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Workshop 6

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 03:01:59 -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/t11954661255rb13y8d3hjmukh.htm/, Retrieved Mon, 19 Nov 2007 10:56:16 +0100

User-defined keywords:

Dataseries X:

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110.40 72.50 0 96.40 59.40 0 101.90 85.70 0 106.20 88.20 0 81.00 62.80 0 94.70 87.00 0 101.00 79.20 0 109.40 112.00 1 102.30 79.20 1 90.70 132.10 1 96.20 40.10 1 96.10 69.00 1 106.00 59.40 1 103.10 73.80 1 102.00 57.40 1 104.70 81.10 1 86.00 46.60 1 92.10 41.40 1 106.90 71.20 1 112.60 67.90 1 101.70 72.00 1 92.00 145.50 1 97.40 39.70 1 97.00 51.90 1 105.40 73.70 1 102.70 70.90 1 98.10 60.80 1 104.50 61.00 1 87.40 54.50 1 89.90 39.10 1 109.80 66.60 1 111.70 58.50 1 98.60 59.80 1 96.90 80.90 1 95.10 37.30 1 97.00 44.60 1 112.70 48.70 1 102.90 54.00 1 97.40 49.50 1 111.40 61.60 1 87.40 35.00 1 96.80 35.70 1 114.10 51.30 1 110.30 49.00 1 103.90 41.50 1 101.60 72.50 1 94.60 42.10 1 95.90 44.10 1 104.70 45.10 1 102.80 50.30 1 98.10 40.90 1 113.90 47.20 1 80.90 36.90 1 95.70 40.90 1 113.20 38.30 1 105.90 46.30 1 108.80 28.40 1 102.30 78.40 1 99.00 36.80 1 100.70 50.70 1 115.50 42.80 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 Invest[t] = + 129.477741045368 -0.532610496389665Tot.prod[t] -1.22880551638674Tijd[t] + 7.6597101083052M1[t] + 4.87011023185619M2[t] + 1.61852011632155M3[t] + 15.8565145220841M4[t] -16.6968534757561M5[t] -9.40733614237636M6[t] + 11.8432786998468M7[t] + 18.7072378065419M8[t] + 5.1378128884813M9[t] + 48.1266498483989M10[t] -14.0049369537788M11[t] -0.676239716955866t + 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) 129.477741045368 51.292611 2.5243 0.015108 0.007554 Tot.prod -0.532610496389665 0.537457 -0.991 0.326879 0.163439 Tijd -1.22880551638674 6.098418 -0.2015 0.841199 0.4206 M1 7.6597101083052 9.895941 0.774 0.442876 0.221438 M2 4.87011023185619 8.238903 0.5911 0.557339 0.27867 M3 1.61852011632155 7.926833 0.2042 0.839112 0.419556 M4 15.8565145220841 9.911901 1.5997 0.116502 0.058251 M5 -16.6968534757561 10.175477 -1.6409 0.107641 0.05382 M6 -9.40733614237636 7.93386 -1.1857 0.241822 0.120911 M7 11.8432786998468 10.118104 1.1705 0.247827 0.123913 M8 18.7072378065419 10.395067 1.7996 0.078481 0.03924 M9 5.1378128884813 8.34649 0.6156 0.541215 0.270608 M10 48.1266498483989 7.705906 6.2454 0 0 M11 -14.0049369537788 7.711377 -1.8161 0.075869 0.037935 t -0.676239716955866 0.115742 -5.8426 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.879870656126318 R-squared 0.774172371512158 Adjusted R-squared 0.70544222371151 F-TEST (value) 11.2639416076574 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 1.51000545400848e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12.1727554778682 Sum Squared Residuals 6816.09489250269 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 72.5 77.6610126352981 -5.16101263529812 2 59.4 81.6517199913486 -22.2517199913486 3 85.7 74.794532428715 10.9054675712850 4 88.2 86.0660619830461 2.13393801695387 5 62.8 66.2582387772696 -3.4582387772696 6 87 65.574752593155 21.4252474068449 7 79.2 82.7936815911675 -3.59368159116749 8 112 83.2786672948468 28.7213327051532 9 79.2 72.814537184197 6.38546281580308 10 132.1 121.305416185279 10.7945838147212 11 40.1 55.5682319360021 -15.4682319360021 12 69 68.950190222464 0.0498097775360103 13 59.4 70.6608166995556 -11.2608166995556 14 73.8 68.7395475456808 5.06045245431924 15 57.4 65.3975892592189 -7.9975892592189 16 81.1 77.5212956077735 3.5787043922265 17 46.6 54.2515041754641 -7.65150417546413 18 41.4 57.6158577639111 -16.2158577639111 19 71.2 70.3075975426113 0.89240245738866 20 67.9 73.4594371029295 -5.55943710292948 21 72 65.0192268785603 6.98077312143966 22 145.5 112.498145936502 33.0018540634981 23 39.7 46.8142227368641 -7.1142227368641 24 51.9 60.3559641722429 -8.45596417224288 25 73.7 62.865506393919 10.834493606081 26 70.9 60.8377151407662 10.0622848592338 27 60.8 59.3598935916682 1.44010640833180 28 61 69.512941103581 -8.51294110358103 29 54.5 45.3909728770482 9.1090271229518 30 39.1 50.6727242524979 -11.5727242524979 31 66.6 60.6481504996109 5.95184950038907 32 58.5 65.8239099462098 -7.32390994620978 33 59.8 58.5554428138979 1.24455718610209 34 80.9 101.773477900722 -20.8734779007221 35 37.3 39.92435027509 -2.62435027508996 36 44.6 52.2410875687725 -7.64108756877248 37 48.7 50.8625731668041 -2.16257316680406 38 54 52.6163164380179 1.38368356198211 39 49.5 51.6178443356706 -2.11784433567055 40 61.6 57.723052075022 3.87694792497805 41 35 37.2760962735778 -2.27609627357781 42 35.7 38.8828352239389 -3.18283522393885 43 51.3 50.243048761665 1.05695123833502 44 49 58.4546880376849 -9.45468803768492 45 41.5 47.6177305795623 -6.11773057956229 46 72.5 91.1553319642203 -18.6553319642203 47 42.1 32.0757789198144 10.0242210801856 48 44.1 44.7120825113307 -0.612082511330715 49 45.1 47.008580534451 -1.90858053445098 50 50.3 44.5547008841865 5.74529911581352 51 40.9 43.1301403847274 -2.23014038472740 52 47.2 48.2766492305774 -1.07664923057739 53 36.9 32.6231878966402 4.27681210335976 54 40.9 31.3538301664971 9.54616983350292 55 38.3 42.6075216049453 -4.30752160494527 56 46.3 52.683297618329 -6.38329761832904 57 28.4 36.8930625437825 -8.49306254378254 58 78.4 82.667628013277 -4.26762801327708 59 36.8 21.6174161322295 15.1825838677705 60 50.7 34.0406755251899 16.6593244748101 61 42.8 33.1415105699722 9.65848943002778

Charts produced by software:

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Parameters:

par1 = 2 ; 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')

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Software written by Ed van Stee & Patrick Wessa

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