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Regressiemodel 1 paper

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

Title produced by software: Multiple Regression

Date of computation: Thu, 20 Dec 2007 11:31:24 -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/20/t1198174432afvix0ipv76y6b6.htm/, Retrieved Thu, 20 Dec 2007 19:13:53 +0100

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Dataseries X:

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115.4 126.6 117 106.9 93.9 103.8 107.1 89.8 100.8 99.3 93.4 110.6 99.2 101.5 104 108.3 110.4 112.6 105.6 105.9 107.3 99.5 108.4 98.9 107.4 113.9 109.8 93.1 86.1 104.9 88.1 69.4 102.2 110.7 101.2 123.9 113.1 100.5 124.9 99.6 98 112.7 93.6 106.6 121.9 98.6 90.1 100.6 99.6 96.9 104.3 114.3 125.9 120.4 107.8 112 107.5 101.2 100 102.9 112.5 123.9 125.6 100.5 79.8 107.5 93.9 83.4 108.8 116.2 113.6 128.4 112 112.9 121.1 106.4 104 119.5 95.7 109.9 128.7 96 99 108.7 95.8 106.3 105.5 103 128.9 119.8 102.2 111.1 111.3 98.4 102.9 110.6 111.4 130 120.1 86.6 87 97.5 91.3 87.5 107.7 107.9 117.6 127.3 101.8 103.4 117.2 104.4 110.8 119.8 93.4 112.6 116.2 100.1 102.5 111 98.5 112.4 112.4 112.9 135.6 130.6 101.4 105.1 109.1 107.1 127.7 118.8 110.8 137 123.9 90.3 91 101.6 95.5 90.5 112.8 111.4 122.4 128 113 123.3 129.6 107.5 124.3 125.8 95.9 120 119.5 106.3 118.1 115.7 105.2 119 113.6 117.2 142.7 129.7 106.9 123.6 112 108.2 129.6 116.8 113 151.6 127 96.1 108.7 112.9 100.2 99.3 113.3 108.1 126.4 121.7

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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Cons.[t] = + 48.8917446449141 + 0.338889029387975Inter.[t] + 0.280590797362096Inv.[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) 48.8917446449141 11.517501 4.245 8.1e-05 4.1e-05 Inter. 0.338889029387975 0.149519 2.2665 0.027232 0.013616 Inv. 0.280590797362096 0.06899 4.0671 0.000148 7.4e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.738425103738406 R-squared 0.545271633831076 Adjusted R-squared 0.529316252561991 F-TEST (value) 34.1747793196009 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 1.76170522614427e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.17091580655335 Sum Squared Residuals 2170.57150781949 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 117 123.522333582328 -6.52233358232784 2 103.8 111.466457758790 -7.66645775878951 3 100.8 110.383813295483 -9.58381329548251 4 110.6 108.750605736760 1.84939426324015 5 104 110.989502292454 -6.98950229245403 6 112.6 116.570650556407 -3.97065055640726 7 107.3 114.392991588930 -7.09299158893029 8 98.9 113.027245503069 -14.1272455030689 9 109.8 117.247718220725 -7.44771822072542 10 104.9 104.601180933811 0.298819066188908 11 102.2 98.2208694709242 3.97913052907578 12 123.9 114.802548891207 9.09745110879289 13 124.9 115.419469003585 9.48053099641522 14 112.7 110.142990113442 2.55700988655813 15 121.9 110.522736794428 11.3772632055720 16 100.6 107.587433784893 -6.98743378489335 17 104.3 109.834340236344 -5.53434023634358 18 120.4 122.953142091848 -2.55314209184759 19 107.5 116.850151317493 -9.35015131749262 20 102.9 111.246394155187 -8.34639415518683 21 125.6 121.781960244225 3.81803975577495 22 107.5 105.341237727901 2.15876227209909 23 108.8 104.114697004444 4.68530299555617 24 128.4 120.145764440131 8.25423555986904 25 121.1 118.526016958548 2.57398304145199 26 119.5 114.130980297453 5.36901970254731 27 128.7 112.160353387438 16.5396466125623 28 108.7 109.203580405007 -0.503580405007262 29 105.5 111.184115419873 -5.68411541987297 30 119.8 119.965468451850 -0.165468451849764 31 111.3 114.699841035294 -3.39984103529407 32 110.6 111.111218185251 -0.511218185250589 33 120.1 123.120786175807 -3.02078617580706 34 97.5 102.650933960415 -5.15093396041514 35 107.7 104.384007797220 3.31599220278033 36 127.3 118.455348685659 8.84465131434084 37 117.2 112.403736283851 4.79626371614926 38 119.8 115.361219660739 4.43878033926101 39 116.2 112.138503772723 4.06149622727697 40 111 111.575093216265 -0.575093216265297 41 112.4 113.810719663129 -1.41071966312928 42 130.6 125.200428185117 5.39957181488324 43 109.1 112.745185027611 -3.64518502761112 44 118.8 121.018204515506 -2.21820451550594 45 123.9 124.881588339709 -0.981588339708936 46 101.6 105.027186558599 -3.42718655859905 47 112.8 106.649114112735 6.15088588726453 48 128 120.988296115855 7.01170388414487 49 129.6 121.783050280502 7.81694971949822 50 125.8 120.19975141623 5.60024858376999 51 119.5 115.062098246672 4.43790175332752 52 115.7 118.053421637319 -2.35342163731944 53 113.6 117.933175422619 -4.33317542261856 54 129.7 128.649845672756 1.05015432724406 55 112 119.800004440444 -7.80000444044375 56 116.8 121.924104962821 -5.1241049628207 57 127 129.723769845849 -2.72376984584908 58 112.9 111.959200042358 0.940799957641614 59 113.3 110.711091567645 2.58890843235461 60 121.7 120.992325508323 0.707674491676811

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal 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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