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WS 8 - Q3 Tot vrouwen

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 06:59:21 -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/15/t1195135505ivewigctv8xjw9v.htm/, Retrieved Thu, 15 Nov 2007 15:05:16 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

8.7 0 8.5 0 8.2 0 8.3 0 8 0 8.1 0 8.7 0 9.3 0 8.9 0 8.8 0 8.4 0 8.4 0 7.3 0 7.2 0 7 0 7 0 6.9 0 6.9 0 7.1 0 7.5 0 7.4 0 8.9 0 8.3 1 8.3 0 9 0 8.9 0 8.8 0 7.8 0 7.8 0 7.8 0 9.2 0 9.3 0 9.2 0 8.6 0 8.5 0 8.5 0 9 0 9 0 8.8 0 8 0 7.9 0 8.1 0 9.3 0 9.4 0 9.4 0 9.3 1 9 0 9.1 0 9.7 0 9.7 0 9.6 0 8.3 0 8.2 0 8.4 0 10.6 0 10.9 0 10.9 0 9.6 0 9.3 0 9.3 0 9.6 0 9.5 0 9.5 0 9 0 8.9 0 9 0 10.1 0 10.2 0 10.2 0 9.5 0 9.3 0 9.3 0 9.4 0 9.3 0 9.1 0 9 0 8.9 0 9 0 9.8 0 10 0 9.8 0 9.4 0 9 1 8.9 0 9.3 0 9.1 0 8.8 0 8.9 1 8.7 0 8.6 0 9.1 0 9.3 0 8.9 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 Vrouw[t] = + 8.01790922619047 -0.162552083333333x[t] + 0.25587255084325M1[t] + 0.138983754960317M2[t] -0.0529050409226189M3[t] -0.48697482638889M4[t] -0.649182632688493M5[t] -0.59107142857143M6[t] + 0.392039775545634M7[t] + 0.625150979662699M8[t] + 0.458262183779762M9[t] + 0.385570746527778M10[t] + 0.063332248263889M11[t] + 0.0168887958829365t + 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) 8.01790922619047 0.257842 31.0962 0 0 x -0.162552083333333 0.346189 -0.4695 0.639972 0.319986 M1 0.25587255084325 0.316544 0.8083 0.421327 0.210663 M2 0.138983754960317 0.316463 0.4392 0.661731 0.330865 M3 -0.0529050409226189 0.3164 -0.1672 0.867633 0.433816 M4 -0.48697482638889 0.319377 -1.5248 0.131311 0.065656 M5 -0.649182632688493 0.316328 -2.0522 0.043458 0.021729 M6 -0.59107142857143 0.316319 -1.8686 0.065386 0.032693 M7 0.392039775545634 0.316328 1.2393 0.218886 0.109443 M8 0.625150979662699 0.316355 1.9761 0.051634 0.025817 M9 0.458262183779762 0.3164 1.4484 0.151473 0.075736 M10 0.385570746527778 0.330533 1.1665 0.246917 0.123459 M11 0.063332248263889 0.341428 0.1855 0.853318 0.426659 t 0.0168887958829365 0.002386 7.0777 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.738589178461846 R-squared 0.545513974540945 Adjusted R-squared 0.470725134908442 F-TEST (value) 7.29405586744613 F-TEST (DF numerator) 13 F-TEST (DF denominator) 79 p-value 3.84266307662529e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.611185973035292 Sum Squared Residuals 29.5103151971726 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.29067057291669 0.409329427083314 2 8.5 8.19067057291667 0.309329427083333 3 8.2 8.01567057291666 0.184329427083335 4 8.3 7.59848958333333 0.701510416666666 5 8 7.45317057291667 0.546829427083333 6 8.1 7.52817057291666 0.571829427083335 7 8.7 8.52817057291667 0.171829427083333 8 9.3 8.77817057291666 0.521829427083337 9 8.9 8.62817057291667 0.271829427083334 10 8.8 8.57236793154762 0.227632068452381 11 8.4 8.26701822916667 0.132981770833334 12 8.4 8.22057477678572 0.179425223214285 13 7.3 8.4933361235119 -1.1933361235119 14 7.2 8.3933361235119 -1.19333612351191 15 7 8.2183361235119 -1.21833612351190 16 7 7.80115513392857 -0.80115513392857 17 6.9 7.6558361235119 -0.755836123511903 18 6.9 7.7308361235119 -0.830836123511904 19 7.1 8.7308361235119 -1.63083612351190 20 7.5 8.9808361235119 -1.48083612351190 21 7.4 