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Paper_multiple_linear_regression_2dummies_LT

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

Title produced by software: Multiple Regression

Date of computation: Fri, 14 Dec 2007 06:35:31 -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/14/t1197638495dljo3j6ipxpae6l.htm/, Retrieved Fri, 14 Dec 2007 14:21:46 +0100

User-defined keywords:

s065921, s0650125

Dataseries X:

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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 graanprijzen[t] = + 87.782122435839 + 15.6852291055731ontkoppelde_bedrijfstoeslag[t] + 12.9295760919322graanomzet[t] + 0.651272079367334t + 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) 87.782122435839 3.928437 22.3453 0 0 ontkoppelde_bedrijfstoeslag 15.6852291055731 5.957753 2.6327 0.009951 0.004975 graanomzet 12.9295760919322 3.166638 4.0831 9.5e-05 4.8e-05 t 0.651272079367334 0.099753 6.5289 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.833389660968943 R-squared 0.694538327009929 Adjusted R-squared 0.6844681619663 F-TEST (value) 68.969905061224 F-TEST (DF numerator) 3 F-TEST (DF denominator) 91 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16.2262570785637 Sum Squared Residuals 23959.5191089472 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.7 88.4333945152065 14.2666054847935 2 103.2 89.0846665945736 14.1153334054264 3 105.6 89.735938673941 15.8640613260591 4 103.9 90.3872107533083 13.5127892466917 5 107.2 91.0384828326757 16.1615171673243 6 100.7 91.689754912043 9.010245087957 7 92.1 92.3410269914103 -0.241026991410338 8 90.3 92.9922990707777 -2.69229907077767 9 93.4 93.643571150145 -0.243571150144992 10 98.5 94.2948432295123 4.20515677048767 11 100.8 94.9461153088797 5.85388469112033 12 102.3 95.597387388247 6.702612611753 13 104.7 96.2486594676143 8.45134053238566 14 101.1 96.8999315469817 4.20006845301832 15 101.4 97.551203626349 3.848796373651 16 99.5 98.2024757057163 1.29752429428366 17 98.4 98.8537477850837 -0.453747785083666 18 96.3 99.505019864451 -3.20501986445101 19 100.7 100.156291943818 0.543708056181662 20 101.2 100.807564023186 0.392435976814327 21 100.3 101.458836102553 -1.15883610255301 22 97.8 102.110108181920 -4.31010818192035 23 97.4 102.761380261288 -5.36138026128767 24 98.6 103.412652340655 -4.81265234065502 25 99.7 104.063924420022 -4.36392442002235 26 99 104.715196499390 -5.71519649938968 27 98.1 105.366468578757 -7.26646857875702 28 97 106.017740658124 -9.01774065812435 29 98.5 106.669012737492 -8.16901273749168 30 103.8 107.320284816859 -3.52028481685902 31 114.4 107.971556896226 6.42844310377365 32 124.5 108.622828975594 15.8771710244063 33 134.2 109.274101054961 24.9258989450390 34 131.8 109.925373134328 21.8746268656717 35 125.6 110.576645213696 15.0233547863043 36 119.9 111.227917293063 8.67208270693698 37 114.9 111.879189372430 3.02081062756965 38 115.5 112.530461451798 2.96953854820230 39 112.5 113.181733531165 -0.68173353116503 40 111.4 113.833005610532 -2.43300561053236 41 115.3 114.484277689900 0.8157223101003 42 110.8 115.135549769267 -4.33554976926704 43 103.7 115.786821848634 -12.0868218486344 44 111.1 129.367670019934 -18.2676700199340 45 113 130.018942099301 -17.0189420993013 46 111.2 130.670214178669 -19.4702141786686 47 117.6 131.321486258036 -13.7214862580360 48 121.7 131.972758337403 -10.2727583374033 49 127.3 132.624030416771 -5.32403041677062 50 129.8 133.275302496138 -3.47530249613795 51 137.1 133.926574575505 3.17342542449471 52 141.4 134.577846654873 6.82215334512738 53 137.4 135.22911873424 2.17088126576005 54 130.7 135.880390813607 -5.18039081360731 55 117.2 136.531662892975 -19.3316628929746 56 110.8 111.323782788477 -0.523782788477468 57 111.4 111.975054867845 -0.575054867844793 58 108.2 112.626326947212 -4.42632694721213 59 108.8 113.277599026579 -4.47759902657947 60 110.2 113.928871105947 -3.7288711059468 61 109.5 114.580143185314 -5.08014318531414 62 109.5 115.231415264681 -5.73141526468147 63 116 115.882687344049 0.117312655951195 64 111.2 116.533959423416 -5.33395942341613 65 112.1 117.185231502783 -5.08523150278348 66 114 117.836503582151 -3.83650358215081 67 119.1 118.487775661518 0.61222433848185 68 114.1 134.824276846459 -20.7242768464586 69 115.1 135.475548925826 -20.3755489258260 70 115.4 136.126821005193 -20.7268210051933 71 110.8 149.707669176493 -38.9076691764929 72 116 150.358941255860 -34.3589412558602 73 119.2 151.010213335228 -31.8102133352275 74 126.5 151.661485414595 -25.1614854145949 75 127.8 152.312757493962 -24.5127574939622 76 131.3 152.964029573330 -21.6640295733295 77 140.3 153.615301652697 -13.3153016526969 78 137.3 154.266573732064 -16.9665737320642 79 143 154.917845811432 -11.9178458114316 80 134.5 155.569117890799 -21.0691178907989 81 139.9 156.220389970166 -16.3203899701662 82 159.3 156.871662049534 2.42833795046645 83 170.4 157.522934128901 12.8770658710991 84 175 158.174206208268 16.8257937917318 85 175.8 158.825478287636 16.9745217123644 86 180.9 159.476750367003 21.4232496329971 87 180.3 160.128022446370 20.1719775536298 88 169.6 160.779294525738 8.82070547426243 89 172.3 161.430566605105 10.8694333948951 90 184.8 162.081838684472 22.7181613155278 91 177.7 162.733110763840 14.9668892361604 92 184.6 163.384382843207 21.2156171567931 93 211.4 164.035654922574 47.3643450774258 94 215.3 164.686927001942 50.6130729980584 95 215.9 165.338199081309 50.5618009186911

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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