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multiple lineair regression (btw-ind.prod)

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

Title produced by software: Multiple Regression

Date of computation: Mon, 17 Dec 2007 01:57:06 -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/17/t1197881061vphg14fyt7uarf5.htm/, Retrieved Mon, 17 Dec 2007 09:44:32 +0100

User-defined keywords:

Dataseries X:

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98.8 106.0 100.5 100.9 110.4 114.3 96.4 101.2 101.9 109.2 106.2 111.6 81.0 91.7 94.7 93.7 101.0 105.7 109.4 109.5 102.3 105.3 90.7 102.8 96.2 100.6 96.1 97.6 106.0 110.3 103.1 107.2 102.0 107.2 104.7 108.1 86.0 97.1 92.1 92.2 106.9 112.2 112.6 111.6 101.7 115.7 92.0 111.3 97.4 104.2 97.0 103.2 105.4 112.7 102.7 106.4 98.1 102.6 104.5 110.6 87.4 95.2 89.9 89.0 109.8 112.5 111.7 116.8 98.6 107.2 96.9 113.6 95.1 101.8 97.0 102.6 112.7 122.7 102.9 110.3 97.4 110.5 111.4 121.6 87.4 100.3 96.8 100.7 114.1 123.4 110.3 127.1 103.9 124.1 101.6 131.2 94.6 111.6 95.9 114.2 104.7 130.1 102.8 125.9 98.1 119.0 113.9 133.8 80.9 107.5 95.7 113.5 113.2 134.4 105.9 126.8 108.8 135.6 102.3 139.9 99.0 129.8 100.7 131.0 115.5 153.1 100.7 134.1 109.9 144.1 114.6 155.9 85.4 123.3 100.5 128.1 114.8 144.3 116.5 153.0 112.9 149.9 102.0 150.9 106.0 141.0 105.3 138.9 118.8 157.4 106.1 142.9 109.3 151.7 117.2 161.0 91.9 138.6 103.9 136.0 115.9 151.9

