regressie 2

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

Title produced by software: Multiple Regression

Date of computation: Wed, 09 Jan 2008 05:10:56 -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/Jan/09/t11998808352epdxu4w3luocqn.htm/, Retrieved Wed, 09 Jan 2008 13:14:06 +0100

User-defined keywords:

Dataseries X:

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1.0137 89.97 0.9834 99.8 0.9643 112.99 0.947 93.69 0.906 108.02 0.9492 99.11 0.9397 94.33 0.9041 83.75 0.8721 106.37 0.8552 109.63 0.8564 105.5 0.8973 96.13 0.9383 102.48 0.9217 101.37 0.9095 112.76 0.892 95.57 0.8742 102.81 0.8532 104.13 0.8607 97.52 0.9005 85.29 0.9111 101.01 0.9059 108.48 0.8883 101.33 0.8924 87.57 0.8833 97.44 0.87 96.06 0.8758 106.67 0.8858 102.67 0.917 104.54 0.9554 102.46 0.9922 103.35 0.9778 83.27 0.9808 108.22 0.9811 115.23 1.0014 103.7 1.0183 93.61 1.0622 100.25 1.0773 100.56 1.0807 108.86 1.0848 105.43 1.1582 104.77 1.1663 109.13 1.1372 106.13 1.1139 82.27 1.1222 113.6 1.1692 117.73 1.1702 104.83 1.2286 104.61 1.2613 102.93 1.2646 106.95 1.2262 123.45 1.1985 111.99 1.2007 103.95 1.2138 122.05 1.2266 108.04 1.2176 93.72 1.2218 119.61 1.249 118.29 1.2991 117.14 1.3408 112.76 1.3119 105.97 1.3014 107.96 1.3201 122.27 1.2938 114.54 1.2694 110.15 1.2165 120.02 1.2037 103.94 1.2292 96.18 1.2256 121.01 1.2015 110.55 1.1786 120.04 1.1856 114.19

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation (1-B)uit[t] = + 0.387755793465986 -19.2592282494765`(1-B)wk`[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) 0.387755793465986 1.424774 0.2722 0.786317 0.393159 `(1-B)wk` -19.2592282494765 53.326139 -0.3612 0.719084 0.359542 Multiple Linear Regression - Regression Statistics Multiple R 0.0434374270323568 R-squared 0.00188681006719132 Adjusted R-squared -0.0125785984825597 F-TEST (value) 0.130436002599029 F-TEST (DF numerator) 1 F-TEST (DF denominator) 69 p-value 0.719083885131171 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.9559627531964 Sum Squared Residuals 9863.2081295516 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.83 0.971310409425126 8.85868959057487 2 13.19 0.755607053030991 12.434392946969 3 -19.3 0.72094044218193 -20.0209404421819 4 14.33 1.17738415169452 13.1526158483055 5 -8.91 -0.444242866911400 -8.4657571330886 6 -4.78 0.570718461836014 -5.35071846183602 7 -10.58 1.07338431914735 -11.6533843191473 8 22.62 1.00405109744923 21.6159489025508 9 3.25999999999999 0.71323675088214 2.54676324911785 10 -4.13000000000000 0.364644719566613 -4.49464471956661 11 -9.37 -0.399946641937602 -8.9700533580624 12 6.35000000000001 -0.401872564762551 6.75187256476256 13 -1.11 0.707458982407297 -1.81745898240730 14 11.39 0.622718378109598 10.7672816218904 15 -17.19 0.724792287831825 -17.9147922878318 16 7.24000000000001 0.73057005630667 6.50942994369334 17 1.31999999999999 0.792199586704993 0.527800413295 18 -6.61 0.243311581594911 -6.85331158159491 19 -12.23 -0.37876149086318 -11.8512385091368 20 15.72 0.183607974021532 15.5363920259785 21 7.47 0.487903780363264 6.98209621963673 22 -7.15 0.726718210656775 -7.87671821065678 23 -13.76 0.308792957643131 -14.0687929576431 24 9.87 0.563014770536222 9.30698522946378 25 -1.38000000000000 0.643903529184023 -2.02390352918402 26 10.61 0.276052269619020 10.3339477303810 27 -4 0.195163510971221 -4.19516351097122 28 1.87000000000000 -0.213132127917681 2.08313212791769 29 -2.08000000000001 -0.351798571313912 -1.7282014286861 30 0.89 -0.320983806114748 1.21098380611475 31 -20.08 0.66508868025845 -20.7450886802584 32 24.95 0.329978108717555 24.6200218912824 33 7.01 0.381978024991144 6.62802197500886 34 -11.53 -0.0032065399983896 -11.5267934600016 35 -10.09 0.0622748360498342 -10.1522748360498 36 6.64 -0.457724326686033 7.09772432668603 37 0.310000000000002 0.096941446898893 0.213058553101109 38 8.3 0.322274417417765 7.97772558258223 39 -3.42999999999999 0.308792957643133 -3.73879295764313 40 -0.660000000000011 -1.02587156004559 0.365871560045577 41 4.36 0.231756044645227 4.12824395535477 42 -3 0.94819933552575 -3.94819933552575 43 -23.86 0.836495811678791 -24.6964958116788 44 31.33 0.227904198995329 31.1020958010047 45 4.13000000000001 -0.517427934259409 4.64742793425942 46 -12.9 0.36849656521651 -13.2684965652165 47 -0.219999999999999 -0.736983136303442 0.516983136303443 48 -1.67999999999999 -0.242020970291899 -1.43797902970809 49 4.02 0.324200340242716 3.69579965975728 50 16.5 1.12731015824588 15.3726898417541 51 -11.46 0.921236415976486 -12.3812364159765 52 -8.04 0.345385491317133 -8.38538549131713 53 18.1 0.135459903397848 17.9645400966021 54 -14.01 0.141237671872688 -14.1512376718727 55 -14.32 0.561088847711272 -14.8810888477113 56 25.89 0.306867034818186 25.5831329651818 57 -1.31999999999999 -0.136095214919778 -1.18390478508022 58 -1.15000000000001 -0.577131541832783 -0.572868458167222 59 -4.3800 -0.415354024537187 -3.96464597546281 60 -6.79000000000001 0.944347489875855 -7.73434748987586 61 1.98999999999999 0.589977690085493 1.40002230991450 62 14.31 0.0276082252007708 14.2823917747992 63 -7.72999999999999 0.894273496427218 -8.6242734964272 64 -4.39 0.857680962753212 -5.24768096275321 65 9.87 1.40656896786330 8.4634310321367 66 -16.08 0.634273915059286 -16.7142739150593 67 -7.75999999999999 -0.103354526895667 -7.65664547310432 68 24.83 0.457089015164104 24.3729109848359 69 -10.46 0.85190319427837 -11.3119031942784 70 9.49 0.828792120378996 8.66120787962101 71 -5.85000000000001 0.252941195719653 -6.10294119571966 72 -0.0303 NA NA

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = First Differences ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = First Differences ;

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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