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Lineaire regressie Nigeria

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

Title produced by software: Multiple Regression

Date of computation: Tue, 18 Dec 2007 03:54:50 -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/18/t11979748340yvc6mbtxo7a5cw.htm/, Retrieved Tue, 18 Dec 2007 11:47:25 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

25.62 0 27.5 0 24.5 0 25.66 0 28.31 0 27.85 1 24.61 0 25.68 0 25.62 1 20.54 1 18.8 0 18.71 0 19.46 0 20.12 0 23.54 0 25.6 0 25.39 0 24.09 0 25.69 0 26.56 0 28.33 0 27.5 0 24.23 0 28.23 0 31.29 0 32.72 0 30.46 0 24.89 0 25.68 0 27.52 0 28.4 0 29.71 0 26.85 0 29.62 0 28.69 0 29.76 0 31.3 0 30.86 0 33.46 1 33.15 1 37.99 1 35.24 1 38.24 1 43.16 1 43.33 0 49.67 0 43.17 0 39.56 1 44.36 1 45.22 1 53.1 1 52.1 1 48.52 1 54.84 1 57.57 1 64.14 1 62.85 1 58.75 1 55.33 1 57.03 1 63.18 1 60.19 1 62.12 1 70.12 1 69.75 1 68.56 1 73.77 1 73.23 1 61.96 1 57.81 1 58.76 1 62.47 1 53.68 1 57.56 1 62.05 1 67.49 1 67.21 1 71.05 1 76.93 1 70.76 1

