.150810030485414 14 3 3.17065036966238 -0.170650369662379 15 3 3.17587151155105 -0.175871511551054 16 3 3.06518330351114 -0.0651833035111438 17 4 3.4129113532969 0.587088646703099 18 4 3.51942264782587 0.480577352174129 19 3 3.20824259126084 -0.208242591260840 20 3 3.27716166419135 -0.27716166419135 21 4 3.69067610177441 0.309323898225588 22 4 3.56223601131301 0.437763988686993 23 3 3.09442169808772 -0.094421698087724 24 3 3.18109265343973 -0.181092653439729 25 3 3.44632666138442 -0.446326661384421 26 3 3.76690477334907 -0.766904773349068 27 3 3.16020808588503 -0.160208085885029 28 3 3.44945934651763 -0.449459346517626 29 4 3.76272785983813 0.237272140161872 30 4 3.85566418545654 0.144335814543457 31 3 3.06727176026661 -0.0672717602666138 32 3 3.04951987784512 -0.0495198778451188 33 4 3.75019711930531 0.249802880694692 34 4 3.57581098022356 0.424189019776438 35 4 3.82329310574676 0.176706894253242 36 3 3.5382187586251 -0.538218758625102 37 3 3.36487684792109 -0.364876847921091 38 3 3.6603934788201 -0.660393478820097 39 3 3.04743142108965 -0.0474314210896487 40 4 4.02587341102735 -0.0258734110273494 41 4 3.50898036404852 0.491019635951479 42 4 3.49749385189344 0.502506148106564 43 3 3.11843895077563 -0.118438950775629 44 4 3.86297378410069 0.137026215899312 45 4 3.54135144375831 0.458648556241693 46 4 3.67814536124159 0.321854638758408 47 3 3.85044304356787 -0.850443043567868 48 3 3.94860051107496 -0.94860051107496 49 3 3.26985206554721 -0.269852065547205 50 3 3.74497597741663 -0.744975977416633 51 3 3.26960215114735 -0.269602151147346 52 4 4.17390392626586 -0.173903926265861 53 4 3.72488572383981 0.275114276160192 54 4 3.35314042136615 0.646859578633854 55 4 3.95148328180830 0.0485167181916953 56 4 3.94208522640869 0.0579147735913102 57 4 3.41474989565251 0.585250104347488 58 4 3.60166677526708 0.398333224732922 59 4 3.885696894011 0.114303105989001 60 4 4.19165580868736 -0.191655808687356 61 3 3.58078220771238 -0.580782207712378 62 3 3.93999676965322 -0.93999676965322 63 3 3.34896350785521 -0.348963507855206 64 3 3.22678878766021 -0.226788787660211 65 4 3.65074550902062 0.349254490979377 66 4 3.60793214553349 0.392067854466512 67 3 3.21321381874966 -0.213213818749656 68 4 3.99325241691770 0.00674758308229498 69 4 3.5306592455811 0.469340754418903 70 4 3.83975084539066 0.160249154609341 71 3 3.33643276732239 -0.336432767322386 72 3 3.22261187414927 -0.222611874149271

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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