Q3 bis

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Sat, 22 Nov 2008 06:20:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/22/t12273600585fwky73crj5ydfy.htm/, Retrieved Sat, 22 Nov 2008 13:21:06 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/22/t12273600585fwky73crj5ydfy.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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15859.4 0 15258.9 0 15498.6 0 15106.5 0 15023.6 0 12083.0 0 15761.3 0 16942.6 0 15070.3 0 13659.6 0 14768.9 0 14725.1 0 15998.1 0 15370.6 0 14956.9 0 15469.7 0 15101.8 0 11703.7 0 16283.6 0 16726.5 0 14968.9 0 14861.0 0 14583.3 0 15305.8 0 17903.9 0 16379.4 0 15420.3 0 17870.5 0 15912.8 0 13866.5 0 17823.2 0 17872.0 0 17422.0 0 16704.5 0 15991.2 0 16583.6 0 19123.5 0 17838.7 0 17209.4 0 18586.5 0 16258.1 0 15141.6 1 19202.1 1 17746.5 1 19090.1 1 18040.3 1 17515.5 1 17751.8 1 21072.4 1 17170.0 1 19439.5 1 19795.4 1 17574.9 1 16165.4 1 19464.6 1 19932.1 1 19961.2 1 17343.4 1 18924.2 1 18574.1 1 21350.6 1

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 computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation x[t] = + 15459.8063917526 + 2820.68402061856`y `[t] + 2151.28226804125M1[t] + 379.576804123713M2[t] + 480.996804123713M3[t] + 1341.77680412372M4[t] -49.7031958762865M5[t] -2796.04000000000M6[t] + 1118.88000000000M7[t] + 1255.86M8[t] + 714.420000000002M9[t] -466.319999999998M10[t] -231.459999999998M11[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) 15459.8063917526 495.635035 31.1919 0 0 `y ` 2820.68402061856 299.060475 9.4318 0 0 M1 2151.28226804125 651.558457 3.3017 0.001819 0.000909 M2 379.576804123713 682.83656 0.5559 0.580873 0.290437 M3 480.996804123713 682.83656 0.7044 0.484581 0.242291 M4 1341.77680412372 682.83656 1.965 0.055216 0.027608 M5 -49.7031958762865 682.83656 -0.0728 0.942276 0.471138 M6 -2796.04000000000 680.211939 -4.1105 0.000153 7.7e-05 M7 1118.88000000000 680.211939 1.6449 0.106525 0.053262 M8 1255.86 680.211939 1.8463 0.071023 0.035511 M9 714.420000000002 680.211939 1.0503 0.298844 0.149422 M10 -466.319999999998 680.211939 -0.6856 0.496294 0.248147 M11 -231.459999999998 680.211939 -0.3403 0.735133 0.367567 Multiple Linear Regression - Regression Statistics Multiple R 0.878038173179367 R-squared 0.77095103356016 Adjusted R-squared 0.7136887919502 F-TEST (value) 13.4635147329976 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 1.49376067071216e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1075.50950872357 Sum Squared Residuals 55522593.7610308 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15859.4 17611.0886597938 -1751.68865979379 2 15258.9 15839.3831958763 -580.483195876288 3 15498.6 15940.8031958763 -442.203195876289 4 15106.5 16801.5831958763 -1695.08319587629 5 15023.6 15410.1031958763 -386.503195876288 6 12083 12663.7663917526 -580.766391752582 7 15761.3 16578.6863917526 -817.386391752576 8 16942.6 16715.6663917526 226.933608247417 9 15070.3 16174.2263917526 -1103.92639175258 10 13659.6 14993.4863917526 -1333.88639175258 11 14768.9 15228.3463917526 -459.446391752578 12 14725.1 15459.8063917526 -734.706391752574 13 15998.1 17611.0886597938 -1612.98865979382 14 15370.6 15839.3831958763 -468.78319587629 15 14956.9 15940.8031958763 -983.903195876289 16 15469.7 16801.5831958763 -1331.88319587629 17 15101.8 15410.1031958763 -308.30319587629 18 11703.7 12663.7663917526 -960.066391752576 19 16283.6 16578.6863917526 -295.086391752577 20 16726.5 16715.6663917526 10.8336082474235 21 14968.9 16174.2263917526 -1205.32639175258 22 14861 14993.4863917526 -132.486391752578 23 14583.3 15228.3463917526 -645.046391752579 24 15305.8 15459.8063917526 -154.006391752576 25 17903.9 17611.0886597938 292.811340206181 26 16379.4 15839.3831958763 540.01680412371 27 15420.3 15940.8031958763 -520.503195876290 28 17870.5 16801.5831958763 1068.91680412371 29 15912.8 15410.1031958763 502.69680412371 30 13866.5 12663.7663917526 1202.73360824742 31 17823.2 16578.6863917526 1244.51360824742 32 17872 16715.6663917526 1156.33360824742 33 17422 16174.2263917526 1247.77360824742 34 16704.5 14993.4863917526 1711.01360824742 35 15991.2 15228.3463917526 762.853608247423 36 16583.6 15459.8063917526 1123.79360824742 37 19123.5 17611.0886597938 1512.41134020618 38 17838.7 15839.3831958763 1999.31680412371 39 17209.4 15940.8031958763 1268.59680412371 40 18586.5 16801.5831958763 1784.91680412371 41 16258.1 15410.1031958763 847.996804123711 42 15141.6 15484.4504123711 -342.850412371133 43 19202.1 19399.3704123711 -197.270412371135 44 17746.5 19536.3504123711 -1789.85041237113 45 19090.1 18994.9104123711 95.1895876288655 46 18040.3 17814.1704123711 226.129587628865 47 17515.5 18049.0304123711 -533.530412371134 48 17751.8 18280.4904123711 -528.690412371132 49 21072.4 20431.7726804124 640.627319587625 50 17170 18660.0672164948 -1490.06721649485 51 19439.5 18761.4872164948 678.012783505156 52 19795.4 19622.2672164948 173.132783505154 53 17574.9 18230.7872164948 -655.887216494844 54 16165.4 15484.4504123711 680.949587628867 55 19464.6 19399.3704123711 65.2295876288649 56 19932.1 19536.3504123711 395.749587628866 57 19961.2 18994.9104123711 966.289587628868 58 17343.4 17814.1704123711 -470.770412371132 59 18924.2 18049.0304123711 875.169587628867 60 18574.1 18280.4904123711 293.609587628867 61 21350.6 20431.7726804124 918.827319587622

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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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