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 Brent[t] = + 11.0348138217140 + 5.49236972579178Aanslagen[t] + 2.54901862907124M1[t] + 2.69586780410164M2[t] + 3.45523558973322M3[t] + 4.24494190762077M4[t] + 4.18607679693687M5[t] + 3.69401601113987M6[t] + 6.16548943271195M7[t] + 6.70519575059948M8[t] + 4.01897628443263M9[t] + 2.56987307851065M10[t] + 0.392831493553957M11[t] + 0.607436539255319t + 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) 11.0348138217140 2.952076 3.738 0.00039 0.000195 Aanslagen 5.49236972579178 2.212294 2.4827 0.015591 0.007796 M1 2.54901862907124 3.571501 0.7137 0.477922 0.238961 M2 2.69586780410164 3.570263 0.7551 0.452881 0.226441 M3 3.45523558973322 3.579046 0.9654 0.337865 0.168933 M4 4.24494190762077 3.575925 1.1871 0.239448 0.119724 M5 4.18607679693687 3.573424 1.1714 0.245631 0.122815 M6 3.69401601113987 3.599403 1.0263 0.308504 0.154252 M7 6.16548943271195 3.570289 1.7269 0.088866 0.044433 M8 6.70519575059948 3.569657 1.8784 0.064746 0.032373 M9 4.01897628443263 3.705443 1.0846 0.282039 0.141019 M10 2.56987307851065 3.703941 0.6938 0.490229 0.245115 M11 0.392831493553957 3.717838 0.1057 0.916172 0.458086 t 0.607436539255319 0.047189 12.8725 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.942101045896997 R-squared 0.887554380680216 Adjusted R-squared 0.865406001117228 F-TEST (value) 40.0731068454060 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.41333060691364 Sum Squared Residuals 2714.63342525597 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25.62 14.1912689900407 11.4287310099593 2 27.5 14.9455547043264 12.5544452956736 3 24.5 16.3123590292132 8.18764097078677 4 25.66 17.7095018863561 7.95049811364394 5 28.31 18.2580733149275 10.0519266850725 6 27.85 23.8658187941776 3.98418120582239 7 24.61 21.4523590292132 3.15764097078678 8 25.68 22.5995018863561 3.08049811364392 9 25.62 26.0130886852363 -0.393088685236307 10 20.54 25.1714220185696 -4.63142201856963 11 18.8 18.1094472470765 0.690552752923494 12 18.71 18.3240522927779 0.385947707222133 13 19.46 21.4805074611044 -2.02050746110443 14 20.12 22.2347931753901 -2.11479317539011 15 23.54 23.6015975002770 -0.0615975002770488 16 25.6 24.9987403574199 0.601259642580092 17 25.39 25.5473117859913 -0.157311785991335 18 24.09 25.6626875394497 -1.57268753944966 19 25.69 28.7415975002770 -3.05159750027704 20 26.56 29.8887403574199 -3.32874035741991 21 28.33 27.8099574305084 0.520042569491622 22 27.5 26.9682907638417 0.53170923615829 23 24.23 25.3986857181403 -1.16868571814034 24 28.23 25.6132907638417 2.6167092361583 25 31.29 28.7697459321683 2.52025406783174 26 32.72 29.524031646454 3.19596835354601 27 30.46 30.8908359713409 -0.430835971340876 28 24.89 32.2879788284837 -7.39797882848374 29 25.68 32.8365502570552 -7.15655025705516 30 27.52 32.9519260105135 -5.43192601051348 31 28.4 36.0308359713409 -7.63083597134088 32 29.71 37.1779788284837 -7.46797882848373 33 26.85 35.0991959015722 -8.2491959015722 34 29.62 34.2575292349055 -4.63752923490554 35 28.69 32.6879241892042 -3.99792418920416 36 29.76 32.9025292349055 -3.14252923490553 37 31.3 36.0589844032321 -4.75898440323209 38 30.86 36.8132701175178 -5.95327011751782 39 33.46 43.6724441681965 -10.2124441681965 40 33.15 45.0695870253393 -11.9195870253393 41 37.99 45.6181584539108 -7.62815845391076 42 35.24 45.7335342073691 -10.4935342073691 43 38.24 48.8124441681965 -10.5724441681965 44 43.16 49.9595870253393 -6.79958702533933 45 43.33 42.388434372636 0.941565627363964 46 49.67 41.5467677059694 8.12323229403063 47 43.17 39.977162660268 3.19283733973200 48 39.56 45.6841374317611 -6.12413743176112 49 44.36 48.8405926000877 -4.48059260008768 50 45.22 49.5948783143734 -4.37487831437341 51 53.1 50.9616826392603 2.13831736073971 52 52.1 52.3588254964032 -0.258825496403159 53 48.52 52.9073969249746 -4.38739692497458 54 54.84 53.0227726784329 1.8172273215671 55 57.57 56.1016826392603 1.4683173607397 56 64.14 57.2488254964032 6.89117450359684 57 62.85 55.1700425694916 7.67995743050838 58 58.75 54.328375902825 4.42162409717504 59 55.33 52.7587708571236 2.57122914287641 60 57.03 52.9733759028249 4.05662409717505 61 63.18 56.1298310711515 7.05016892884849 62 60.19 56.8841167854372 3.30588321456276 63 62.12 58.2509211103241 3.86907888967587 64 70.12 59.648063967467 10.4719360325330 65 69.75 60.1966353960384 9.55336460396159 66 68.56 60.3120111494967 8.24798885050328 67 73.77 63.3909211103241 10.3790788896759 68 73.23 64.538063967467 8.69193603253302 69 61.96 62.4592810405555 -0.499281040555453 70 57.81 61.6176143738888 -3.80761437388879 71 58.76 60.0480093281874 -1.28800932818742 72 62.47 60.2626143738888 2.20738562611122 73 53.68 63.4190695422153 -9.73906954221534 74 57.56 64.1733552565011 -6.61335525650106 75 62.05 65.540159581388 -3.49015958138796 76 67.49 66.9373024385308 0.55269756146918 77 67.21 67.4858738671022 -0.275873867102245 78 71.05 67.6012496205606 3.44875037943943 79 76.93 70.680159581388 6.24984041861205 80 70.76 71.8273024385308 -1.06730243853081

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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