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Workshop: Seatbelt Law _ Eigen geg.

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 12:11:37 -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/22/t11957582703qrvkhufm9c0w8x.htm/, Retrieved Thu, 22 Nov 2007 20:04:40 +0100

User-defined keywords:

Tinne Van der Eycken Workshop 2

Dataseries X:

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103.4 0 101.87 0 101.11 0 98.47 0 97.8 0 97.37 0 97.29 0 93.06 0 92.39 0 93.73 0 94.81 0 93.24 0 90.09 0 89.86 0 87.92 0 86.3 0 86.5 0 87.93 0 88.6 0 90.08 0 88.84 0 87.91 0 88.31 0 87.77 0 86.11 0 82.8 0 81.65 0 82.36 0 82.91 0 81.99 0 83.32 0 84.12 0 85.66 0 86.67 0 85.31 0 85.13 0 86.6 0 87.92 0 87.19 0 85.56 0 86.21 0 86.16 0 85.04 0 82.01 0 83.05 0 83.34 0 82.87 0 83.18 0 83.97 0 82.98 1 82.2 1 83.68 1 83.49 1 82.68 1 81.56 1 81.19 1 81.07 1 79.81 1 79.72 1 78.32 1 76.6 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 Y[t] = + 97.0079108280255 + 2.84945063694268X[t] + 0.688398221868353M1[t] + 0.210833067940549M2[t] -0.526450238853509M3[t] -0.93173354564756M4[t] -0.48901685244162M5[t] -0.31030015923567M6[t] -0.0395834660297264M7[t] -0.774866772823781M8[t] -0.33015007961784M9[t] + 0.094566613588108M10[t] + 0.341283306794053M11[t] -0.334716693205945t + 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) 97.0079108280255 1.751451 55.3872 0 0 X 2.84945063694268 1.442362 1.9755 0.054095 0.027047 M1 0.688398221868353 1.943126 0.3543 0.724718 0.362359 M2 0.210833067940549 2.051333 0.1028 0.918576 0.459288 M3 -0.526450238853509 2.046272 -0.2573 0.798091 0.399046 M4 -0.93173354564756 2.041733 -0.4563 0.650244 0.325122 M5 -0.48901685244162 2.037719 -0.24 0.811387 0.405694 M6 -0.31030015923567 2.034234 -0.1525 0.879415 0.439707 M7 -0.0395834660297264 2.03128 -0.0195 0.984535 0.492268 M8 -0.774866772823781 2.028861 -0.3819 0.704241 0.35212 M9 -0.33015007961784 2.026977 -0.1629 0.871313 0.435656 M10 0.094566613588108 2.02563 0.0467 0.962962 0.481481 M11 0.341283306794053 2.024822 0.1685 0.866874 0.433437 t -0.334716693205945 0.033039 -10.131 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.878609736788236 R-squared 0.771955069579093 Adjusted R-squared 0.70887881222863 F-TEST (value) 12.2384412456491 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 5.14712716892518e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.20109786680331 Sum Squared Residuals 481.610294984076 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.4 97.361592356688 6.03840764331207 2 101.87 96.5493105095541 5.32068949044586 3 101.11 95.4773105095541 5.63268949044586 4 98.47 94.7373105095541 3.73268949044586 5 97.8 94.8453105095541 2.95468949044586 6 97.37 94.6893105095541 2.68068949044587 7 97.29 94.6253105095541 2.66468949044587 8 93.06 93.5553105095541 -0.495310509554137 9 92.39 93.6653105095541 -1.27531050955414 10 93.73 93.7553105095541 -0.0253105095541347 11 94.81 93.6673105095541 1.14268949044586 12 93.24 92.9913105095541 0.248689490445852 13 90.09 93.3449920382165 -3.25499203821655 14 89.86 92.5327101910828 -2.67271019108281 15 87.92 91.4607101910828 -3.5407101910828 16 86.3 90.7207101910828 -4.42071019108280 17 86.5 90.8287101910828 -4.32871019108279 18 87.93 90.6727101910828 -2.7427101910828 19 88.6 90.6087101910828 -2.00871019108281 20 90.08 89.5387101910828 0.541289808917195 21 88.84 89.6487101910828 -0.808710191082797 22 87.91 89.7387101910828 -1.82871019108281 23 88.31 89.6507101910828 -1.34071019108280 24 87.77 88.9747101910828 -1.20471019108281 25 86.11 89.3283917197452 -3.21839171974521 26 82.8 88.5161098726115 -5.71610987261147 27 81.65 87.4441098726115 -5.79410987261146 28 82.36 86.7041098726115 -4.34410987261147 29 82.91 86.8121098726115 -3.90210987261147 30 81.99 86.6561098726115 -4.66610987261147 31 83.32 86.5921098726115 -3.27210987261147 32 84.12 85.5221098726115 -1.40210987261146 33 85.66 85.6321098726115 0.0278901273885345 34 86.67 85.7221098726115 0.947890127388538 35 85.31 85.6341098726115 -0.324109872611465 36 85.13 84.9581098726115 0.171890127388528 37 86.6 85.311791401274 1.28820859872612 38 87.92 84.4995095541401 3.42049044585987 39 87.19 83.4275095541401 3.76249044585987 40 85.56 82.6875095541401 2.87249044585987 41 86.21 82.7955095541401 3.41449044585987 42 86.16 82.6395095541401 3.52049044585987 43 85.04 82.5755095541401 2.46449044585988 44 82.01 81.5055095541401 0.504490445859873 45 83.05 81.6155095541401 1.43449044585987 46 83.34 81.7055095541401 1.63449044585987 47 82.87 81.6175095541401 1.25249044585987 48 83.18 80.9415095541401 2.23849044585987 49 83.97 81.2951910828025 2.67480891719746 50 82.98 83.3323598726115 -0.35235987261146 51 82.2 82.2603598726115 -0.0603598726114599 52 83.68 81.5203598726115 2.15964012738854 53 83.49 81.6283598726115 1.86164012738853 54 82.68 81.4723598726115 1.20764012738854 55 81.56 81.4083598726115 0.151640127388538 56 81.19 80.3383598726115 0.851640127388531 57 81.07 80.4483598726115 0.62164012738853 58 79.81 80.5383598726115 -0.728359872611464 59 79.72 80.4503598726115 -0.730359872611468 60 78.32 79.7743598726115 -1.45435987261147 61 76.6 80.1280414012739 -3.52804140127388

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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Software written by Ed van Stee & Patrick Wessa

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