8.8308361235119 -1.43083612351190 22 8.9 8.77503348214286 0.124966517857144 23 8.3 8.30713169642857 -0.0071316964285707 24 8.3 8.42324032738095 -0.123240327380952 25 9 8.69600167410714 0.30399832589286 26 8.9 8.59600167410714 0.303998325892858 27 8.8 8.42100167410714 0.378998325892858 28 7.8 8.00382068452381 -0.203820684523809 29 7.8 7.85850167410714 -0.0585016741071427 30 7.8 7.93350167410714 -0.133501674107143 31 9.2 8.93350167410714 0.266498325892857 32 9.3 9.18350167410714 0.116498325892857 33 9.2 9.03350167410714 0.166498325892856 34 8.6 8.9776990327381 -0.377699032738096 35 8.5 8.67234933035714 -0.172349330357143 36 8.5 8.62590587797619 -0.125905877976191 37 9 8.89866722470238 0.101332775297622 38 9 8.79866722470238 0.201332775297619 39 8.8 8.62366722470238 0.176332775297620 40 8 8.20648623511905 -0.206486235119047 41 7.9 8.06116722470238 -0.161167224702380 42 8.1 8.13616722470238 -0.0361672247023817 43 9.3 9.13616722470238 0.16383277529762 44 9.4 9.38616722470238 0.0138327752976187 45 9.4 9.23616722470238 0.163832775297619 46 9.3 9.0178125 0.282187500000001 47 9 8.87501488095238 0.124985119047619 48 9.1 8.82857142857143 0.271428571428571 49 9.7 9.10133277529762 0.598667224702383 50 9.7 9.00133277529762 0.69866722470238 51 9.6 8.82633277529762 0.77366722470238 52 8.3 8.40915178571429 -0.109151785714285 53 8.2 8.26383277529762 -0.0638327752976198 54 8.4 8.33883277529762 0.0611672247023809 55 10.6 9.33883277529762 1.26116722470238 56 10.9 9.58883277529762 1.31116722470238 57 10.9 9.43883277529762 1.46116722470238 58 9.6 9.38303013392857 0.216969866071428 59 9.3 9.07768043154762 0.222319568452381 60 9.3 9.03123697916667 0.268763020833333 61 9.6 9.30399832589285 0.296001674107145 62 9.5 9.20399832589286 0.296001674107143 63 9.5 9.02899832589286 0.471001674107142 64 9 8.61181733630952 0.388182663690476 65 8.9 8.46649832589286 0.433501674107143 66 9 8.54149832589286 0.458501674107142 67 10.1 9.54149832589286 0.558501674107143 68 10.2 9.79149832589286 0.408501674107142 69 10.2 9.64149832589286 0.558501674107142 70 9.5 9.58569568452381 -0.0856956845238098 71 9.3 9.28034598214286 0.0196540178571431 72 9.3 9.2339025297619 0.0660974702380949 73 9.4 9.5066638764881 -0.106663876488092 74 9.3 9.4066638764881 -0.106663876488095 75 9.1 9.2316638764881 -0.131663876488096 76 9 8.81448288690476 0.185517113095237 77 8.9 8.6691638764881 0.230836123511905 78 9 8.7441638764881 0.255836123511904 79 9.8 9.7441638764881 0.0558361235119051 80 10 9.9941638764881 0.00583612351190393 81 9.8 9.8441638764881 -0.0441638764880953 82 9.4 9.78836123511905 -0.388361235119048 83 9 9.32045944940476 -0.320459449404763 84 8.9 9.43656808035714 -0.536568080357144 85 9.3 9.70932942708333 -0.40932942708333 86 9.1 9.60932942708333 -0.509329427083334 87 8.8 9.43432942708333 -0.634329427083334 88 8.9 8.85459635416667 0.0454036458333332 89 8.7 8.87182942708333 -0.171829427083335 90 8.6 8.94682942708334 -0.346829427083335 91 9.1 9.94682942708333 -0.846829427083334 92 9.3 10.1968294270833 -0.896829427083334 93 8.9 10.0468294270833 -1.14682942708333

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')

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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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