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Stat Opdr3 Q3-3

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 06:36:07 -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/t1195652068k6gvn55bc10pibv.htm/, Retrieved Wed, 21 Nov 2007 14:34:38 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation d[t] = + 4.06381011360178 -0.000997140206824086b[t] + 0.377513336249788V3[t] -0.129077142629322M1[t] -0.406319224862594M2[t] + 0.0329291272892397M3[t] + 0.0835361072517711M4[t] + 0.650307396372812M5[t] + 0.719903916079853M6[t] + 0.121171868775522M7[t] + 0.173130306921246M8[t] + 0.716967371285332M9[t] + 0.712919767814436M10[t] + 0.144101926714828M11[t] -0.00877096709077283t + 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) 4.06381011360178 0.124093 32.7482 0 0 b -0.000997140206824086 9.8e-05 -10.1261 0 0 V3 0.377513336249788 0.096855 3.8977 0.000258 0.000129 M1 -0.129077142629322 0.132275 -0.9758 0.333277 0.166638 M2 -0.406319224862594 0.130163 -3.1216 0.002823 0.001412 M3 0.0329291272892397 0.133649 0.2464 0.806269 0.403134 M4 0.0835361072517711 0.130576 0.6398 0.524898 0.262449 M5 0.650307396372812 0.130364 4.9884 6e-06 3e-06 M6 0.719903916079853 0.130465 5.518 1e-06 0 M7 0.121171868775522 0.130861 0.926 0.358372 0.179186 M8 0.173130306921246 0.129767 1.3342 0.187458 0.093729 M9 0.716967371285332 0.129796 5.5238 1e-06 0 M10 0.712919767814436 0.129897 5.4883 1e-06 0 M11 0.144101926714828 0.129446 1.1132 0.270287 0.135144 t -0.00877096709077283 0.002157 -4.0654 0.000149 7.4e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.925142872593637 R-squared 0.855889334710807 Adjusted R-squared 0.820493732709952 F-TEST (value) 24.1806689624927 F-TEST (DF numerator) 14 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.224163140490993 Sum Squared Residuals 2.86419947262272 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 3.12426127759510 -0.124261277595104 2 3 3.15035311300702 -0.150353113007017 3 4 3.91985816838827 0.0801418316117342 4 4 3.85898873995714 0.141011260042856 5 4 3.95531314622786 0.0446868537721399 6 4 3.86756480802734 0.132435191972659 7 4 4.12258807253507 -0.122588072535071 8 3 3.41094040702419 -0.410940407024188 9 4 3.92406941974737 0.0759305802526282 10 5 4.67306596719930 0.326934032800695 11 4 3.81627790109818 0.183722098901821 12 4 3.49289403192566 0.507105968074339 13 3 2.93225847451215 0.0677415254878475 14 3 2.66519108911777 0.334808910882235 15 3 3.10065417521295 -0.100654175212947 16 3 3.03679332616135 -0.0367933261613525 17 4 3.92684133706404 0.0731586629359593 18 4 4.08937519077637 -0.0893751907763667 19 3 3.18472439474768 -0.184724394747685 20 3 3.29372311945303 -0.293723119453025 21 4 4.22365673862868 -0.223656738628677 22 4 4.08818992262765 -0.0881899226276457 23 3 3.06388230178007 -0.0638823017800735 24 3 2.99377204514087 0.00622795485912769 25 3 3.10919754795409 -0.109197547954095 26 3 3.12930654212504 -0.129306542125044 27 3 2.98044546702131 0.0195545329786887 28 3 3.29848931718334 -0.298489317183342 29 4 4.15563170126084 -0.155631701260836 30 4 4.30520273228445 -0.305202732284448 31 3 2.94485886173716 0.0551411382628406 32 3 2.9710949492761 0.0289050507238995 33 4 4.17524212532838 -0.175242125328376 34 4 3.99590114022708 0.00409885977291507 35 4 3.65463456105401 0.345365438945989 36 3 3.22954239078544 -0.229542390785436 37 3 2.92616900673254 0.0738309932674578 38 3 2.92234663593971 0.0776533640602866 39 3 2.76750271959504 0.232497280404964 40 4 3.74365910626096 0.256340893739036 41 4 3.80807502591331 0.191924974086691 42 4 3.85793203625451 0.142067963745487 43 3 2.88846712678227 0.111532873217734 44 4 3.64261556530279 0.357384434697211 45 4 3.87056247887428 0.129437521125715 46 4 3.98836927540657 0.0116307245934289 47 3 3.57530860134216 -0.575308601342164 48 3 3.51616688697803 -0.516166886978028 49 3 2.73017764282228 0.269822357177724 50 3 2.89786338760319 0.102136612396809 51 3 3.13050420957654 -0.130504209576542 52 4 4.03586364155796 -0.0358636415579589 53 4 4.16509367465387 -0.16509367465387 54 4 3.87093731364076 0.129062686359236 55 4 3.83479563775586 0.165204362244139 56 4 3.86900884694940 0.130991153050605 57 4 3.90051913977655 0.0994808602234545 58 4 4.06618866623639 -0.066188666236388 59 4 3.75982199430216 0.240178005697842 60 4 3.89911118109601 0.100888818903985 61 3 3.17793605038383 -0.177936050383829 62 3 3.23493923220727 -0.23493923220727 63 3 3.1010352602059 -0.101035260205898 64 3 3.02620586887924 -0.0262058688792390 65 4 3.98904511488009 0.0109548851199144 66 4 4.00898791901657 -0.00898791901656703 67 3 3.02456590644196 -0.0245659064419586 68 4 3.8126171119945 0.187382888005499 69 4 3.90595009764474 0.094049902355255 70 4 4.18828502830301 -0.188285028303006 71 3 3.13007464042341 -0.130074640423415 72 3 2.86851346407399 0.131486535926011

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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