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

Title produced by software: Multiple Regression

Date of computation: Fri, 14 Dec 2007 06:01:09 -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/14/t1197636356q2sugv4dxxtpq30.htm/, Retrieved Fri, 14 Dec 2007 13:45:57 +0100

User-defined keywords:

Dataseries X:

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112.61 0 113.4 0 115.18 0 121.01 0 119.44 0 116.68 0 117.07 0 117.41 0 119.58 0 120.92 0 117.09 0 116.77 0 119.39 0 122.49 0 124.08 1 118.29 1 112.94 1 113.79 1 114.43 1 118.7 1 120.36 1 118.27 1 118.34 1 117.82 1 117.65 1 118.18 1 121.02 1 124.78 1 131.16 1 130.14 1 131.75 1 134.73 1 135.35 1 140.32 1 136.35 1 131.6 1 128.9 1 133.89 1 138.25 1 146.23 1 144.76 1 149.3 1 156.8 1 159.08 1 165.12 1 163.14 1 153.43 1 151.01 1 154.72 1 154.58 1 155.63 1 161.67 1 163.51 1 162.91 1 164.80 1 164.98 1 154.54 1 148.60 1 149.19 1 150.61 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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation indexcijfers[t] = + 102.582580419580 -14.8322027972028Irak[t] + 3.21714277389274M1[t] + 3.88099883449884M2[t] + 7.98129545454546M3[t] + 10.3551515151515M4[t] + 9.13100757575758M5[t] + 8.14286363636364M6[t] + 9.3587196969697M7[t] + 10.1785757575758M8[t] + 8.99843181818182M9[t] + 7.06828787878788M10[t] + 2.50814393939394M11[t] + 1.19014393939394t + 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) 102.582580419580 3.311385 30.9788 0 0 Irak -14.8322027972028 2.867743 -5.1721 5e-06 2e-06 M1 3.21714277389274 3.994352 0.8054 0.42472 0.21236 M2 3.88099883449884 3.988772 0.973 0.335652 0.167826 M3 7.98129545454546 4.010144 1.9903 0.052522 0.026261 M4 10.3551515151515 3.999639 2.589 0.012843 0.006422 M5 9.13100757575758 3.990346 2.2883 0.026765 0.013383 M6 8.14286363636364 3.982276 2.0448 0.046623 0.023312 M7 9.3587196969697 3.975434 2.3541 0.022892 0.011446 M8 10.1785757575758 3.969827 2.564 0.01368 0.00684 M9 8.99843181818182 3.965461 2.2692 0.027991 0.013995 M10 7.06828787878788 3.962339 1.7839 0.081043 0.040521 M11 2.50814393939394 3.960465 0.6333 0.529677 0.264839 t 1.19014393939394 0.070353 16.9167 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.949764132186859 R-squared 0.902051906788657 Adjusted R-squared 0.874370923924582 F-TEST (value) 32.5874233302372 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.26105705301434 Sum Squared Residuals 1803.23842937063 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.61 106.989867132867 5.62013286713272 2 113.4 108.843867132867 4.55613286713287 3 115.18 114.134307692308 1.04569230769232 4 121.01 117.698307692308 3.31169230769233 5 119.44 117.664307692308 1.77569230769233 6 116.68 117.866307692308 -1.18630769230769 7 117.07 120.272307692308 -3.2023076923077 8 117.41 122.282307692308 -4.87230769230769 9 119.58 122.292307692308 -2.71230769230769 10 120.92 121.552307692308 -0.632307692307678 11 117.09 118.182307692308 -1.09230769230769 12 116.77 116.864307692308 -0.0943076923076862 13 119.39 121.271594405594 -1.88159440559436 14 122.49 123.125594405594 -0.635594405594401 15 124.08 113.583832167832 10.4961678321678 16 118.29 117.147832167832 1.14216783216783 17 112.94 117.113832167832 -4.17383216783217 18 113.79 117.315832167832 -3.52583216783216 19 114.43 119.721832167832 -5.29183216783216 20 118.7 121.731832167832 -3.03183216783216 21 120.36 121.741832167832 -1.38183216783217 22 118.27 121.001832167832 -2.73183216783217 23 118.34 117.631832167832 0.708167832167837 24 117.82 116.313832167832 1.50616783216783 25 117.65 120.721118881119 -3.07111888111884 26 118.18 122.575118881119 -4.39511888111887 27 121.02 127.865559440559 -6.84555944055945 28 124.78 131.429559440559 -6.64955944055944 29 131.16 131.395559440559 -0.235559440559442 30 130.14 131.597559440559 -1.45755944055945 31 131.75 134.003559440559 -2.25355944055945 32 134.73 136.013559440559 -1.28355944055945 33 135.35 136.023559440559 -0.673559440559444 34 140.32 135.283559440559 5.03644055944056 35 136.35 131.913559440559 4.43644055944055 36 131.6 130.595559440559 1.00444055944055 37 128.9 135.002846153846 -6.10284615384612 38 133.89 136.856846153846 -2.96684615384617 39 138.25 142.147286713287 -3.89728671328672 40 146.23 145.711286713287 0.51871328671328 41 144.76 145.677286713287 -0.91728671328672 42 149.3 145.879286713287 3.42071328671330 43 156.8 148.285286713287 8.51471328671329 44 159.08 150.295286713287 8.7847132867133 45 165.12 150.305286713287 14.8147132867133 46 163.14 149.565286713287 13.5747132867133 47 153.43 146.195286713287 7.23471328671329 48 151.01 144.877286713287 6.13271328671328 49 154.72 149.284573426573 5.4354265734266 50 154.58 151.138573426573 3.44142657342658 51 155.63 156.429013986014 -0.799013986013992 52 161.67 159.993013986014 1.67698601398599 53 163.51 159.959013986014 3.550986013986 54 162.91 160.161013986014 2.74898601398601 55 164.8 162.567013986014 2.23298601398602 56 164.98 164.577013986014 0.402986013986004 57 154.54 164.587013986014 -10.047013986014 58 148.6 163.847013986014 -15.247013986014 59 149.19 160.477013986014 -11.287013986014 60 150.61 159.159013986014 -8.54901398601397

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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