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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: Mon, 19 Nov 2007 11:11:07 -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/t1195495446hkpz0wrv102ri52.htm/, Retrieved Mon, 19 Nov 2007 19:04:06 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

-183.923544 0 -177.0726091 0 -228.6351091 0 -237.4476091 0 -127.7601091 0 -193.0101091 0 -220.6351091 0 -164.5101091 0 -268.3226091 0 -333.6976091 0 -34.26010911 0 -154.8851091 0 -97.74528053 0 101.1056549 0 2.543154874 0 -43.26934513 0 -163.5818451 0 -162.8318451 0 46.54315487 0 26.66815487 0 -107.1443451 0 42.48065487 0 76.91815487 0 196.2931549 0 201.4329835 0 12.28391886 0 -0.278581137 0 42.90891886 0 87.59641886 0 84.34641886 0 57.72141886 0 173.8464189 0 -185.9660811 0 47.65891886 0 89.09641886 0 -68.52858114 0 272.6112475 0 146.4621829 0 162.8996829 0 10.08718285 0 279.7746829 0 212.5246829 0 248.8996829 0 -41.97531715 0 -5.787817149 0 52.83718285 0 274.2746829 0 414.6496829 0 310.7895114 0 362.6404468 0 26.07794684 0 403.2654468 0 327.9529468 0 193.7029468 0 317.0779468 0 202.2029468 0 321.3904468 0 178.0154468 0 16.45294684 0 -68.17205316 0 -157.0322246 0 -76.18128917 0 -81.74378917 0 -134.5562892 0 77.13121083 0 199.8812108 0 105.2562108 0 198.3812108 0 262.5687108 0 196.1937108 0 11.63121083 0 -145.9937892 0 -166.8539606 0 -202.0030252 0 43.43447482 0 -113.3780252 0 -113.6905252 0 -155.9405252 0 -210.5655252 0 -124.4405252 0 -64.25302518 0 -298.6280252 0 -154.1905252 0 23.18447482 0 -249.6756966 0 118.1752388 0 -180.3872612 0 -79.19976119 0 -81.51226119 0 -246.7622612 0 -105.3872612 0 -319.2622612 0 -72.07476119 0 -90.44976119 0 -80.01226119 0 119.3627388 0 -53.49743261 0 -114.6464972 0 -155.2089972 0 -50.02149721 0 -196.3339972 0 -14.58399721 0 -82.20899721 0 17.91600279 0 -162.8964972 0 -132.2714972 0 -16.83399721 0 81.54100279 0 275.6808314 0 -32.46823322 0 17.96926678 0 27.15676678 0 -123.1557332 0 108.5942668 0 67.96926678 0 34.09426678 0 -13.71823322 0 -113.0932332 0 54.34426678 0 149.7192668 0 153.8590954 0 -28.28996923 0 238.1475308 0 50.33503077 0 8.022530771 0 -61.22746923 0 -140.8524692 0 -28.72746923 0 9.460030771 0 -121.9149692 0 41.52253077 0 115.8975308 0 27.03735936 0 -91.11170524 0 3.325794759 0 -29.48670524 0 -73.79920524 0 50.95079476 0 -86.67420524 0 -9.54920524 0 -66.36170524 0 73.26329476 0 -216.2992052 0 -128.9242052 0 -142.7843767 0 27.06655875 0 60.50405875 0 35.69155875 0 16.37905875 0 -64.87094125 0 115.5040587 0 -30.37094125 0 87.81655875 0 205.4415587 0 -64.12094125 0 -322.7459413 0 -139.6061127 0 35.24482274 0 -4.317677263 0 17.86982274 0 2.557322737 0 129.3073227 0 -16.31767726 0 164.8073227 0 21.99482274 0 138.6198227 0 87.05732274 0 51.43232274 0 -80.42784867 0 -105.1918797 1 5.245620328 1 68.43312033 1 -0.879379672 1 -105.1293797 1 -82.75437967 1 -132.6293797 1 102.5581203 1 23.18312033 1 -180.3793797 1 -267.0043797 1 30.13544892 1 23.98638432 1 90.42388432 1 31.61138432 1 81.29888432 1 25.04888432 1 -13.57611568 1 33.54888432 1 140.7363843 1 132.3613843 1 94.79888432 1 4.173884316 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2.17742567439308e-08 + 