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Q3, w6, paper

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

Title produced by software: Multiple Regression

Date of computation: Tue, 20 Nov 2007 12:12:00 -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/20/t1195585574n6kc1snv39g1oi1.htm/, Retrieved Tue, 20 Nov 2007 20:06:14 +0100

User-defined keywords:

paper, multiple regression

Dataseries X:

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88.74 88.95 88.92 88.81 88.77 88.9 89.17 90.15 89.61 90.92 89.52 90.78 89.74 90.81 89.4 89.46 89.36 89.22 89.38 88.89 89.36 89.41 89.29 89.59 89.59 90.25 89.79 90.2 89.86 90.27 90.21 90.71 90.37 91.18 90.19 90.66 90.33 89.72 90.22 88.72 90.42 88.91 90.54 89.15 90.73 89.15 91.02 89.08 91.19 89.28 91.53 89.47 91.88 89.53 92.06 90.72 92.32 90.91 92.67 91.38 92.85 91.49 92.82 90.9 93.46 90.93 93.23 90.57 93.54 91.28 93.29 90.83 93.2 91.5 93.6 91.58 93.81 92.49 94.62 94.16 95.22 95.46 95.38 95.8 95.31 95.32 95.3 95.41 95.57 95.35 95.42 95.68 95.53 95.59 95.33 94.96 95.90 96.92 96.06 96.06 96.31 96.59 96.34 96.67 96.49 97.27 96.22 96.38 96.53 96.47 96.50 96.05 96.77 96.76 96.66 96.51 96.58 96.55 96.63 95.97 97.06 97.00 97.73 97.46 98.01 97.90 97.76 98.42 97.49 98.54 97.77 99.00 97.96 98.94 98.23 99.02 98.51 100.07 98.19 98.72 98.37 98.73 98.31 98.04 98.60 99.08 98.97 99.22 99.11 99.57 99.64 100.44 100.03 100.84 99.98 100.75 100.32 100.49 100.44 99.98 100.51 99.96 101.00 99.76 100.88 100.11 100.55 99.79 100.83 100.29 101.51 101.12 102.16 102.65 102.39 102.71 102.54 103.39 102.85 102.80 103.47 102.07 103.57 102.15 103.69 101.21 103.50 101.27 103.47 101.86 103.45 101.65 103.48 101.94 103.93 102.62 103.89 102.71 104.40 103.39 104.79 104.51 104.77 104.09 105.13 104.29 105.26 104.57 104.96 105.39 104.75 105.15 105.01 106.13 105.15 105.46 105.20 106.47 105.77 106.62 105.78 106.52 106.26 108.04 106.13 107.15 106.12 107.32 106.57 107.76 106.44 107.26 106.54 107.89

