*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 19 Nov 2009 07:19:07 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258640418jo76c0n9hzb6fke.htm/, Retrieved Thu, 19 Nov 2009 15:20:30 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258640418jo76c0n9hzb6fke.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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88.9 94.8 104.2 110.8 110.5 89.8 58.5 88.9 104.2 110.8 90 62.4 89.8 88.9 104.2 93.9 56.7 90 89.8 88.9 91.3 65.1 93.9 90 89.8 87.8 114.4 91.3 93.9 90 99.7 50.7 87.8 91.3 93.9 73.5 44.5 99.7 87.8 91.3 79.2 72 73.5 99.7 87.8 96.9 61.2 79.2 73.5 99.7 95.2 68.4 96.9 79.2 73.5 95.6 78.7 95.2 96.9 79.2 89.7 64.1 95.6 95.2 96.9 92.8 64.6 89.7 95.6 95.2 88 71.9 92.8 89.7 95.6 101.1 71 88 92.8 89.7 92.7 76.4 101.1 88 92.8 95.8 117.3 92.7 101.1 88 103.8 66.1 95.8 92.7 101.1 81.8 57.3 103.8 95.8 92.7 87.1 75 81.8 103.8 95.8 105.9 63.8 87.1 81.8 103.8 108.1 62.2 105.9 87.1 81.8 102.6 75.4 108.1 105.9 87.1 93.7 58 102.6 108.1 105.9 103.5 62.1 93.7 102.6 108.1 100.6 99.2 103.5 93.7 102.6 113.3 70.7 100.6 103.5 93.7 102.4 73.3 113.3 100.6 103.5 102.1 111.2 102.4 113.3 100.6 106.9 68.9 102.1 102.4 113.3 87.3 57.6 106.9 102.1 102.4 93.1 72.9 87.3 106.9 102.1 109.1 75.9 93.1 87.3 106.9 120.3 79.4 109.1 93.1 87.3 104.9 96.9 120.3 109.1 93.1 92.6 75.2 104.9 120.3 109.1 109.8 60.3 92.6 104.9 12 etc...

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 computational 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2.86447730374015 -0.086292836908664X[t] + 0.721869390818033Y1[t] + 0.393165691970004Y2[t] -0.186439845201419`Y3 `[t] -2.21022856211889M1[t] + 14.2880488022346M2[t] + 13.5451642013673M3[t] + 16.0560856606977M4[t] + 8.10130396936484M5[t] + 11.6360412404237M6[t] + 17.3124338852545M7[t] -6.22433255674431M8[t] + 7.36102001165116M9[t] + 30.850583715014M10[t] + 16.4618484131315M11[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) 2.86447730374015 9.19809 0.3114 0.757098 0.378549 X -0.086292836908664 0.083492 -1.0335 0.307557 0.153779 Y1 0.721869390818033 0.169515 4.2584 0.000121 6.1e-05 Y2 0.393165691970004 0.213275 1.8435 0.072678 0.036339 `Y3 ` -0.186439845201419 0.177096 -1.0528 0.298769 0.149385 M1 -2.21022856211889 5.269972 -0.4194 0.677167 0.338584 M2 14.2880488022346 6.68478 2.1374 0.03873 0.019365 M3 13.5451642013673 5.952244 2.2756 0.028298 0.014149 M4 16.0560856606977 4.3289 3.709 0.000632 0.000316 M5 8.10130396936484 4.820458 1.6806 0.100633 0.050317 M6 11.6360412404237 5.204382 2.2358 0.03101 0.015505 M7 17.3124338852545 5.361671 3.2289 0.002484 0.001242 M8 -6.22433255674431 5.08543 -1.224 0.22813 0.114065 M9 7.36102001165116 6.037021 1.2193 0.229867 0.114933 M10 30.850583715014 7.629176 4.0438 0.000233 0.000117 M11 16.4618484131315 5.015844 3.282 0.002144 0.001072 Multiple Linear Regression - Regression Statistics Multiple R 0.918965867543781 R-squared 0.844498265710494 Adjusted R-squared 0.78618511535193 F-TEST (value) 14.4821238522995 F-TEST (DF numerator) 15 F-TEST (DF denominator) 40 p-value 1.10615960835503e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.66210143823518 Sum Squared Residuals 1282.37570787460 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 88.9 90.6536341014388 -1.75363410143879 2 89.8 96.5889142454982 -6.78891424549823 3 90 91.3742379236116 -1.37423792361164 4 93.9 97.7277811858398 -3.82778118583978 5 91.3 91.7742675663772 -0.474267566377228 6 87.8 90.6739657913548 -2.87396579135480 7 99.7 97.5713230839968 2.12867691600318 8 73.5 82.268481657195 -8.76848165719501 9 79.2 79.8990143638178 -0.699014363817748 10 96.9 95.915620945946 0.984379054054067 11 95.2 100.808433824306 -5.60843382430649 12 95.6 88.126916856846 7.47308314315395 