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Q3,W6, multiple regression, 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 12:06:45 -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/t1195585220jalwtyy8k7jmvlw.htm/, Retrieved Tue, 20 Nov 2007 20:00:30 +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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 71.192346155451 + 0.189215809505315X[t] + 0.130691870654899t + 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) 71.192346155451 3.104658 22.9308 0 0 X 0.189215809505315 0.035615 5.3129 1e-06 0 t 0.130691870654899 0.006099 21.4278 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.996691571344112 R-squared 0.993394088388395 Adjusted R-squared 0.993278195202227 F-TEST (value) 8571.63497898886 F-TEST (DF numerator) 2 F-TEST (DF denominator) 114 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.453540662683154 Sum Squared Residuals 23.4497011286064 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 88.74 88.1537842816038 0.586215718396221 2 88.92 88.2579859389278 0.662014061072154 3 88.77 88.4057072324382 0.364292767561744 4 89.17 88.7729188649748 0.397081135025204 5 89.61 89.0493069089488 0.560693091051211 6 89.52 89.153508566273 0.366491433727052 7 89.74 89.289876911213 0.450123088786993 8 89.4 89.1651274390357 0.234872560964283 9 89.36 89.2504075154093 0.109592484590652 10 89.38 89.3186581689275 0.0613418310725031 11 89.36 89.5477422605252 -0.187742260525154 12 89.29 89.712492976891 -0.422492976891004 13 89.59 89.9680672818194 -0.378067281819413 14 89.79 90.089298361999 -0.299298361999043 15 89.86 90.2332353393193 -0.37323533931932 16 90.21 90.4471821661566 -0.237182166156562 17 90.37 90.666805467279 -0.296805467278951 18 90.19 90.6991051169911 -0.50910511699109 19 90.33 90.651934126711 -0.321934126710993 20 90.22 90.5934101878606 -0.373410187860576 21 90.42 90.7600530623215 -0.34005306232148 22 90.54 90.9361567272577 -0.396156727257652 23 90.73 91.0668485979126 -0.336848597912553 24 91.02 91.1842953619021 -0.164295361902086 25 91.19 91.352830394458 -0.162830394458047 26 91.53 91.519473268919 0.0105267310810493 27 91.88 91.6615180881442 0.218481911855825 28 92.06 92.0173767721104 0.0426232278896090 29 92.32 92.1840196465713 0.135980353428692 30 92.67 92.4036429476937 0.266357052306304 31 92.85 92.5551485573942 0.294851442605812 32 92.82 92.574203100441 0.245796899559047 33 93.46 92.710571445381 0.749428554618989 34 93.23 92.773145624614 0.456854375386017 35 93.54 93.0381807200177 0.501819279982345 36 93.29 93.0837254763952 0.206274523604838 37 93.2 93.3411919394186 -0.141191939418625 38 93.6 93.487021074834 0.112978925166043 39 93.81 93.7898993321387 0.0201006678613164 40 94.62 94.2365816046675 0.383418395332543 41 95.22 94.6132540276793 0.606745972320729 42 95.38 94.808279273566 0.57172072643402 43 95.31 94.8481475556583 0.461852444341679 44 95.3 94.9958688491687 0.304131150831297 45 95.57 95.1152077712533 0.454792228746713 46 95.42 95.308340859045 0.111659140955067 47 95.53 95.4220033068444 0.107996693155647 48 95.33 95.433489217511 -0.103489217510904 49 95.9 95.9350440747962 -0.0350440747962152 50 96.06 95.9030103492765 0.156989650723454 51 96.31 96.1339865989693 0.176013401030738 52 96.34 96.2798157343846 0.0601842656154157 53 96.49 96.5240370907427 -0.0340370907426796 54 96.22 96.4863268909378 -0.266326890937844 55 96.53 96.6340481844482 -0.104048184448219 56 96.5 96.685269415111 -0.185269415110886 57 96.77 96.9503045105146 -0.180304510514564 58 96.66 97.0336924287931 -0.373692428793133 59 96.58 97.1719529318282 -0.591952931828241 60 96.63 97.19289963297 -0.56289963297006 61 97.06 97.5184837874154 -0.458483787415427 62 97.73 97.7362149304428 -0.00621493044276782 63 98.01 97.95016175728 0.0598382427199937 64 97.76 98.1792458488777 -0.419245848877668 65 97.49 98.3326436166732 -0.842643616673216 66 97.77 98.5503747597006 -0.780374759700557 67 97.96 98.6697136817851 -0.709713681785139 68 98.23 98.8155428172005 -0.585542817200452 69 98.51 99.144911287836 -0.63491128783593 70 98.19 99.0201618156587 -0.830161815658661 71 98.37 99.1527458444086 -0.782745844408607 72 98.31 99.1528788065048 -0.842878806504841 73 98.6 99.4803551190453 -0.880355119045274 74 98.97 99.637537203031 -0.667537203030912 75 99.11 99.8344546070127 -0.72445460701267 76 99.64 100.129764231937 -0.489764231937193 77 100.03 100.336142426394 -0.306142426394218 78 99.98 100.449804874194 -0.469804874193634 79 100.32 100.531300634377 -0.211300634377161 80 100.44 100.565492442184 -0.125492442184346 81 100.51 100.692399996649 -0.182399996649129 82 101 100.785248705403 0.214751294597028 83 100.88 100.982166109385 -0.102166109384734 84 100.55 101.052308920998 -0.502308920997932 85 100.83 101.277608696405 -0.447608696405487 86 101.51 101.565349688950 -0.0553496889497899 87 102.16 101.985541748148 0.174458251852170 88 102.39 102.127586567373 0.262413432626959 89 102.54 102.386945188492 0.15305481150845 90 102.85 102.405999731538 0.444000268461676 91 103.47 102.398564061254 1.07143593874566 92 103.57 102.544393196670 1.02560680333033 93 103.69 102.497222206390 1.19277779361044 94 103.5 102.639267025615 0.86073297438522 95 103.47 102.881596223878 0.588403776122183 96 103.45 102.972552774537 0.477447225463404 97 103.48 103.158117229948 0.321882770051967 98 103.93 103.417475851067 0.512524148933455 99 103.89 103.565197144577 0.324802855423074 100 104.4 103.824555765695 0.575444234304564 101 104.79 104.167169342996 0.622830657003712 102 104.77 104.218390573659 0.551609426341036 103 105.13 104.386925606215 0.743074393785074 104 105.26 104.570597903531 0.689402096468699 105 104.96 104.856446737981 0.103553262019429 106 104.75 104.941726814354 -0.191726814354188 107 105.01 105.257850178324 -0.247850178324289 108 105.15 105.261767456611 -0.111767456610626 109 105.2 105.583567294866 -0.383567294865896 110 105.77 105.742641536947 0.0273584630534 111 105.78 105.854411826651 -0.0744118266509604 112 106.26 106.272711727754 -0.0127117277539372 113 106.13 106.235001527949 -0.105001527949114 114 106.12 106.397860086220 -0.277860086219905 115 106.57 106.611806913057 -0.0418069130571564 116 106.44 106.647890878959 -0.207890878959393 117 106.54 106.897788709603 -0.35778870960263

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal 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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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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