9.18380456424851e-09T[t] + 2.37968489558231e-08M1[t] -5.342838992659e-09M2[t] + 5.28955941669531e-10M3[t] -9.97425785522416e-09M4[t] -1.28997541035386e-09M5[t] -8.35568271161252e-09M6[t] -8.17139072699052e-09M7[t] -1.17371037337928e-08M8[t] -5.80283206036438e-09M9[t] -1.19935330071584e-08M10[t] -1.18422603138965e-09M11[t] -1.84286943719420e-10t + 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) 2.17742567439308e-08 44.029939 0 1 0.5 T 9.18380456424851e-09 41.037226 0 1 0.5 M1 2.37968489558231e-08 53.942919 0 1 0.5 M2 -5.342838992659e-09 53.941479 0 1 0.5 M3 5.28955941669531e-10 53.931287 0 1 0.5 M4 -9.97425785522416e-09 53.922166 0 1 0.5 M5 -1.28997541035386e-09 53.914117 0 1 0.5 M6 -8.35568271161252e-09 53.907141 0 1 0.5 M7 -8.17139072699052e-09 53.901237 0 1 0.5 M8 -1.17371037337928e-08 53.896405 0 1 0.5 M9 -5.80283206036438e-09 53.892648 0 1 0.5 M10 -1.19935330071584e-08 53.889963 0 1 0.5 M11 -1.18422603138965e-09 53.888353 0 1 0.5 t -1.84286943719420e-10 0.240551 0 1 0.5 Multiple Linear Regression - Regression Statistics Multiple R 8.78616408123945e-11 R-squared 7.71966792624623e-21 Adjusted R-squared -0.0730337078651686 F-TEST (value) 1.05700068528602e-19 F-TEST (DF numerator) 13 F-TEST (DF denominator) 178 p-value 1 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 152.417759553726 Sum Squared Residuals 4135148.8700732 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -183.923544 4.5386883584797e-08 -183.923544045387 2 -177.0726091 1.60628133016871e-08 -177.072609116063 3 -228.6351091 2.17504521060619e-08 -228.635109121750 4 -237.4476091 1.10628661786905e-08 -237.447609111063 5 -127.7601091 1.95628899746225e-08 -127.760109119563 6 -193.0101091 1.23128245377302e-08 -193.010109112313 7 -220.6351091 1.23128245377302e-08 -220.635109112313 8 -164.5101091 8.56289261719212e-09 -164.510109108563 9 -268.3226091 1.43128318086383e-08 -268.322609114313 10 -333.6976091 7.93784238339867e-09 -333.697609107938 11 -34.26010911 1.85628366011770e-08 -34.2601091285628 12 -154.8851091 1.95628047094942e-08 -154.885109119563 13 -97.74528053 4.31753619523079e-08 -97.7452805731754 14 101.1056549 1.38513627234715e-08 101.105654886149 15 2.543154874 1.95389047163985e-08 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-180.3793797 -3.2134721550392e-09 -180.379379696787 180 -267.0043797 -2.21353957385872e-09 -267.004379697786 181 30.13544892 2.13989679309634e-08 30.1354488986010 182 23.98638432 -7.92500287616349e-09 23.986384327925 183 90.42388432 -2.23749907490856e-09 90.4238843222375 184 31.61138432 -1.29249642100149e-08 31.6113843329250 185 81.29888432 -4.42499015207432e-09 81.298884324425 186 25.04888432 -1.16749845346931e-08 25.048884331675 187 -13.57611568 -1.16749685474815e-08 -13.5761156683250 188 33.54888432 -1.54249661932226e-08 33.5488843354250 189 140.7363843 -9.6750056854944e-09 140.736384309675 190 132.3613843 -1.60499951107340e-08 132.36138431605 191 94.79888432 -5.42497957667365e-09 94.798884325425 192 4.173884316 -4.42500702746429e-09 4.17388432042501

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')

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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