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Workshop 6, question 3

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 05:19:38 -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/t1195128846fa3o30aiwajf4b2.htm/, Retrieved Thu, 15 Nov 2007 13:14:19 +0100

User-defined keywords:

Workshop 6, question 3, Workshop 6, question 3, multiple lineair regression, seasonality

Dataseries X:

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108.4 106.7 117 100.6 103.8 101.2 100.8 93.1 110.6 84.2 104 85.8 112.6 91.8 107.3 92.4 98.9 80.3 109.8 79.7 104.9 62.5 102.2 57.1 123.9 100.8 124.9 100.7 112.7 86.2 121.9 83.2 100.6 71.7 104.3 77.5 120.4 89.8 107.5 80.3 102.9 78.7 125.6 93.8 107.5 57.6 108.8 60.6 128.4 91 121.1 85.3 119.5 77.4 128.7 77.3 108.7 68.3 105.5 69.9 119.8 81.7 111.3 75.1 110.6 69.9 120.1 84 97.5 54.3 107.7 60 127.3 89.9 117.2 77 119.8 85.3 116.2 77.6 111 69.2 112.4 75.5 130.6 85.7 109.1 72.2 118.8 79.9 123.9 85.3 101.6 52.2 112.8 61.2 128 82.4 129.6 85.4 125.8 78.2 119.5 70.2 115.7 70.2 113.6 69.3 129.7 77.5 112 66.1 116.8 69 126.3 75.3 112.9 58.2 115.9 59.7

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 Y[t] = + 108.556757497134 -0.44607926102607X[t] + 40.5602074612777M1[t] + 35.6470691776054M2[t] + 28.9911821454183M3[t] + 24.101869332547M4[t] + 12.9286273182358M5[t] + 15.2019595232404M6[t] + 31.4414814898826M7[t] + 17.4821568295589M8[t] + 15.8935295113231M9[t] + 29.101284183564M10[t] -4.81196460071992M11[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) 108.556757497134 16.217621 6.6938 0 0 X -0.44607926102607 0.145379 -3.0684 0.003567 0.001783 M1 40.5602074612777 4.833112 8.3922 0 0 M2 35.6470691776054 4.761548 7.4864 0 0 M3 28.9911821454183 4.513244 6.4236 0 0 M4 24.101869332547 4.551152 5.2958 3e-06 2e-06 M5 12.9286273182358 4.402397 2.9367 0.005123 0.002561 M6 15.2019595232404 4.407878 3.4488 0.001198 0.000599 M7 31.4414814898826 4.798928 6.5518 0 0 M8 17.4821568295589 4.40234 3.9711 0.000244 0.000122 M9 15.8935295113231 4.40237 3.6102 0.000741 0.00037 M10 29.101284183564 4.717412 6.1689 0 0 M11 -4.81196460071992 4.452839 -1.0807 0.285366 0.142683 Multiple Linear Regression - Regression Statistics Multiple R 0.87286876382315 R-squared 0.761899878858152 Adjusted R-squared 0.701108358566617 F-TEST (value) 12.532995970562 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 6.69052591106833e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.96070391037835 Sum Squared Residuals 2277.21574961396 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 100.761973063186 5.93802693681423 2 100.6 92.0125531346893 8.5874468653107 3 101.2 91.2449123480464 9.9550876519536 4 93.1 87.6938373182533 5.4061626817467 5 84.2 72.1490185458866 12.0509814541133 6 85.8 77.3664738736632 8.43352612633676 7 91.8 89.7697141954812 2.03028580451877 8 92.4 78.1746096185958 14.2253903814042 9 80.3 80.3330480929789 -0.0330480929789354 10 79.7 88.6785388200356 -8.9785388200356 11 62.5 56.9510784147795 5.54892158522053 12 57.1 62.9674570202698 -5.8674570202698 13 100.8 93.8477445172818 6.95225548271823 14 100.7 88.4885269725834 12.2114730274167 15 86.2 87.2748069249144 -1.07480692491437 16 83.2 78.2815649106032 4.91843508939681 17 71.7 76.6098111561473 -4.90981115614733 18 77.5 77.2326500953554 0.267349904644579 19 89.8 86.2902959594779 3.50970404052213 20 80.3 78.0853937663906 2.21460623360942 21 78.7 78.5487310488747 0.151268951125325 22 93.8 81.6304864958237 12.1695135041763 23 57.6 55.7912723361117 1.80872766388830 24 60.6 60.0233338974977 0.576666102502276 25 91 91.8403878426645 -0.840387842664454 26 85.3 90.1836281644824 -4.88362816448243 27 77.4 84.2414679499371 -6.8414679499371 28 77.3 75.2482259356259 2.05177406437407 29 68.3 72.9965691418362 -4.69656914183617 30 69.9 76.6973549821241 -6.79735498212413 31 81.7 86.5579435160935 -4.85794351609352 32 75.1 76.3902925744915 -1.29029257449151 33 69.9 75.113920738974 -5.21392073897393 34 84 84.0839224314671 -0.0839224314671194 35 54.3 60.2520649463724 -5.95206494637241 36 60 60.5140210846264 -0.5140210846264 37 89.9 92.3310750297931 -2.43107502979313 38 77 91.9233372824841 -14.9233372824841 39 85.3 84.1076441716293 1.19235582837072 40 77.6 80.8242166984518 -3.2242166984518 41 69.2 71.9705868414762 -2.77058684147619 42 75.5 73.6194080810442 1.88059191895575 43 85.7 81.740287497012 3.95971250298805 44 72.2 77.3716669487489 -5.17166694874886 45 79.9 71.4560707985602 8.44392920143985 46 85.3 82.388821239568 2.91117876043194 47 52.2 58.4231399761655 -6.22313997616551 48 61.2 58.2390168533934 2.96098314660656 49 82.4 92.0188195470749 -9.61881954707488 50 85.4 86.3919544457608 -0.991954445760813 51 78.2 81.4311686054729 -3.23116860547286 52 70.2 79.3521551370658 -9.15215513706576 53 70.2 69.8740143146537 0.325985685346336 54 69.3 73.084112967813 -3.78411296781297 55 77.5 82.1417588319354 -4.64175883193543 56 66.1 76.0780370917733 -9.97803709177327 57 69 72.3482293206123 -3.3482293206123 58 75.3 81.3182310131055 -6.01823101310548 59 58.2 53.3824443265709 4.81755567342909 60 59.7 56.8561711442126 2.84382885578738

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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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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