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 BTW[t] = -31.8463850565652 + 1.39895751478604ind.prod[t] -9.76684852967163M1[t] -12.2717930785072M2[t] -12.9140502156034M3[t] -12.0171272716871M4[t] -10.5711495990552M5[t] -13.8771596829217M6[t] -1.15716967740919M7[t] -16.4205288703031M8[t] -18.5653579448258M9[t] -18.7134939399829M10[t] -11.4563560380362M11[t] + 0.482891608857794t + 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) -31.8463850565652 17.783683 -1.7908 0.077848 0.038924 ind.prod 1.39895751478604 0.190539 7.3421 0 0 M1 -9.76684852967163 3.004249 -3.251 0.001801 0.000901 M2 -12.2717930785072 3.015085 -4.0701 0.000126 6.3e-05 M3 -12.9140502156034 3.920473 -3.294 0.00158 0.00079 M4 -12.0171272716871 3.127886 -3.8419 0.000274 0.000137 M5 -10.5711495990552 3.136741 -3.3701 0.00125 0.000625 M6 -13.8771596829217 3.857704 -3.5973 0.00061 0.000305 M7 -1.15716967740919 3.765508 -0.3073 0.759562 0.379781 M8 -16.4205288703031 3.008904 -5.4573 1e-06 0 M9 -18.5653579448258 3.869337 -4.7981 9e-06 5e-06 M10 -18.7134939399829 4.06099 -4.6081 1.9e-05 9e-06 M11 -11.4563560380362 3.398561 -3.3709 0.001247 0.000623 t 0.482891608857794 0.034687 13.9212 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.96305775769146 R-squared 0.927480244649703 Adjusted R-squared 0.913409247342929 F-TEST (value) 65.914321808817 F-TEST (DF numerator) 13 F-TEST (DF denominator) 67 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.37970400989492 Sum Squared Residuals 1939.06142068332 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106 97.0866604834821 8.91333951651786 2 100.9 97.4428353186403 3.45716468135969 3 114.3 111.133149186784 3.16685081321634 4 101.2 92.9275585325533 8.27244146744675 5 109.2 102.550694145366 6.6493058546338 6 111.6 105.743092983937 5.85690701606255 7 91.7 83.6922452256995 8.0077547743005 8 93.7 88.0774955942322 5.6225044057678 9 105.7 95.2289904717193 10.4710095282807 10 109.5 107.314989209623 2.18501079037723 11 105.3 105.122420365446 0.177579634553670 12 102.8 100.833760840822 1.96623915917771 13 100.6 99.2440702513316 1.35592974866835 14 97.6 97.0821215598753 0.517878440124718 15 110.3 110.772435428019 -0.472435428018609 16 107.2 108.095273187913 -0.895273187913257 17 107.2 108.485289203138 -1.28528920313832 18 108.1 109.439356018052 -1.33935601805191 19 97.1 96.4817321059232 0.618267894076764 20 92.2 90.234905362082 1.96509463791802 21 112.2 109.277539115250 2.92246088474956 22 111.6 117.586352563232 -5.98635256323163 23 115.7 110.077745162868 5.62225483713175 24 111.3 108.447104916338 2.85289508366236 25 104.2 106.717518575368 -2.51751857536843 26 103.2 104.135882629476 -0.935882629476248 27 112.7 115.727760225441 -3.02776022544052 28 106.4 113.330389488292 -6.93038948829238 29 102.6 108.824054201766 -6.22405420176629 30 110.6 114.954263821388 -4.35426382138823 31 95.2 104.234971932917 -9.03497193291722 32 89 92.9518981358462 -3.95189813584624 33 112.5 119.129215214423 -6.62921521442349 34 116.8 122.121990106218 -5.32199010621772 35 107.2 111.535676173325 -4.33567617332504 36 113.6 121.096696045083 -7.49669604508278 37 101.8 109.294615597654 -7.49461559765405 38 102.6 109.930581935770 -7.33058193576979 39 122.7 131.734849389672 -9.03484938967215 40 110.3 119.404880297543 -9.10488029754313 41 110.5 113.639483247710 -3.1394832477096 42 121.6 130.401769979705 -8.80176997970545 43 100.3 110.029671239211 -9.72967123921076 44 100.7 108.399404294163 -7.69940429416345 45 123.4 130.939431834297 -7.53943183429698 46 127.1 125.958148891811 1.14185110818920 47 124.1 124.744850307985 -0.644850307984609 48 131.2 133.466495670871 -2.26649567087069 49 111.6 114.389836146555 -2.78983614655456 50 114.2 114.186427975799 0.0135720242013283 51 130.1 126.337888577677 3.76211142232265 52 125.9 125.059683852358 0.840316147641959 53 119 120.413452814353 -1.41345281435334 54 133.8 139.693863072964 -5.89386307296407 55 107.5 106.731146699395 0.768853300604977 56 113.5 112.655250334192 0.844749665807667 57 134.4 135.475069377283 -1.07506937728309 58 126.8 125.597435133046 1.20256486695425 59 135.6 137.394441436730 -1.79444143672973 60 139.9 140.240465237514 -0.340465237514446 61 129.8 126.339948517907 3.46005148209333 62 131 126.696123353065 4.3038766469348 63 153.1 147.241329043660 5.85867095633987 64 134.1 127.916572377601 6.1834276223991 65 144.1 142.715850795122 1.38414920487782 66 155.9 146.467832639608 9.43216736039218 67 123.3 118.821154822226 4.47884517777426 68 128.1 125.164945711459 2.93505428854113 69 144.3 143.508100707234 0.791899292765735 70 153 146.221084096071 6.77891590392868 71 149.9 148.924866553646 0.975133446353958 72 150.9 145.615477289372 5.28452271062783 73 141 141.927350427702 -0.9273504277025 74 138.9 138.926027227375 -0.0260272273745058 75 157.4 157.652588148748 -0.252588148747583 76 142.9 141.265642263739 1.63435773626097 77 151.7 147.671175592544 4.02882440745592 78 161 155.899821484345 5.10017851565493 79 138.6 133.709077974629 4.89092202537147 80 136 135.716100568025 0.283899431975055 81 151.9 150.841653279792 1.05834672020754

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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