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

Title produced by software: Multiple Regression

Date of computation: Thu, 13 Dec 2007 01:08:50 -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/Dec/13/t1197532433ae428haf5a6ws01.htm/, Retrieved Thu, 13 Dec 2007 08:54:05 +0100

User-defined keywords:

fredje

Dataseries X:

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12398.4 0 13882.3 0 15861.5 0 13286.1 0 15634.9 0 14211 0 13646.8 0 12224.6 0 15916.4 0 16535.9 0 15796 0 14418.6 0 15044.5 0 14944.2 0 16754.8 0 14254 0 15454.9 0 15644.8 0 14568.3 0 12520.2 0 14803 0 15873.2 0 14755.3 0 12875.1 0 14291.1 1 14205.3 1 15859.4 1 15258.9 1 15498.6 1 14106.5 1 15023.6 1 12083 1 15761.3 1 16943 1 15070.3 1 13659.6 1 14768.9 1 14725.1 1 15998.1 1 15370.6 1 14956.9 1 15469.7 1 15101.8 1 11703.7 1 16283.6 1 16726.5 1 14968.9 1 14861 1 14583.3 1 15305.8 1 17903.9 1 16379.4 1 15420.3 1 17870.5 1 15912.8 1 13866.5 1 17823.2 1 17872 1 17420.4 1 16704.4 1 15991.2 1 16583.6 1 19123.5 1 17838.7 1 17209.4 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] = + 12815.4593063584 -1141.77225433526x[t] + 414.909267822725M1[t] + 777.13304431599M2[t] + 2687.02348747591M3[t] + 1102.1805973025M4[t] + 1334.13770712909M5[t] + 1352.31734104046M6[t] + 676.551117533716M7[t] -1760.43510597303M8[t] + 1811.53867052023M9[t] + 2418.23244701349M10[t] + 1164.36622350674M11[t] + 65.9262235067438t + 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) 12815.4593063584 373.439499 34.3174 0 0 x -1141.77225433526 346.35093 -3.2966 0.001786 0.000893 M1 414.909267822725 444.426373 0.9336 0.354918 0.177459 M2 777.13304431599 443.227498 1.7534 0.085551 0.042775 M3 2687.02348747591 442.205619 6.0764 0 0 M4 1102.1805973025 441.361967 2.4972 0.015786 0.007893 M5 1334.13770712909 440.697564 3.0273 0.003863 0.001931 M6 1352.31734104046 462.268303 2.9254 0.005124 0.002562 M7 676.551117533716 461.319182 1.4666 0.148636 0.074318 M8 -1760.43510597303 460.541174 -3.8225 0.000361 0.00018 M9 1811.53867052023 459.935146 3.9387 0.00025 0.000125 M10 2418.23244701349 459.50178 5.2627 3e-06 1e-06 M11 1164.36622350674 459.241564 2.5354 0.01434 0.00717 t 65.9262235067438 8.926957 7.3851 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.906748503016145 R-squared 0.82219284772202 Adjusted R-squared 0.776869455964888 F-TEST (value) 18.1405851558459 F-TEST (DF numerator) 13 F-TEST (DF denominator) 51 p-value 9.65894031423886e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 725.987471786154 Sum Squared Residuals 26879948.2687130 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12398.4 13296.2947976879 -897.894797687909 2 13882.3 13724.4447976879 157.85520231214 3 15861.5 15700.2614643545 161.238535645470 4 13286.1 14181.3447976879 -895.244797687861 5 15634.9 14479.2281310212 1155.67186897881 6 14211 14563.3339884393 -352.333988439303 7 13646.8 13953.4939884393 -306.693988439302 8 12224.6 11582.4339884393 642.166011560695 9 15916.4 15220.3339884393 696.066011560696 10 16535.9 15892.9539884393 642.946011560698 11 15796 14705.0139884393 1090.98601156070 12 14418.6 13606.5739884393 812.026011560695 13 15044.5 14087.4094797688 957.090520231225 14 14944.2 14515.5594797688 428.640520231217 15 16754.8 16491.3761464355 263.423853564549 16 14254 14972.4594797688 -718.459479768784 17 15454.9 15270.3428131021 184.557186897881 18 15644.8 15354.4486705202 290.351329479769 19 14568.3 14744.6086705202 -176.308670520231 20 12520.2 12373.5486705202 146.651329479771 21 14803 16011.4486705202 -1208.44867052023 22 15873.2 16684.0686705202 -810.86867052023 23 14755.3 15496.1286705202 -740.82867052023 24 12875.1 14397.6886705202 -1522.58867052023 25 14291.1 13736.7519075144 554.34809248556 26 14205.3 14164.9019075144 40.3980924855489 27 15859.4 16140.7185741811 -281.318574181116 28 15258.9 14621.8019075145 637.098092485549 29 15498.6 14919.6852408478 578.914759152215 30 14106.5 15003.7910982659 -897.291098265896 31 15023.6 14393.9510982659 629.648901734103 32 12083 12022.8910982659 60.1089017341033 33 15761.3 15660.7910982659 100.508901734103 34 16943 16333.4110982659 609.588901734103 35 15070.3 15145.4710982659 -75.1710982658971 36 13659.6 14047.0310982659 -387.431098265898 37 14768.9 14527.8665895954 241.033410404633 38 14725.1 14956.0165895954 -230.916589595376 39 15998.1 16931.8332562620 -933.733256262041 40 15370.6 15412.9165895954 -42.3165895953756 41 14956.9 15710.7999229287 -753.899922928711 42 15469.7 15794.9057803468 -325.205780346821 43 15101.8 15185.0657803468 -83.2657803468231 44 11703.7 12814.0057803468 -1110.30578034682 45 16283.6 16451.9057803468 -168.305780346821 46 16726.5 17124.5257803468 -398.025780346822 47 14968.9 15936.5857803468 -967.685780346822 48 14861 14838.1457803468 22.8542196531758 49 14583.3 15318.9812716763 -735.681271676292 50 15305.8 15747.1312716763 -441.331271676302 51 17903.9 17722.9479383430 180.952061657034 52 16379.4 16204.0312716763 175.368728323698 53 15420.3 16501.9146050096 -1081.61460500964 54 17870.5 16586.0204624277 1284.47953757225 55 15912.8 15976.1804624277 -63.3804624277486 56 13866.5 13605.1204624277 261.379537572253 57 17823.2 17243.0204624277 580.179537572254 58 17872 17915.6404624277 -43.6404624277479 59 17420.4 16727.7004624277 692.699537572254 60 16704.4 15629.2604624277 1075.13953757225 61 15991.2 16110.0959537572 -118.895953757216 62 16583.6 16538.2459537572 45.3540462427719 63 19123.5 18514.0626204239 609.437379576107 64 17838.7 16995.1459537572 843.554046242774 65 17209.4 17293.0292870906 -83.6292870905593

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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