Multiple Regression Voeding

*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: Wed, 10 Dec 2008 13:09:17 -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/Dec/10/t12289401939mdxxrumay32f64.htm/, Retrieved Wed, 10 Dec 2008 20:16:33 +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/Dec/10/t12289401939mdxxrumay32f64.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

100 0 100 0 100 0 100,1 0 100 0 100 0 99,8 0 100 0 99,9 0 99,2 0 98,7 0 98,7 0 98,9 1 99,2 1 99,8 1 100,5 1 100,1 1 100,5 1 98,4 1 98,6 1 99 1 99,1 1 98,9 1 98,5 1 96,9 1 96,8 1 97 1 97 1 96,9 1 97,1 1 97,2 1 97,9 1 98,9 1 99,2 1 99,5 1 99,3 1 99,9 1 100 1 100,3 1 100,5 1 100,7 1 100,9 1 100,8 1 100,9 1 101 1 100,3 1 100,1 1 99,8 1 99,9 1 99,9 1 100,2 1 99,7 1 100,4 1 100,9 1 101,3 1 101,4 1 101,3 1 100,9 1 100,9 1 100,9 1 101,1 1 101,1 1 101,3 1 101,8 1 102,9 1 103,2 1 103,3 1 104,5 1 105 1 104,9 1 104,9 1 105,4 1 106 1 105,7 1 105,9 1 106,2 1 106,4 1 106,9 1 107,3 1 107,9 1 109,2 1 110,2 1 110,2 1 110,5 1 110,6 1 110,8 1 111,3 1 111,1 1 111,2 1 111,2 1 111,1 1 111,5 1 112,1 1 111,4 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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 97.9817316017316 -5.04878787878788x[t] + 0.737189754689754M1[t] + 0.590997474747473M2[t] + 0.707305194805193M3[t] + 0.673612914862912M4[t] + 0.714920634920636M5[t] + 0.806228354978355M6[t] + 0.447536075036072M7[t] + 0.713843795093796M8[t] + 1.00515151515151M9[t] + 0.683959235209236M10[t] + 0.185477994227995M11[t] + 0.17119227994228t + 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) 97.9817316017316 0.912832 107.3382 0 0 x -5.04878787878788 0.748778 -6.7427 0 0 M1 0.737189754689754 1.021858 0.7214 0.472754 0.236377 M2 0.590997474747473 1.021411 0.5786 0.564478 0.282239 M3 0.707305194805193 1.021047 0.6927 0.490488 0.245244 M4 0.673612914862912 1.020767 0.6599 0.511208 0.255604 M5 0.714920634920636 1.020571 0.7005 0.485641 0.24282 M6 0.806228354978355 1.020458 0.7901 0.431825 0.215913 M7 0.447536075036072 1.02043 0.4386 0.662151 0.331075 M8 0.713843795093796 1.020485 0.6995 0.48626 0.24313 M9 1.00515151515151 1.020624 0.9848 0.327672 0.163836 M10 0.683959235209236 1.020848 0.67 0.504793 0.252396 M11 0.185477994227995 1.053875 0.176 0.860742 0.430371 t 0.17119227994228 0.009252 18.5038 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.907516079871135 R-squared 0.823585435224672 Adjusted R-squared 0.794918068448682 F-TEST (value) 28.7290228523687 F-TEST (DF numerator) 13 F-TEST (DF denominator) 80 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.97154340408979 Sum Squared Residuals 310.958671536796 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100 98.8901136363636 1.10988636363636 2 100 98.9151136363636 1.08488636363637 3 100 99.2026136363636 0.797386363636364 4 100.1 99.3401136363636 0.759886363636359 5 100 99.5526136363636 0.44738636363636 6 100 99.8151136363636 0.184886363636360 7 99.8 99.6276136363636 0.172386363636364 8 100 100.065113636364 -0.0651136363636372 9 99.9 100.527613636364 -0.62761363636363 10 99.2 100.377613636364 -1.17761363636364 11 98.7 100.050324675325 -1.35032467532468 12 98.7 100.036038961039 -1.33603896103896 13 98.9 95.8956331168831 3.00436688311689 14 99.2 95.9206331168831 3.27936688311688 15 99.8 96.2081331168831 3.59186688311688 16 100.5 96.3456331168831 4.15436688311688 17 100.1 96.5581331168831 3.54186688311688 18 100.5 96.8206331168831 3.67936688311688 19 98.4 96.6331331168831 1.76686688311689 20 98.6 97.0706331168831 