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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 13:05:34 -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/t1197575459fv8382v7h6qbzo6.htm/, Retrieved Thu, 13 Dec 2007 20:51:09 +0100

User-defined keywords:

zonder iets

Dataseries X:

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103,1 98,6 98,1 98,6 100,6 98 101,1 98 103,1 106,8 111,1 106,8 95,5 96,6 93,3 96,7 90,5 100,1 100 100,2 90,9 107,7 108 107,7 88,8 91,5 70,4 92 90,7 97,8 75,4 98,4 94,3 107,4 105,5 107,4 104,6 117,5 112,3 117,7 111,1 105,6 102,5 105,7 110,8 97,4 93,5 97,5 107,2 99,5 86,7 99,9 99 98 95,2 98,2 99 104,3 103,8 104,5 91 100,6 97 100,8 96,2 101,1 95,5 101,5 96,9 103,9 101 103,9 96,2 96,9 67,5 99,6 100,1 95,5 64 98,4 99 108,4 106,7 112,7 115,4 117 100,6 118,4 106,9 103,8 101,2 108,1 107,1 100,8 93,1 105,4 99,3 110,6 84,2 114,6 99,2 104 85,8 106,9 108,3 112,6 91,8 115,9 105,6 107,3 92,4 109,8 99,5 98,9 80,3 101,8 107,4 109,8 79,7 114,2 93,1 104,9 62,5 110,8 88,1 102,2 57,1 108,4 110,7 123,9 100,8 127,5 113,1 124,9 100,7 128,6 99,6 112,7 86,2 116,6 93,6 121,9 83,2 127,4 98,6 100,6 71,7 105 99,6 104,3 77,5 108,3 114,3 120,4 89,8 125 107,8 107,5 80,3 111,6 101,2 102,9 78,7 106,5 112,5 125,6 93,8 130,3 100,5 107,5 57,6 115 93,9 108,8 60,6 116,1 116,2 128,4 91 134 112 121,1 85,3 126,5 106,4 119,5 77,4 125,8 95,7 128,7 77,3 136,4 96 108,7 68,3 114,9 95,8 105,5 69,9 110,9 103 119,8 81,7 125,5 102,2 111,3 75,1 116,8 98,4 110,6 69,9 116,8 111,4 120,1 84 125,5 86,6 97,5 54,3 104,2 91,3 107,7 60 115,1 107,9 127,3 89,9 132,8 101,8 117,2 77 123,3 104,4 119,8 85,3 124,8 93,4 116,2 77,6 122 100,1 111 69,2 117,4 98,5 112,4 75,5 117,9 112,9 130,6 85,7 137,4 101,4 109,1 72,2 114,6 107,1 118,8 79,9 124,7 110,8 123,9 85,3 129,6 90,3 101,6 52,2 109,4 95,5 112,8 61,2 120,9 111,4 128 82,4 134,9 113 129,6 85,4 136,3 107,5 125,8 78,2 133,2 95,9 119,5 70,2 127,2 106,3 115,7 70,2 122,7 105,2 113,6 69,3 120,5 117,2 129,7 77,5 137,8 106,9 112 66,1 119,1 108,2 116,8 69 124,3 110 126,3 75,3 134,3 96,1 112,9 58,2 121,7 100,6 115,9 59,7 125

