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WS6 tabel1

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 03:08:54 -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/t1195466551cvwsc409lgy3t3t.htm/, Retrieved Mon, 19 Nov 2007 11:03:12 +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] = + 62.826214719616 + 0.137386490692146Tot.prod[t] -19.0234796796854Tijd[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) 62.826214719616 35.776982 1.7561 0.084359 0.042179 Tot.prod 0.137386490692146 0.352245 0.39 0.697942 0.348971 Tijd -19.0234796796854 8.857292 -2.1478 0.035922 0.017961 Multiple Linear Regression - Regression Statistics Multiple R 0.272384919863927 R-squared 0.0741935445692779 Adjusted R-squared 0.0422691840371839 F-TEST (value) 2.32404168267334 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 0.106926643940794 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.9495379548793 Sum Squared Residuals 27943.3685530958 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 72.5 77.9936832920288 -5.49368329202883 2 59.4 76.0702724223388 -16.6702724223389 3 85.7 76.8258981211457 8.87410187885435 4 88.2 77.4166600311219 10.7833399688781 5 62.8 73.9545204656798 -11.1545204656798 6 87 75.8367153881622 11.1632846118378 7 79.2 76.7022502795228 2.49774972047724 8 112 58.8328171216514 53.1671828783486 9 79.2 57.8573730377371 21.3426269622629 10 132.1 56.2636897457082 75.8363102542917 11 40.1 57.019315444515 -16.9193154445150 12 69 57.0055767954458 11.9944232045542 13 59.4 58.3657030532981 1.03429694670191 14 73.8 57.9672822302909 15.8327177697091 15 57.4 57.8161570905295 -0.416157090529503 16 81.1 58.1871006153983 22.9128993846017 17 46.6 55.6179732394552 -9.01797323945515 18 41.4 56.4560308326772 -15.0560308326772 19 71.2 58.489350894921 12.7106491050790 20 67.9 59.2724538918663 8.62754610813375 21 72 57.7749411433219 14.2250588566781 22 145.5 56.442292183608 89.057707816392 23 39.7 57.1841792333456 -17.4841792333456 24 51.9 57.1292246370688 -5.22922463706877 25 73.7 58.2832711588828 15.4167288411172 26 70.9 57.912327634014 12.987672365986 27 60.8 57.2803497768301 3.51965022316987 28 61 58.1596233172599 2.84037668274013 29 54.5 55.8103143264242 -1.31031432642416 30 39.1 56.1537805531545 -17.0537805531545 31 66.6 58.8877717179282 7.71222828207175 32 58.5 59.1488060502433 -0.648806050243326 33 59.8 57.3490430221762 2.45095697782380 34 80.9 57.1154859879995 23.7845140120005 35 37.3 56.8681903047537 -19.5681903047537 36 44.6 57.1292246370688 -12.5292246370688 37 48.7 59.2861925409355 -10.5861925409355 38 54 57.9398049321524 -3.93980493215243 39 49.5 57.1841792333456 -7.68417923334563 40 61.6 59.1075901030357 2.49240989696432 41 35 55.8103143264242 -20.8103143264242 42 35.7 57.1017473389303 -21.4017473389303 43 51.3 59.4785336279045 -8.17853362790448 44 49 58.9564649632743 -9.95646496327432 45 41.5 58.0771914228446 -16.5771914228446 46 72.5 57.7612024942526 14.7387975057474 47 42.1 56.7994970594076 -14.6994970594076 48 44.1 56.9780994973074 -12.8780994973074 49 45.1 58.1871006153983 -13.0871006153983 50 50.3 57.9260662830832 -7.62606628308322 51 40.9 57.2803497768301 -16.3803497768301 52 47.2 59.4510563297660 -12.2510563297660 53 36.9 54.9173021369252 -18.0173021369252 54 40.9 56.950622199169 -16.0506221991690 55 38.3 59.3548857862815 -21.0548857862816 56 46.3 58.3519644042289 -12.0519644042289 57 28.4 58.7503852272361 -30.3503852272361 58 78.4 57.8573730377371 20.5426269622629 59 36.8 57.4039976184531 -20.6039976184531 60 50.7 57.6375546526297 -6.93755465262971 61 42.8 59.6708747148735 -16.8708747148735

Charts produced by software:

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Parameters:

par1 = 2 ; 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')

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Software written by Ed van Stee & Patrick Wessa

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