1.52936688311688 21 99 97.5331331168831 1.46686688311688 22 99.1 97.3831331168831 1.71686688311688 23 98.9 97.0558441558442 1.84415584415585 24 98.5 97.0415584415584 1.45844155844156 25 96.9 97.9499404761905 -1.04994047619047 26 96.8 97.9749404761905 -1.17494047619048 27 97 98.2624404761905 -1.26244047619048 28 97 98.3999404761905 -1.39994047619048 29 96.9 98.6124404761905 -1.71244047619048 30 97.1 98.8749404761905 -1.77494047619049 31 97.2 98.6874404761905 -1.48744047619047 32 97.9 99.1249404761905 -1.22494047619047 33 98.9 99.5874404761905 -0.687440476190472 34 99.2 99.4374404761905 -0.237440476190477 35 99.5 99.1101515151515 0.389848484848482 36 99.3 99.0958658008658 0.204134199134194 37 99.9 100.004247835498 -0.104247835497830 38 100 100.029247835498 -0.0292478354978352 39 100.3 100.316747835498 -0.0167478354978383 40 100.5 100.454247835498 0.0457521645021657 41 100.7 100.666747835498 0.0332521645021633 42 100.9 100.929247835498 -0.0292478354978325 43 100.8 100.741747835498 0.0582521645021616 44 100.9 101.179247835498 -0.279247835497833 45 101 101.641747835498 -0.641747835497837 46 100.3 101.491747835498 -1.19174783549784 47 100.1 101.164458874459 -1.06445887445888 48 99.8 101.150173160173 -1.35017316017316 49 99.9 102.058555194805 -2.15855519480519 50 99.9 102.083555194805 -2.18355519480519 51 100.2 102.371055194805 -2.17105519480519 52 99.7 102.508555194805 -2.80855519480519 53 100.4 102.721055194805 -2.32105519480519 54 100.9 102.983555194805 -2.08355519480519 55 101.3 102.796055194805 -1.49605519480520 56 101.4 103.233555194805 -1.83355519480519 57 101.3 103.696055194805 -2.3960551948052 58 100.9 103.546055194805 -2.64605519480519 59 100.9 103.218766233766 -2.31876623376623 60 100.9 103.204480519481 -2.30448051948052 61 101.1 104.112862554113 -3.01286255411256 62 101.1 104.137862554113 -3.03786255411256 63 101.3 104.425362554113 -3.12536255411256 64 101.8 104.562862554113 -2.76286255411255 65 102.9 104.775362554113 -1.87536255411255 66 103.2 105.037862554113 -1.83786255411255 67 103.3 104.850362554113 -1.55036255411256 68 104.5 105.287862554113 -0.787862554112556 69 105 105.750362554113 -0.750362554112555 70 104.9 105.600362554113 -0.700362554112551 71 104.9 105.273073593074 -0.37307359307359 72 105.4 105.258787878788 0.141212121212125 73 106 106.16716991342 -0.167169913419916 74 105.7 106.19216991342 -0.492169913419909 75 105.9 106.47966991342 -0.579669913419907 76 106.2 106.61716991342 -0.417169913419911 77 106.4 106.82966991342 -0.429669913419912 78 106.9 107.09216991342 -0.19216991341991 79 107.3 106.90466991342 0.395330086580084 80 107.9 107.34216991342 0.55783008658009 81 109.2 107.80466991342 1.39533008658009 82 110.2 107.65466991342 2.54533008658009 83 110.2 107.327380952381 2.87261904761905 84 110.5 107.313095238095 3.18690476190476 85 110.6 108.221477272727 2.37852272727272 86 110.8 108.246477272727 2.55352272727272 87 111.3 108.533977272727 2.76602272727273 88 111.1 108.671477272727 2.42852272727272 89 111.2 108.883977272727 2.31602272727273 90 111.2 109.146477272727 2.05352272727273 91 111.1 108.958977272727 2.14102272727273 92 111.5 109.396477272727 2.10352272727272 93 112.1 109.858977272727 2.24102272727272 94 111.4 109.708977272727 1.69102272727273

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 0 ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 0 ;

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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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