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 Y[t] = + 73.8042336411469 + 0.156334829849718X[t] + 0.0548151015977865M1[t] + 0.297576758775181M2[t] + 0.276411043319977M3[t] + 0.337865016199548M4[t] + 0.341348849186215M5[t] + 0.272164575593166M6[t] + 0.435077360364255M7[t] + 0.356009147021685M8[t] + 0.346983700939432M9[t] + 0.227580410026349M10[t] + 0.126346141928972M11[t] + 0.136100788004864t + 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) 73.8042336411469 3.559799 20.7327 0 0 X 0.156334829849718 0.041299 3.7854 0.000258 0.000129 M1 0.0548151015977865 0.21443 0.2556 0.798745 0.399373 M2 0.297576758775181 0.214265 1.3888 0.167882 0.083941 M3 0.276411043319977 0.215965 1.2799 0.20346 0.10173 M4 0.337865016199548 0.223098 1.5144 0.132982 0.066491 M5 0.341348849186215 0.227473 1.5006 0.136515 0.068257 M6 0.272164575593166 0.223346 1.2186 0.225788 0.112894 M7 0.435077360364255 0.219361 1.9834 0.049986 0.024993 M8 0.356009147021685 0.214425 1.6603 0.099897 0.049948 M9 0.346983700939432 0.214793 1.6154 0.109276 0.054638 M10 0.227580410026349 0.217467 1.0465 0.297776 0.148888 M11 0.126346141928972 0.218098 0.5793 0.563645 0.281823 t 0.136100788004864 0.007037 19.3419 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.996923633472064 R-squared 0.993856730975143 Adjusted R-squared 0.993081366923462 F-TEST (value) 1281.79366688516 F-TEST (DF numerator) 13 F-TEST (DF denominator) 103 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.46013305322092 Sum Squared Residuals 21.8074099466398 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 88.74 87.9011326458822 0.838867354117786 2 88.92 88.2581082148853 0.661891785114661 3 88.77 88.3871134221215 0.38288657787852 4 89.17 88.780086720318 0.389913279681941 5 89.61 89.0400491602939 0.569950839706126 6 89.52 89.0850787985267 0.434921201473268 7 89.74 89.3887824161982 0.351217583801822 8 89.4 89.2347629705634 0.165237029436660 9 89.36 89.324317953322 0.0356820466779737 10 89.38 89.2894249565634 0.0905750434365953 11 89.36 89.4055855879927 -0.0455855879927416 12 89.29 89.4434805034416 -0.153480503441577 13 89.59 89.737577380745 -0.147577380745045 14 89.79 90.1086230844348 -0.318623084434817 15 89.86 90.234501595074 -0.374501595073962 16 90.21 90.5008436810923 -0.290843681092279 17 90.37 90.7139056721132 -0.343905672113169 18 90.19 90.6995280750031 -0.509528075003136 19 90.33 90.8515869077203 -0.521586907720353 20 90.22 90.752284652533 -0.532284652532929 21 90.42 90.909063612127 -0.489063612126983 22 90.54 90.9632814683827 -0.423281468382694 23 90.73 90.9981479882902 -0.268147988290183 24 91.02 90.9969591962766 0.0230408037233981 25 91.19 91.2191420518492 -0.0291420518491953 26 91.53 91.6277081147029 -0.097708114702897 27 91.88 91.7520232770435 0.127976722956454 28 92.06 92.1356164854491 -0.0756164854491397 29 92.32 92.3049047241121 0.0150952758878739 30 92.67 92.4452986085533 0.224701391446699 31 92.85 92.7615090126127 0.08849098738727 32 92.82 92.7263040376637 0.0936959623363068 33 93.46 92.8580694244818 0.601930575518205 34 93.23 92.8184863828277 0.411513617172335 35 93.54 92.9643506319285 0.575649368071547 36 93.29 92.903754604572 0.386245395428029 37 93.2 93.199414830174 0.000585169826062811 38 93.6 93.5907840617442 0.00921593825581825 39 93.81 93.847983829457 -0.0379838294570775 40 94.62 94.3066177561905 0.313382243809459 41 95.22 94.6494376559867 0.570562344013289 42 95.38 94.7695080125474 0.610491987452565 43 95.31 94.9934808669955 0.316519133004485 44 95.3 95.0645835763443 0.23541642365571 45 95.57 95.182278828476 0.387721171524078 46 95.42 95.2505668194181 0.169433180581896 47 95.53 95.2713632046391 0.258636795360883 48 95.33 95.1826269079097 0.147373092090312 49 95.9 95.6799590640178 0.22004093598222 50 96.06 95.9243735555293 0.135626444470715 51 96.31 96.1221660878993 0.187833912100703 52 96.34 96.3322276351717 0.007772364828292 53 96.49 96.565613154073 -0.0756131540730777 54 96.22 96.4933916699186 -0.27339166991864 55 96.53 96.806475377381 -0.276475377381066 56 96.5 96.7978473235065 -0.297847323506479 57 96.77 97.0359203946224 -0.265920394622396 58 96.66 97.0135341842517 -0.353534184251747 59 96.58 97.0546540973532 -0.474654097353221 60 96.63 96.9737345421163 -0.343734542116279 61 97.06 97.3256753064641 -0.265675306464133 62 97.73 97.7764517733773 -0.04645177337726 63 98.01 97.9601741710608 0.0498258289392028 64 97.76 98.239023043467 -0.479023043467086 65 97.49 98.3973678440406 -0.907367844040594 66 97.77 98.5361983801833 -0.766198380183278 67 97.96 98.8258318631682 -0.86583186316825 68 98.23 98.8953712242185 -0.665371224218511 69 98.51 99.1865981374833 -0.676598137483325 70 98.19 98.992243614278 -0.802243614277995 71 98.37 99.028673482484 -0.658673482483973 72 98.31 98.9305570959636 -0.620557095963563 73 98.6 99.28406120861 -0.684061208609927 74 98.97 99.6848105299711 -0.714810529971143 75 99.11 99.8544627929682 -0.744462792968203 76 99.64 100.188028855822 -0.548028855821893 77 100.03 100.390147408753 -0.360147408753312 78 99.98 100.442993788479 -0.462993788478649 79 100.32 100.701360305494 -0.381360305493685 80 100.44 100.678662116933 -0.23866211693262 81 100.51 100.802610762258 -0.292610762258228 82 101 100.78804129338 0.211958706619928 83 100.88 100.877625003735 0.0023749962650349 84 100.55 100.837352504259 -0.287352504258947 85 100.83 101.106435808786 -0.276435808786456 86 101.51 101.615056162744 -0.105056162743974 87 102.16 101.969183524964 0.190816475036287 88 102.39 102.176118375639 0.213881624360874 89 102.54 102.422010680928 0.117989319071539 90 102.85 102.396689645729 0.453310354271046 91 103.47 102.581578792715 0.888421207285392 92 103.57 102.651118153765 0.918881846235113 93 103.69 102.631238755629 1.05876124437124 94 103.5 102.657316342512 0.84268365748848 95 103.47 102.784420412030 0.685579587969658 96 103.45 102.761344743838 0.68865525616221 97 103.48 102.997597734097 0.482402265903143 98 103.93 103.482767863577 0.447232136423077 99 103.89 103.611773070813 0.278226929186937 100 104.4 103.915635515995 0.484364484004697 101 104.79 104.230315146419 0.559684853581482 102 104.77 104.231571032293 0.538428967706538 103 105.13 104.561851571039 0.56814842896064 104 105.26 104.662657898060 0.597342101940437 105 104.96 104.917927800459 0.0420721995410439 106 104.75 104.897104938387 -0.147104938386800 107 105.01 105.085179591547 -0.075179591547005 108 105.15 104.990189901624 0.159810098376415 109 105.2 105.339003969374 -0.139003969374454 110 105.77 105.741316639034 0.0286833609658205 111 105.78 105.840618228599 -0.0606182285988618 112 106.26 106.275801930855 -0.0158019308548665 113 106.13 106.276248553280 -0.146248553280158 114 106.12 106.369741988766 -0.249741988766414 115 106.57 106.737542886676 -0.167542886676257 116 106.44 106.716408046414 -0.276408046413688 117 106.54 106.941974331142 -0.401974331141612

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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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