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ws 6 vraag 3 09/2005

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

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 03:34:49 -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/Nov/19/t1195468110txfolgozcf2gz8l.htm/, Retrieved Mon, 19 Nov 2007 11:28:42 +0100

User-defined keywords:

groep 1 ws 6 vraag 3 09/2005

Dataseries X:

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97,3 0 101 0 113,2 0 101 0 105,7 0 113,9 0 86,4 0 96,5 0 103,3 0 114,9 0 105,8 0 94,2 0 98,4 0 99,4 0 108,8 0 112,6 0 104,4 0 112,2 0 81,1 0 97,1 0 112,6 0 113,8 0 107,8 0 103,2 0 103,3 0 101,2 0 107,7 0 110,4 0 101,9 0 115,9 0 89,9 0 88,6 0 117,2 0 123,9 0 100 0 103,6 0 94,1 0 98,7 0 119,5 0 112,7 0 104,4 0 124,7 0 89,1 0 97 0 121,6 0 118,8 0 114 0 111,5 0 97,2 0 102,5 0 113,4 0 109,8 0 104,9 0 126,1 0 80 0 96,8 0 117,2 1 112,3 1 117,3 1 111,1 1 102,2 1 104,3 1 122,9 1 107,6 1 121,3 1 131,5 1 89 1 104,4 1 128,9 1 135,9 1 133,3 1 121,3 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 146,6 1 103,4 1 117,2 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 y[t] = + 97.6646949404762 + 6.81015624999999x[t] -4.40325609410436M1[t] -2.5115557681406M2[t] + 11.0087159863946M3[t] + 4.65755916950114M4[t] + 3.84925949546485M5[t] + 17.2552455357143M6[t] -18.9244827097506M7[t] -7.86135381235829M8[t] + 9.85585140306123M9[t] + 12.8094564909297M10[t] + 5.72972824546485M11[t] + 0.179728245464853t + 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) 97.6646949404762 2.892524 33.7645 0 0 x 6.81015624999999 2.461431 2.7667 0.007338 0.003669 M1 -4.40325609410436 3.385008 -1.3008 0.197847 0.098923 M2 -2.5115557681406 3.383171 -0.7424 0.460499 0.230249 M3 11.0087159863946 3.382043 3.255 0.00179 0.000895 M4 4.65755916950114 3.381624 1.3773 0.173068 0.086534 M5 3.84925949546485 3.381914 1.1382 0.259156 0.129578 M6 17.2552455357143 3.382913 5.1007 3e-06 2e-06 M7 -18.9244827097506 3.384621 -5.5913 0 0 M8 -7.86135381235829 3.387037 -2.321 0.023385 0.011692 M9 9.85585140306123 3.511583 2.8067 0.006573 0.003287 M10 12.8094564909297 3.509875 3.6495 0.00052 0.00026 M11 5.72972824546485 3.508849 1.6329 0.107245 0.053622 t 0.179728245464853 0.048977 3.6696 0.000487 0.000244 Multiple Linear Regression - Regression Statistics Multiple R 0.907219211715824 R-squared 0.823046698106281 Adjusted R-squared 0.788192259854488 F-TEST (value) 23.6138276612144 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.07691307608852 Sum Squared Residuals 2437.30558726615 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 93.441167091837 3.85883290816302 2 101 95.5125956632653 5.4874043367347 3 113.2 109.212595663265 3.98740433673472 4 101 103.041167091837 -2.04116709183671 5 105.7 102.412595663265 3.28740433673472 6 113.9 115.998309948980 -2.09830994897960 7 86.4 79.9983099489796 6.40169005102042 8 96.5 91.2411670918367 5.25883290816328 9 103.3 109.138100552721 -5.83810055272106 10 114.9 112.271433886054 2.62856611394561 11 105.8 105.371433886054 0.428566113945586 12 94.2 99.8214338860544 -5.62143388605441 13 98.4 95.597906037415 2.80209396258508 14 99.4 97.6693346088435 1.73066539115647 15 108.8 111.369334608844 -2.56933460884354 16 112.6 105.197906037415 7.40209396258503 17 104.4 104.569334608844 -0.169334608843526 18 112.2 118.155048894558 -5.95504889455781 19 81.1 82.1550488945578 -1.05504889455782 20 97.1 93.397906037415 3.70209396258503 21 112.6 111.294839498299 1.30516050170067 22 113.8 114.428172831633 -0.628172831632658 23 107.8 107.528172831633 0.271827168367349 24 103.2 101.978172831633 1.22182716836736 25 103.3 97.7546449829932 5.54535501700684 26 101.2 99.8260735544218 1.37392644557824 27 107.7 113.526073554422 -5.82607355442177 28 110.4 107.354644982993 3.04535501700681 29 101.9 106.726073554422 -4.82607355442176 30 115.9 120.311787840136 -4.41178784013604 31 89.9 84.311787840136 5.58821215986395 32 88.6 95.5546449829932 -6.9546449829932 33 117.2 113.451578443878 3.74842155612244 34 123.9 116.584911777211 7.31508822278912 35 100 109.684911777211 -9.68491177721089 36 103.6 104.134911777211 -0.534911777210889 37 94.1 99.9113839285714 -5.8113839285714 38 98.7 101.9828125 -3.2828125 39 119.5 115.6828125 3.81718749999999 40 112.7 109.511383928571 3.18861607142857 41 104.4 108.8828125 -4.4828125 42 124.7 122.468526785714 2.23147321428572 43 89.1 86.4685267857143 2.63147321428570 44 97 97.7113839285714 -0.711383928571432 45 121.6 115.608317389456 5.9916826105442 46 118.8 118.741650722789 0.0583492772108681 47 114 111.841650722789 2.15834927721087 48 111.5 106.291650722789 5.20834927721088 49 97.2 102.068122874150 -4.86812287414962 50 102.5 104.139551445578 -1.63955144557824 51 113.4 117.839551445578 -4.43955144557824 52 109.8 111.668122874150 -1.86812287414967 53 104.9 111.039551445578 -6.13955144557823 54 126.1 124.625265731293 1.47473426870747 55 80 88.6252657312925 -8.62526573129252 56 96.8 99.8681228741497 -3.06812287414967 57 117.2 124.575212585034 -7.37521258503401 58 112.3 127.708545918367 -15.4085459183674 59 117.3 120.808545918367 -3.50854591836735 60 111.1 115.258545918367 -4.15854591836735 61 102.2 111.035018069728 -8.83501806972785 62 104.3 113.106446641156 -8.80644664115647 63 122.9 126.806446641156 -3.90644664115646 64 107.6 120.635018069728 -13.0350180697279 65 121.3 120.006446641156 1.29355335884353 66 131.5 133.592160926871 -2.09216092687074 67 89 97.5921609268707 -8.59216092687075 68 104.4 108.835018069728 -4.43501806972789 69 128.9 126.731951530612 2.16804846938775 70 135.9 129.865284863946 6.03471513605442 71 133.3 122.965284863946 10.3347151360544 72 121.3 117.415284863946 3.88471513605442 73 120.5 113.191757015306 7.30824298469392 74 120.4 115.263185586735 5.13681441326531 75 137.9 128.963185586735 8.9368144132653 76 126.1 122.791757015306 3.30824298469387 77 133.2 122.163185586735 11.0368144132653 78 146.6 135.748899872449 10.851100127551 79 103.4 99.748899872449 3.65110012755102 80 117.2 110.991757015306 6.20824298469387

Charts produced by software:

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Parameters:

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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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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