Q3

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 05:43:33 -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/27/t1227789889e6shtt5htf90aq0.htm/, Retrieved Thu, 27 Nov 2008 12:44:49 +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/27/t1227789889e6shtt5htf90aq0.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?

No (this computation is public)

User-defined keywords:

Dataseries X:

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107,1 0 110,7 0 117,1 0 118,7 0 126,5 0 127,5 0 134,6 0 131,8 0 135,9 0 142,7 0 141,7 0 153,4 0 145,0 0 137,7 0 148,3 0 152,2 0 169,4 0 168,6 0 161,1 0 174,1 0 179,0 0 190,6 0 190,0 0 181,6 0 174,8 0 180,5 1 196,8 1 193,8 1 197,0 1 216,3 1 221,4 1 217,9 1 229,7 1 227,4 1 204,2 1 196,6 1 198,8 1 207,5 1 190,7 1 201,6 1 210,5 1 223,5 1 223,8 1 231,2 1 244,0 1 234,7 1 250,2 1 265,7 1 287,6 1 283,3 1 295,4 1 312,3 1 333,8 1 347,7 1 383,2 1 407,1 1 413,6 1 362,7 1 321,9 1 239,4 1

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation PIC_grondstoffen[t] = + 56.69 -38.4000000000001Dummy[t] + 20.7119444444444M1[t] + 24.8472222222222M2[t] + 25.7425M3[t] + 26.9777777777778M4[t] + 33.8730555555556M5[t] + 38.3283333333333M6[t] + 41.6036111111111M7[t] + 44.3788888888889M8[t] + 47.5741666666667M9[t] + 33.9294444444444M10[t] + 19.0847222222222M11[t] + 4.82472222222222t + 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) 56.69 16.95364 3.3438 0.00165 0.000825 Dummy -38.4000000000001 16.313647 -2.3539 0.022907 0.011454 M1 20.7119444444444 19.784852 1.0469 0.300634 0.150317 M2 24.8472222222222 20.134857 1.234 0.223456 0.111728 M3 25.7425 20.029944 1.2852 0.205156 0.102578 M4 26.9777777777778 19.935606 1.3532 0.18259 0.091295 M5 33.8730555555556 19.851995 1.7063 0.0947 0.04735 M6 38.3283333333333 19.779246 1.9378 0.0588 0.0294 M7 41.6036111111111 19.71748 2.11 0.040329 0.020165 M8 44.3788888888889 19.666799 2.2565 0.028832 0.014416 M9 47.5741666666667 19.627291 2.4239 0.019346 0.009673 M10 33.9294444444444 19.599022 1.7312 0.090123 0.045061 M11 19.0847222222222 19.58204 0.9746 0.334855 0.167427 t 4.82472222222222 0.470934 10.245 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.930648906349803 R-squared 0.866107386890084 Adjusted R-squared 0.828268170141629 F-TEST (value) 22.8891467983532 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 8.88178419700125e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 30.9529694672511 Sum Squared Residuals 44071.9706666667 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 107.1 82.2266666666668 24.8733333333332 2 110.7 91.1866666666667 19.5133333333333 3 117.1 96.9066666666666 20.1933333333334 4 118.7 102.966666666667 15.7333333333334 5 126.5 114.686666666667 11.8133333333333 6 127.5 123.966666666667 3.53333333333336 7 134.6 132.066666666667 2.53333333333335 8 131.8 139.666666666667 -7.86666666666665 9 135.9 147.686666666667 -11.7866666666667 10 142.7 138.866666666667 3.83333333333335 11 141.7 128.846666666667 12.8533333333333 12 153.4 114.586666666667 38.8133333333333 13 145 140.123333333333 4.87666666666671 14 137.7 149.083333333333 -11.3833333333333 15 148.3 154.803333333333 -6.50333333333333 16 152.2 160.863333333333 -8.66333333333337 17 169.4 172.583333333333 -3.18333333333333 18 168.6 181.863333333333 -13.2633333333333 19 161.1 189.963333333333 -28.8633333333333 20 174.1 197.563333333333 -23.4633333333334 21 179 205.583333333333 -26.5833333333334 22 190.6 196.763333333333 -6.16333333333334 23 190 186.743333333333 3.25666666666667 24 181.6 172.483333333333 9.11666666666666 25 174.8 198.02 -23.2200000000000 26 180.5 168.58 11.92 27 196.8 174.3 22.5 28 193.8 180.36 13.4400000000000 29 197 192.08 4.92 30 216.3 201.36 14.94 31 221.4 209.46 11.94 32 217.9 217.06 0.840000000000009 33 229.7 225.08 4.61999999999999 34 227.4 216.26 11.1400000000000 35 204.2 206.24 -2.03999999999997 36 196.6 191.98 4.62000000000001 37 198.8 217.516666666667 -18.7166666666666 38 207.5 226.476666666667 -18.9766666666667 39 190.7 232.196666666667 -41.4966666666667 40 201.6 238.256666666667 -36.6566666666667 41 210.5 249.976666666667 -39.4766666666667 42 223.5 259.256666666667 -35.7566666666667 43 223.8 267.356666666667 -43.5566666666667 44 231.2 274.956666666667 -43.7566666666667 45 244 282.976666666667 -38.9766666666667 46 234.7 274.156666666667 -39.4566666666667 47 250.2 264.136666666667 -13.9366666666667 48 265.7 249.876666666667 15.8233333333333 49 287.6 275.413333333333 12.1866666666667 50 283.3 284.373333333333 -1.07333333333333 51 295.4 290.093333333333 5.30666666666663 52 312.3 296.153333333333 16.1466666666667 53 333.8 307.873333333333 25.9266666666667 54 347.7 317.153333333333 30.5466666666666 55 383.2 325.253333333333 57.9466666666666 56 407.1 332.853333333333 74.2466666666667 57 413.6 340.873333333333 72.7266666666667 58 362.7 332.053333333333 30.6466666666666 59 321.9 322.033333333333 -0.133333333333337 60 239.4 307.773333333333 -68.3733333333333

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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