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The Seatbelt Law

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

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 16:38:38 -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/t1195428898ighys6oyh3vce4n.htm/, Retrieved Mon, 19 Nov 2007 00:34:58 +0100

User-defined keywords:

Q3

Dataseries X:

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99,20 101,30 93,60 102,00 104,20 109,20 95,30 88,60 102,70 94,30 103,10 98,30 100,00 86,40 107,20 80,60 107,00 104,10 119,00 108,20 110,40 93,40 101,70 71,90 102,40 94,10 98,80 94,90 105,60 96,40 104,40 91,10 106,30 84,40 107,20 86,40 108,50 88,00 106,90 75,10 114,20 109,70 125,90 103,00 110,60 82,10 110,50 68,00 106,70 96,40 104,70 94,30 107,40 90,00 109,80 88,00 103,40 76,10 114,80 82,50 114,30 81,40 109,60 66,50 118,30 97,20 127,30 94,10 112,30 80,70 114,90 70,50 108,20 87,80 105,40 89,50 122,10 99,60 113,50 84,20 110,00 75,10 125,30 92,00 114,30 80,80 115,60 73,10 127,10 99,80 123,00 90,00 122,20 83,10 126,40 72,40 112,70 78,80 105,80 87,30 120,90 91,00 116,30 80,10 115,70 73,60 127,90 86,40 108,30 74,50 121,10 71,20 128,60 92,40 123,10 81,50 127,70 85,30 126,60 69,90 118,40 84,20 110,00 90,70 129,60 100,30 115,80 79,40 125,90 84,80 128,40 92,90 114,00 81,60 125,60 76,00 128,50 98,70 136,60 89,10 133,10 88,70 124,60 67,10 123,50 93,60 117,20 97,00 135,50 100,80 124,80 80,10 127,80 80,70 132,00 89,60 125,50 81,30 126,90 71,30

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 x[t] = + 120.616360357225 -0.0588814531126326y[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) 120.616360357225 9.727845 12.3991 0 0 y -0.0588814531126326 0.111081 -0.5301 0.597565 0.298783 Multiple Linear Regression - Regression Statistics Multiple R 0.0599114684116451 R-squared 0.00358938404723955 Adjusted R-squared -0.00918511102907793 F-TEST (value) 0.280980502618369 F-TEST (DF numerator) 1 F-TEST (DF denominator) 78 p-value 0.597565042162431 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.3181409560628 Sum Squared Residuals 8304.19455755612 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.2 114.651669156916 -15.4516691569158 2 93.6 114.610452139737 -21.0104521397368 3 104.2 114.186505677326 -9.98650567732587 4 95.3 115.399463611446 -20.0994636114461 5 102.7 115.063839328704 -12.3638393287041 6 103.1 114.828313516254 -11.7283135162536 7 100 115.529002808294 -15.5290028082939 8 107.2 115.870515236347 -8.67051523634717 9 107 114.486801088200 -7.4868010882003 10 119 114.245387130439 4.75461286956149 11 110.4 115.116832636505 -4.71683263650547 12 101.7 116.382783878427 -14.6827838784271 13 102.4 115.075615619327 -12.6756156193266 14 98.8 115.028510456837 -16.2285104568365 15 105.6 114.940188277168 -9.34018827716758 16 104.4 115.252259978665 -10.8522599786645 17 106.3 115.646765714519 -9.34676571451917 18 107.2 115.529002808294 -8.3290028082939 19 108.5 115.434792483314 -6.93479248331369 20 106.9 116.194363228467 -9.29436322846664 21 114.2 114.157064950770 0.042935049230443 22 125.9 114.551570686624 11.3484293133758 23 110.6 115.782193056678 -5.18219305667823 24 110.5 116.612421545566 -6.11242154556634 25 106.7 114.940188277168 -8.24018827716757 26 104.7 115.063839328704 -10.3638393287041 27 107.4 115.317029577088 -7.91702957708842 28 109.8 115.434792483314 -5.63479248331369 29 103.4 116.135481775354 -12.735481775354 30 114.8 115.758640475433 -0.95864047543317 31 114.3 115.823410073857 -1.52341007385707 32 109.6 116.700743725235 -7.1007437252353 33 118.3 114.893083114677 3.40691688532253 34 127.3 115.075615619327 12.2243843806734 35 112.3 115.864627091036 -3.56462709103591 36 114.9 116.465217912785 -1.56521791278475 37 108.2 115.446568773936 -7.24656877393621 38 105.4 115.346470303645 -9.94647030364473 39 122.1 114.751767627207 7.34823237279285 40 113.5 115.658542005142 -2.15854200514169 41 110 116.194363228467 -6.19436322846665 42 125.3 115.199266670863 10.1007333291368 43 114.3 115.858738945725 -1.55873894572465 44 115.6 116.312126134692 -0.71212613469192 45 127.1 114.739991336585 12.3600086634154 46 123 115.317029577088 7.68297042291158 47 122.2 115.723311603566 6.47668839643442 48 126.4 116.353343151871 10.0466568481293 49 112.7 115.97650185195 -3.27650185194990 50 105.8 115.476009500493 -9.67600950049253 51 120.9 115.258148123976 5.64185187602422 52 116.3 115.899955962903 0.400044037096511 53 115.7 116.282685408136 -0.582685408135595 54 127.9 115.529002808294 12.3709971917061 55 108.3 116.229692100334 -7.92969210033423 56 121.1 116.424000895606 4.67599910439408 57 128.6 115.175714089618 13.4242859103819 58 123.1 115.817521928546 7.2824780714542 59 127.7 115.593772406718 12.1062275932822 60 126.6 116.500546784652 10.0994532153477 61 118.4 115.658542005142 2.74145799485831 62 110 115.275812559910 -5.27581255990958 63 129.6 114.710550610028 14.8894493899717 64 115.8 115.941172980082 -0.141172980082330 65 125.9 115.623213133274 10.2767868667259 66 128.4 115.146273363062 13.2537266369382 67 114 115.811633783235 -1.81163378323454 68 125.6 116.141369920665 9.45863007933472 69 128.5 114.804760935009 13.6952390649915 70 136.6 115.370022884890 21.2299771151102 71 133.1 115.393575466135 17.7064245338651 72 124.6 116.665414853368 7.93458514663229 73 123.5 115.105056345883 8.39494365411706 74 117.2 114.9048594053 2.29514059470001 75 135.5 114.681109883472 20.818890116528 76 124.8 115.899955962903 8.90004403709651 77 127.8 115.864627091036 11.9353729089641 78 132 115.340582158333 16.6594178416665 79 125.5 115.829298219168 9.67070178083167 80 126.9 116.418112750295 10.4818872497054

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal 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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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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