Multiple regression (met dummies en trend) - goudprijs (EUR/kg)

*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: Mon, 24 Nov 2008 23:52:48 -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/Nov/25/t1227596025hxy4dyq0nswztyp.htm/, Retrieved Tue, 25 Nov 2008 06:53:46 +0000

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/Nov/25/t1227596025hxy4dyq0nswztyp.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}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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10413.00 0.00 10709.00 0.00 10662.00 0.00 10570.00 0.00 10297.00 0.00 10635.00 0.00 10872.00 0.00 10296.00 0.00 10383.00 0.00 10431.00 0.00 10574.00 0.00 10653.00 0.00 10805.00 0.00 10872.00 0.00 10625.00 0.00 10407.00 0.00 10463.00 0.00 10556.00 0.00 10646.00 0.00 10702.00 0.00 11353.00 0.00 11346.00 0.00 11451.00 0.00 11964.00 0.00 12574.00 0.00 13031.00 0.00 13812.00 0.00 14544.00 0.00 14931.00 0.00 14886.00 0.00 16005.00 1.00 17064.00 1.00 15168.00 1.00 16050.00 1.00 15839.00 1.00 15137.00 1.00 14954.00 0.00 15648.00 1.00 15305.00 1.00 15579.00 1.00 16348.00 1.00 15928.00 1.00 16171.00 1.00 15937.00 1.00 15713.00 1.00 15594.00 1.00 15683.00 1.00 16438.00 1.00 17032.00 1.00 17696.00 1.00 17745.00 1.00 19394.00 1.00 20148.00 1.00 20108.00 1.00 18584.00 1.00 18441.00 1.00 18391.00 1.00 19178.00 1.00 18079.00 1.00 18483.00 1.00

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 8706.52879120879 + 1685.19560439560x[t] + 766.647472527471M1[t] + 731.392967032967M2[t] + 636.177582417582M3[t] + 971.362197802197M4[t] + 1176.14681318681M5[t] + 1027.53142857143M6[t] + 589.676923076923M7[t] + 488.261538461538M8[t] + 68.0461538461537M9[t] + 252.430769230769M10[t] -75.9846153846156M11[t] + 133.815384615385t + 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) 8706.52879120879 513.160585 16.9665 0 0 x 1685.19560439560 485.25236 3.4728 0.001133 0.000566 M1 766.647472527471 606.237367 1.2646 0.212385 0.106192 M2 731.392967032967 602.272851 1.2144 0.230797 0.115399 M3 636.177582417582 601.163179 1.0582 0.29547 0.147735 M4 971.362197802197 600.369301 1.6179 0.112513 0.056256 M5 1176.14681318681 599.892469 1.9606 0.055998 0.027999 M6 1027.53142857143 599.733441 1.7133 0.093388 0.046694 M7 589.676923076923 601.580112 0.9802 0.332108 0.166054 M8 488.261538461538 600.151367 0.8136 0.420086 0.210043 M9 68.0461538461537 599.037766 0.1136 0.910055 0.455028 M10 252.430769230769 598.241067 0.422 0.675023 0.337512 M11 -75.9846153846156 597.762537 -0.1271 0.899403 0.449702 t 133.815384615385 13.812103 9.6883 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.96462604449019 R-squared 0.93050340570879 Adjusted R-squared 0.910863063843882 F-TEST (value) 47.3771491407375 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 944.8932174152 Sum Squared Residuals 41069866.8465934 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10413 9606.99164835165 806.008351648347 2 10709 9705.55252747253 1003.44747252747 3 10662 9744.15252747253 917.847472527473 4 10570 10213.1525274725 356.847472527473 5 10297 10551.7525274725 -254.752527472527 6 10635 10536.9525274725 98.0474725274727 7 10872 10232.9134065934 639.086593406593 8 10296 10265.3134065934 30.6865934065935 9 10383 9978.9134065934 404.086593406593 10 10431 10297.1134065934 133.886593406593 11 10574 10102.5134065934 471.486593406593 12 10653 10312.3134065934 340.686593406593 13 10805 11212.7762637363 -407.776263736262 14 10872 11311.3371428571 -439.337142857142 15 10625 11349.9371428571 -724.937142857143 16 10407 11818.9371428571 -1411.93714285714 17 10463 12157.5371428571 -1694.53714285714 18 10556 12142.7371428571 -1586.73714285714 19 10646 11838.6980219780 -1192.69802197802 20 10702 11871.0980219780 -1169.09802197802 21 11353 11584.6980219780 -231.698021978022 22 11346 11902.8980219780 -556.898021978022 23 11451 11708.2980219780 -257.298021978022 24 11964 11918.0980219780 45.9019780219782 25 12574 12818.5608791209 -244.560879120878 26 13031 12917.1217582418 113.878241758241 27 13812 12955.7217582418 856.278241758242 28 14544 13424.7217582418 1119.27824175824 29 14931 13763.3217582418 1167.67824175824 30 14886 13748.5217582418 1137.47824175824 31 16005 15129.6782417582 875.321758241759 32 17064 15162.0782417582 1901.92175824176 33 15168 14875.6782417582 292.321758241759 34 16050 15193.8782417582 856.121758241758 35 15839 14999.2782417582 839.721758241758 36 15137 15209.0782417582 -72.0782417582415 37 14954 14424.3454945055 529.654505494506 38 15648 16208.1019780220 -560.101978021978 39 15305 16246.7019780220 -941.701978021979 40 15579 16715.7019780220 -1136.70197802198 41 16348 17054.3019780220 -706.301978021978 42 15928 17039.5019780220 -1111.50197802198 43 16171 16735.4628571429 -564.462857142857 44 15937 16767.8628571429 -830.862857142857 45 15713 16481.4628571429 -768.462857142857 46 15594 16799.6628571429 -1205.66285714286 47 15683 16605.0628571429 -922.062857142857 48 16438 16814.8628571429 -376.862857142857 49 17032 17715.3257142857 -683.325714285712 50 17696 17813.8865934066 -117.886593406593 51 17745 17852.4865934066 -107.486593406593 52 19394 18321.4865934066 1072.51340659341 53 20148 18660.0865934066 1487.91340659341 54 20108 18645.2865934066 1462.71340659341 55 18584 18341.2474725275 242.752527472527 56 18441 18373.6474725275 67.3525274725269 57 18391 18087.2474725275 303.752527472527 58 19178 18405.4474725275 772.552527472527 59 18079 18210.8474725275 -131.847472527473 60 18483 18420.6474725275 62.3525274725268

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')

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Software written by Ed van Stee & Patrick Wessa

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