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Ws6 T3

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 03:48:25 -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/t1195468939cjkem217iiyqwhc.htm/, Retrieved Mon, 19 Nov 2007 11:42:29 +0100

User-defined keywords:

Dataseries X:

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110.40 0 96.40 0 101.90 0 106.20 0 81.00 0 94.70 0 101.00 0 109.40 1 102.30 1 90.70 1 96.20 1 96.10 1 106.00 1 103.10 1 102.00 1 104.70 1 86.00 1 92.10 1 106.90 1 112.60 1 101.70 1 92.00 1 97.40 1 97.00 1 105.40 1 102.70 1 98.10 1 104.50 1 87.40 1 89.90 1 109.80 1 111.70 1 98.60 1 96.90 1 95.10 1 97.00 1 112.70 1 102.90 1 97.40 1 111.40 1 87.40 1 96.80 1 114.10 1 110.30 1 103.90 1 101.60 1 94.60 1 95.90 1 104.70 1 102.80 1 98.10 1 113.90 1 80.90 1 95.70 1 113.20 1 105.90 1 108.80 1 102.30 1 99.00 1 100.70 1 115.50 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] = + 94.4102362204725 -0.0548228346456831`x `[t] + 12.1820554461943M1[t] + 5.05808727034122M2[t] + 2.89518208661418M3[t] + 11.4522769028871M4[t] -12.2306282808399M5[t] -3.01353346456693M6[t] + 12.0635613517060M7[t] + 12.9716207349081M8[t] + 5.96871555118111M9[t] -0.474189632545929M10[t] -0.797094816272964M11[t] + 0.082905183727034t + 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) 94.4102362204725 2.03525 46.3875 0 0 `x ` -0.0548228346456831 1.655082 -0.0331 0.973716 0.486858 M1 12.1820554461943 2.01388 6.049 0 0 M2 5.05808727034122 2.110797 2.3963 0.020594 0.010297 M3 2.89518208661418 2.109473 1.3725 0.176433 0.088216 M4 11.4522769028871 2.108548 5.4314 2e-06 1e-06 M5 -12.2306282808399 2.10802 -5.8019 1e-06 0 M6 -3.01353346456693 2.107892 -1.4296 0.159433 0.079717 M7 12.0635613517060 2.108162 5.7223 1e-06 0 M8 12.9716207349081 2.092638 6.1987 0 0 M9 5.96871555118111 2.091231 2.8542 0.0064 0.0032 M10 -0.474189632545929 2.090226 -0.2269 0.821516 0.410758 M11 -0.797094816272964 2.089623 -0.3815 0.704586 0.352293 t 0.082905183727034 0.028991 2.8597 0.006306 0.003153 Multiple Linear Regression - Regression Statistics Multiple R 0.932242951965714 R-squared 0.869076921489749 Adjusted R-squared 0.832864155093296 F-TEST (value) 23.9991861426772 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.30366613927501 Sum Squared Residuals 512.967868110237 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 110.4 106.675196850394 3.72480314960639 2 96.4 99.6341338582677 -3.23413385826771 3 101.9 97.5541338582677 4.34586614173228 4 106.2 106.194133858268 0.00586614173226119 5 81 82.5941338582678 -1.59413385826775 6 94.7 91.8941338582677 2.80586614173227 7 101 107.054133858268 -6.05413385826772 8 109.4 107.990275590551 1.40972440944882 9 102.3 101.070275590551 1.22972440944882 10 90.7 94.7102755905512 -4.01027559055118 11 96.2 94.4702755905512 1.72972440944882 12 96.1 95.3502755905512 0.749724409448813 13 106 107.615236220472 -1.61523622047247 14 103.1 100.574173228346 2.52582677165353 15 102 98.4941732283465 3.50582677165355 16 104.7 107.134173228346 -2.43417322834645 17 86 83.5341732283465 2.46582677165354 18 92.1 92.8341732283465 -0.734173228346458 19 106.9 107.994173228346 -1.09417322834645 20 112.6 108.985137795276 3.6148622047244 21 101.7 102.065137795276 -0.365137795275590 22 92 95.7051377952756 -3.70513779527559 23 97.4 95.4651377952756 1.93486220472441 24 97 96.3451377952756 0.654862204724411 25 105.4 108.610098425197 -3.21009842519687 26 102.7 101.569035433071 1.13096456692913 27 98.1 99.4890354330709 -1.38903543307087 28 104.5 108.129035433071 -3.62903543307086 29 87.4 84.5290354330709 2.87096456692914 30 89.9 93.8290354330709 -3.92903543307086 31 109.8 108.989035433071 0.810964566929128 32 111.7 109.98 1.72000000000000 33 98.6 103.06 -4.46000000000001 34 96.9 96.7 0.200000000000006 35 95.1 96.46 -1.36000000000000 36 97 97.34 -0.339999999999997 37 112.7 109.604960629921 3.09503937007872 38 102.9 102.563897637795 0.336102362204728 39 97.4 100.483897637795 -3.08389763779526 40 111.4 109.123897637795 2.27610236220473 41 87.4 85.5238976377953 1.87610236220473 42 96.8 94.8238976377953 1.97610236220473 43 114.1 109.983897637795 4.11610236220472 44 110.3 110.974862204724 -0.674862204724411 45 103.9 104.054862204724 -0.154862204724404 46 101.6 97.6948622047244 3.90513779527559 47 94.6 97.4548622047244 -2.85486220472441 48 95.9 98.3348622047244 -2.4348622047244 49 104.7 110.599822834646 -5.89982283464569 50 102.8 103.558759842520 -0.758759842519689 51 98.1 101.478759842520 -3.37875984251968 52 113.9 110.118759842520 3.78124015748032 53 80.9 86.5187598425197 -5.61875984251967 54 95.7 95.8187598425197 -0.118759842519676 55 113.2 110.978759842520 2.22124015748032 56 105.9 111.969724409449 -6.06972440944881 57 108.8 105.049724409449 3.75027559055118 58 102.3 98.6897244094488 3.61027559055118 59 99 98.4497244094488 0.550275590551184 60 100.7 99.3297244094488 1.37027559055119 61 115.5 111.59468503937 3.90531496062990

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')

Copyright

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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