13 89.7 83.4969445335067 6.20305546649326 14 92.8 96.16726008721 -3.36726008720991 15 88 94.6379793677417 -6.63797936774166 16 101.1 96.0804000361587 5.01959996384129 17 92.7 94.6509672036549 -1.95096720365488 18 95.8 94.6380063840518 1.16199361594821 19 103.8 101.225433605455 2.57456639454455 20 81.8 87.007907599596 -5.20790759959608 21 87.1 85.7521123723471 1.34788762765290 22 105.9 103.892899635471 2.00710036452891 23 108.1 109.398832181894 -1.29883218189376 24 102.6 99.789414810836 2.81058518916391 25 93.7 92.4702953939761 1.22970460602390 26 103.5 99.6175555834454 3.88244441655459 27 100.6 100.273771253358 0.326228746641827 28 113.3 108.662955734812 4.63704426518812 29 102.4 106.684262941219 -4.28426294121861 30 102.1 104.614005172626 -2.51400517262574 31 106.9 107.070731924917 -0.170731924916517 32 87.3 89.8882922210166 -2.58829222101665 33 93.1 89.9478515996925 3.15214840030745 34 109.1 108.764420439495 0.335579560504907 35 120.3 111.558152440895 8.74184755910534 36 104.9 106.880416528375 -1.98041652837531 37 92.6 96.846372135418 -4.24637213541808 38 109.8 97.6085413400549 12.1914586599451 39 111.4 104.849070730541 6.55092926945927 40 117.9 117.432574673988 0.467425326012318 41 121.6 112.506947863891 9.0930521361085 42 117.8 117.828815862984 -0.0288158629844725 43 124.2 122.825737747959 1.37426225204068 44 106.8 102.907290216113 3.89270978388663 45 102.7 106.501021664143 -3.80102166414261 46 116.8 120.127058979088 -3.32705897908788 47 113.6 115.434581552905 -1.83458155290508 48 96.1 104.403251803943 -8.30325180394254 49 85 86.4327538356603 -1.43275383566029 50 83.2 89.1177287437916 -5.91772874379158 51 84.9 83.7649407247478 1.1350592752522 52 83 89.296288369202 -6.29628836920195 53 79.6 81.9835544248578 -2.38355442485778 54 83.2 78.9452067889832 4.2547932110168 55 83.8 89.7067736376719 -5.90677363767189 56 82.8 70.1280283060789 12.6719716939211 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.345422435171195 0.690844870342390 0.654577564828805 20 0.318058610880222 0.636117221760443 0.681941389119778 21 0.280487093650065 0.56097418730013 0.719512906349935 22 0.180415426058229 0.360830852116459 0.81958457394177 23 0.157399121994516 0.314798243989033 0.842600878005484 24 0.117171324631485 0.234342649262971 0.882828675368515 25 0.0658103896412949 0.131620779282590 0.934189610358705 26 0.111376283301400 0.222752566602800 0.8886237166986 27 0.0770023651314189 0.154004730262838 0.922997634868581 28 0.0506952523331808 0.101390504666362 0.94930474766682 29 0.0467914308294259 0.0935828616588518 0.953208569170574 30 0.0289111608705276 0.0578223217410552 0.971088839129472 31 0.0146359654929023 0.0292719309858045 0.985364034507098 32 0.038786729145181 0.077573458290362 0.961213270854819 33 0.0244103636069287 0.0488207272138574 0.975589636393071 34 0.0135772309203753 0.0271544618407505 0.986422769079625 35 0.0235082557279765 0.0470165114559531 0.976491744272023 36 0.164965639496379 0.329931278992758 0.835034360503621 37 0.111101639792292 0.222203279584584 0.888898360207708 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 4 0.210526315789474 NOK 10% type I error level 7 0.368421052631579 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test 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)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$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') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$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() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() 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') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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