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WS 8 - Q3 (2)

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 07:14:36 -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/t1195135995p82g5u78j8h7hp1.htm/, Retrieved Thu, 15 Nov 2007 15:13:28 +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] = + 8.82857142857143 + 0.125988700564972x[t] + 0.171428571428568M1[t] + 0.0714285714285723M2[t] -0.103571428571428M3[t] -0.55682001614205M4[t] -0.666071428571428M5[t] -0.591071428571429M6[t] + 0.408928571428572M7[t] + 0.658928571428573M8[t] + 0.508928571428572M9[t] + 0.310573042776433M10[t] -0.0359967715899913M11[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) 8.82857142857143 0.293449 30.0855 0 0 x 0.125988700564972 0.436707 0.2885 0.773712 0.386856 M1 0.171428571428568 0.401822 0.4266 0.670796 0.335398 M2 0.0714285714285723 0.401822 0.1778 0.85936 0.42968 M3 -0.103571428571428 0.401822 -0.2578 0.797258 0.398629 M4 -0.55682001614205 0.405513 -1.3731 0.17355 0.086775 M5 -0.666071428571428 0.401822 -1.6576 0.101309 0.050655 M6 -0.591071428571429 0.401822 -1.471 0.14522 0.07261 M7 0.408928571428572 0.401822 1.0177 0.311895 0.155948 M8 0.658928571428573 0.401822 1.6399 0.104963 0.052481 M9 0.508928571428572 0.401822 1.2666 0.208991 0.104495 M10 0.310573042776433 0.419663 0.7401 0.461434 0.230717 M11 -0.0359967715899913 0.433352 -0.0831 0.934007 0.467003 Multiple Linear Regression - Regression Statistics Multiple R 0.507267902262373 R-squared 0.257320724665668 Adjusted R-squared 0.145918833365518 F-TEST (value) 2.30984161635434 F-TEST (DF numerator) 12 F-TEST (DF denominator) 80 p-value 0.0137721805425719 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.776394260228902 Sum Squared Residuals 48.2230437853107 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 9.00000000000002 -0.300000000000019 2 8.5 8.9 -0.399999999999999 3 8.2 8.725 -0.524999999999999 4 8.3 8.27175141242938 0.028248587570621 5 8 8.1625 -0.1625 6 8.1 8.2375 -0.137499999999999 7 8.7 9.2375 -0.537500000000001 8 9.3 9.4875 -0.187499999999997 9 8.9 9.3375 -0.4375 10 8.8 9.13914447134786 -0.339144471347862 11 8.4 8.79257465698144 -0.392574656981437 12 8.4 8.82857142857143 -0.428571428571428 13 7.3 9 -1.70000000000000 14 7.2 8.9 -1.7 15 7 8.725 -1.725 16 7 8.27175141242938 -1.27175141242938 17 6.9 8.1625 -1.2625 18 6.9 8.2375 -1.3375 19 7.1 9.2375 -2.1375 20 7.5 9.4875 -1.9875 21 7.4 9.3375 -1.9375 22 8.9 9.13914447134786 -0.239144471347861 23 8.3 8.9185633575464 -0.618563357546409 24 8.3 8.82857142857143 -0.528571428571428 25 9 9 2.49106291150269e-15 26 8.9 8.9 1.52655665885959e-16 27 8.8 8.725 0.0750000000000004 28 7.8 8.27175141242938 -0.471751412429379 29 7.8 8.1625 -0.3625 30 7.8 8.2375 -0.4375 31 9.2 9.2375 -0.0375000000000007 32 9.3 9.4875 -0.1875 33 9.2 9.3375 -0.137500000000001 34 8.6 9.13914447134786 -0.539144471347861 35 8.5 8.79257465698144 -0.292574656981437 36 8.5 8.82857142857143 -0.328571428571428 37 9 9 2.49106291150269e-15 38 9 8.9 0.0999999999999998 39 8.8 8.725 0.0750000000000004 40 8 8.27175141242938 -0.271751412429379 41 7.9 8.1625 -0.262500000000000 42 8.1 8.2375 -0.137500000000000 43 9.3 9.2375 0.0625000000000007 44 9.4 9.4875 -0.0875000000000004 45 9.4 9.3375 0.0625000000000001 46 9.3 9.26513317191283 0.0348668280871676 47 9 8.79257465698144 0.207425343018563 48 9.1 8.82857142857143 0.271428571428572 49 9.7 9 0.700000000000002 50 9.7 8.9 0.799999999999999 51 9.6 8.725 0.875 52 8.3 8.27175141242938 0.0282485875706221 53 8.2 8.1625 0.0374999999999993 54 8.4 8.2375 0.162500000000000 55 10.6 9.2375 1.3625 56 10.9 9.4875 1.4125 57 10.9 9.3375 1.5625 58 9.6 9.13914447134786 0.460855528652139 59 9.3 8.79257465698144 0.507425343018564 60 9.3 8.82857142857143 0.471428571428573 61 9.6 9 0.600000000000002 62 9.5 8.9 0.6 63 9.5 8.725 0.775 64 9 8.27175141242938 0.728248587570621 65 8.9 8.1625 0.7375 66 9 8.2375 0.7625 67 10.1 9.2375 0.8625 68 10.2 9.4875 0.712499999999999 69 10.2 9.3375 0.8625 70 9.5 9.13914447134786 0.360855528652139 71 9.3 8.79257465698144 0.507425343018564 72 9.3 8.82857142857143 0.471428571428573 73 9.4 9 0.400000000000003 74 9.3 8.9 0.400000000000000 75 9.1 8.725 0.374999999999999 76 9 8.27175141242938 0.728248587570621 77 8.9 8.1625 0.7375 78 9 8.2375 0.7625 79 9.8 9.2375 0.562500000000001 80 10 9.4875 0.512500000000000 81 9.8 9.3375 0.4625 82 9.4 9.13914447134786 0.260855528652139 83 9 8.9185633575464 0.0814366424535907 84 8.9 8.82857142857143 0.0714285714285721 85 9.3 9 0.300000000000003 86 9.1 8.9 0.199999999999999 87 8.8 8.725 0.0750000000000004 88 8.9 8.39774011299435 0.50225988700565 89 8.7 8.1625 0.537499999999999 90 8.6 8.2375 0.362499999999999 91 9.1 9.2375 -0.137500000000000 92 9.3 9.4875 -0.1875 93 8.9 9.3375 -0.4375

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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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