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 Totaal[t] = + 0.985561382674693 + 0.00512745466226638Intermediaire[t] + 0.0791606277930283Duurzame[t] + 0.90284901497009`Niet-Duurzaam`[t] + 0.432723397663192M1[t] + 0.516710710020281M2[t] + 0.490458302459475M3[t] + 0.669615430179371M4[t] + 0.61141179663758M5[t] + 0.753034886197928M6[t] + 0.209506335240211M7[t] + 0.237812110676649M8[t] + 0.227756213647851M9[t] + 0.872187181607412M10[t] + 0.158817514259807M11[t] -0.0396749980712203t + 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) 0.985561382674693 2.772767 0.3554 0.723426 0.361713 Intermediaire 0.00512745466226638 0.017206 0.298 0.766664 0.383332 Duurzame 0.0791606277930283 0.018007 4.396 4.2e-05 2.1e-05 `Niet-Duurzaam` 0.90284901497009 0.019418 46.4959 0 0 M1 0.432723397663192 0.468245 0.9241 0.358885 0.179443 M2 0.516710710020281 0.468198 1.1036 0.273892 0.136946 M3 0.490458302459475 0.477218 1.0277 0.307938 0.153969 M4 0.669615430179371 0.467555 1.4322 0.156963 0.078481 M5 0.61141179663758 0.460817 1.3268 0.18929 0.094645 M6 0.753034886197928 0.460018 1.637 0.106545 0.053273 M7 0.209506335240211 0.612222 0.3422 0.733317 0.366658 M8 0.237812110676649 0.565533 0.4205 0.675521 0.337761 M9 0.227756213647851 0.518448 0.4393 0.661921 0.330961 M10 0.872187181607412 0.517443 1.6856 0.096748 0.048374 M11 0.158817514259807 0.471645 0.3367 0.737421 0.368711 t -0.0396749980712203 0.011194 -3.5444 0.000741 0.000371 Multiple Linear Regression - Regression Statistics Multiple R 0.997583351309772 R-squared 0.995172542810435 Adjusted R-squared 0.994041107531631 F-TEST (value) 879.566477600183 F-TEST (DF numerator) 15 F-TEST (DF denominator) 64 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.776644682526761 Sum Squared Residuals 38.603325625414 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 98.693820820494 -0.0938208204939932 2 98 98.4210869725206 -0.421086972520612 3 106.8 107.104655813211 -0.304655813211284 4 96.6 96.677335061513 -0.0773350615129729 5 100.1 100.244166915197 -0.144166915197194 6 107.7 107.752818623171 -0.0528186231711168 7 91.5 90.0076782793031 1.49232172069685 8 97.8 96.1800880553004 1.61991194469960 9 107.4 106.657192028285 0.742807971714512 10 117.5 117.152397904380 0.347602095620312 11 105.6 104.822719362253 0.777280637747145 12 97.4 96.5068810406312 0.893118959368851 13 99.5 98.5100159703746 0.989984029625405 14 98 97.6503051672215 0.349694832778541 15 104.3 103.953107954921 0.346892045078962 16 100.6 100.172736822890 0.427263177110341 17 101.1 100.61477432431 0.485225675690042 18 103.9 103.322532722853 0.577467277147464 19 96.9 96.2016081601222 0.69839183987783 20 95.5 94.8497549954305 0.650245004569463 21 108.4 111.085283621037 -2.6852836210366 22 117 116.437489403178 0.56251059682184 23 103.8 106.389012895614 -2.58901289561396 24 100.8 103.112652448673 -2.31265244867262 25 110.6 111.067388052266 -0.46738805226578 26 104 104.285907210285 -0.285907210284583 27 112.6 112.867244543568 -0.267244543568163 28 107.3 107.532999930987 -0.232999930986981 29 98.9 99.2232081098778 -0.323208109877778 30 109.8 110.513494502152 -0.713494502152117 31 104.9 105.425718902514 -0.525718902514363 32 102.2 102.794407380558 -0.59440738055769 33 123.9 123.564292581309 0.335707418691071 34 124.9 125.166572296075 -0.266572296074500 35 112.7 112.362289710075 0.337710289924902 36 121.9 121.646319948068 0.253680051931641 37 100.6 100.930840466022 -0.330840466021845 38 104.3 104.418813625571 -0.118813625570833 39 120.4 120.479514075329 -0.0795140753288577 40 107.5 107.735464985040 -0.235464985039839 41 102.9 102.872558171840 0.0274418281604338 42 125.6 125.715578536975 -0.115578536975179 43 107.5 108.391640876849 -0.891640876849039 44 108.8 109.577046253289 -0.777046253289476 45 128.4 128.209138050031 0.190861949969342 46 121.1 121.569775519642 -0.469775519641559 47 119.5 119.53065383807 -0.0306538380700469 48 128.7 128.839581056756 -0.139581056756431 49 108.7 109.110468220753 -0.410468220752892 50 105.5 105.669015988695 -0.169015988694799 51 119.8 119.755697283152 0.0443027168478744 52 111.3 111.513830875397 -0.213830875397224 53 110.6 110.984832651544 -0.384832651543857 54 120.1 120.124388935764 -0.0243889357639288 55 97.5 97.832269846795 -0.332269846794936 56 107.7 108.137269502667 -0.437269502667028 57 127.3 126.519984690943 0.780015309057217 58 117.2 117.495225446645 -0.295225446645365 59 119.8 118.766818896486 1.03318110351429 60 116.2 115.374410306947 0.82558969305282 61 111 110.983757910452 0.016242089547506 62 112.4 111.970002759860 0.429997240140147 63 130.6 130.39090489677 0.209095103229893 64 109.1 108.817795281279 0.28220471872121 65 118.8 118.477455026445 0.322544973555076 66 123.9 123.449802263620 0.45019773637979 67 101.6 101.903719011670 -0.303719011669791 68 112.8 113.014221875572 -0.21422187557207 69 128 127.364109028396 0.635890971604458 70 129.6 129.478539430081 0.121460569919273 71 125.8 125.328505297502 0.471494702497667 72 119.5 119.020155198924 0.479844801075742 73 115.7 115.403708559638 0.296291440361599 74 113.6 113.384868275848 0.21513172415214 75 129.7 129.648875433048 0.0511245669515757 76 112 111.949837042895 0.0501629571054628 77 116.8 116.783004800787 0.0169951992132756 78 126.3 126.421384415465 -0.121384415464915 79 112.9 113.037364922747 -0.137364922746547 80 115.9 116.147211937183 -0.247211937182799

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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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