Paper - Multiple Regression - Olie met Monthly dummies

*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: Sun, 21 Dec 2008 08:49:26 -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/21/t1229874611aiy54z5iojsmht5.htm/, Retrieved Sun, 21 Dec 2008 16:50:20 +0100

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/21/t1229874611aiy54z5iojsmht5.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

20.7246301 0 21.44580352 0 22.09413114 0 21.53321848 0 23.3470789 0 23.5656163 0 26.42117166 0 25.21193138 0 26.43574082 0 29.33500366 0 29.40056488 0 33.05013946 0 28.38072368 0 26.0059506 0 29.31314992 0 30.36212944 0 35.74543406 0 36.15337054 0 34.20838768 0 37.90895432 0 38.70297354 0 42.11944156 0 42.16314904 0 39.79566054 0 37.36261082 0 38.3533137 0 42.60022384 0 41.24529196 0 42.15586446 0 46.94183352 0 47.42990038 0 47.0583868 0 50.18347162 0 50.12519498 0 43.22669772 0 40.04333626 0 40.37114236 0 42.2141411 0 36.99838182 0 39.74466848 0 42.68035422 0 46.2935059 0 46.97097184 0 48.72655562 0 52.36884562 1 50.05234918 1 54.03701444 1 57.78128856 1 64.71620872 1 63.4122689 1 64.3592643 1 66.02743312 1 72.13919574 1 76.60464328 1 86.97060062 1 93.48301514 1 95.58825876 1 81.88596378 1 70.5511573 1 50.38015528 1 36.24807008 0

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Olie[t] = + 31.1648469240712 + 32.613172739822Dumivariabele[t] + 1.36685524595845M1[t] + 0.598814091964379M2[t] + 1.38554873196439M3[t] + 2.09506682396439M4[t] + 5.5261040039644M5[t] + 8.22431243596438M6[t] + 10.7127249639644M7[t] + 12.7902871799644M8[t] + 8.445742052M9[t] + 6.493474612M10[t] + 3.665600656M11[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) 31.1648469240712 5.011889 6.2182 0 0 Dumivariabele 32.613172739822 3.230677 10.0948 0 0 M1 1.36685524595845 6.599865 0.2071 0.836805 0.418403 M2 0.598814091964379 6.878636 0.0871 0.930991 0.465495 M3 1.38554873196439 6.878636 0.2014 0.841215 0.420608 M4 2.09506682396439 6.878636 0.3046 0.762006 0.381003 M5 5.5261040039644 6.878636 0.8034 0.42572 0.21286 M6 8.22431243596438 6.878636 1.1956 0.237714 0.118857 M7 10.7127249639644 6.878636 1.5574 0.125947 0.062974 M8 12.7902871799644 6.878636 1.8594 0.069103 0.034551 M9 8.445742052 6.848222 1.2333 0.223479 0.111739 M10 6.493474612 6.848222 0.9482 0.347778 0.173889 M11 3.665600656 6.848222 0.5353 0.594939 0.29747 Multiple Linear Regression - Regression Statistics Multiple R 0.840168167064713 R-squared 0.70588254894888 Adjusted R-squared 0.6323531861861 F-TEST (value) 9.60000906340224 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 3.97935884244305e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.8279891449774 Sum Squared Residuals 5627.77674833991 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 20.7246301 32.5317021700297 -11.8070720700297 2 21.44580352 31.7636610160356 -10.3178574960356 3 22.09413114 32.5503956560356 -10.4562645160356 4 21.53321848 33.2599137480356 -11.7266952680356 5 23.3470789 36.6909509280356 -13.3438720280356 6 23.5656163 39.3891593600356 -15.8235430600356 7 26.42117166 41.8775718880356 -15.4564002280356 8 25.21193138 43.9551341040356 -18.7432027240356 9 26.43574082 39.6105889760712 -13.1748481560712 10 29.33500366 37.6583215360712 -8.3233178760712 11 29.40056488 34.8304475800712 -5.42988270007121 12 33.05013946 31.1648469240712 1.88529253592878 13 28.38072368 32.5317021700297 -4.15097849002968 14 26.0059506 31.7636610160356 -5.7577104160356 15 29.31314992 32.5503956560356 -3.23724573603561 16 30.36212944 33.2599137480356 -2.89778430803561 17 35.74543406 36.6909509280356 -0.945516868035609 18 36.15337054 39.3891593600356 -3.23578882003561 19 34.20838768 41.8775718880356 -7.6691842080356 20 37.90895432 43.9551341040356 -6.04617978403562 21 38.70297354 39.6105889760712 -0.90761543607121 22 42.11944156 37.6583215360712 4.46112002392878 23 42.16314904 34.8304475800712 7.33270145992879 24 39.79566054 31.1648469240712 8.6308136159288 25 37.36261082 32.5317021700297 4.83090864997033 26 38.3533137 31.7636610160356 6.58965268396441 27 42.60022384 32.5503956560356 10.0498281839644 28 41.24529196 33.2599137480356 7.9853782119644 29 42.15586446 36.6909509280356 5.46491353196439 30 46.94183352 39.3891593600356 7.55267415996439 31 47.42990038 41.8775718880356 5.5523284919644 32 47.0583868 43.9551341040356 3.10325269596438 33 50.18347162 39.6105889760712 10.5728826439288 34 50.12519498 37.6583215360712 12.4668734439288 35 43.22669772 34.8304475800712 8.39625013992879 36 40.04333626 31.1648469240712 8.87848933592879 37 40.37114236 32.5317021700297 7.83944018997032 38 42.2141411 31.7636610160356 10.4504800839644 39 36.99838182 32.5503956560356 4.44798616396439 40 39.74466848 33.2599137480356 6.4847547319644 41 42.68035422 36.6909509280356 5.98940329196439 42 46.2935059 39.3891593600356 6.90434653996439 43 46.97097184 41.8775718880356 5.0933999519644 44 48.72655562 43.9551341040356 4.77142151596438 45 52.36884562 72.2237617158932 -19.8549160958932 46 50.05234918 70.2714942758932 -20.2191450958932 47 54.03701444 67.4436203198932 -13.4066058798932 48 57.78128856 63.7780196638932 -5.99673110389317 49 64.71620872 65.1448749098516 -0.428666189851638 50 63.4122689 64.3768337558575 -0.964564855857551 51 64.3592643 65.1635683958576 -0.804304095857568 52 66.02743312 65.8730864878576 0.15434663214243 53 72.13919574 69.3041236678576 2.83507207214243 54 76.60464328 72.0023320998576 4.60231118014243 55 86.97060062 74.4907446278576 12.4798559921424 56 93.48301514 76.5683068438576 16.9147082961424 57 95.58825876 72.2237617158932 23.3644970441068 58 81.88596378 70.2714942758932 11.6144695041068 59 70.5511573 67.4436203198932 3.10753698010682 60 50.38015528 63.7780196638932 -13.3978643838932 61 36.24807008 32.5317021700297 3.71636790997032

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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