Multiple regression 2

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

Title produced by software: Multiple Regression

Date of computation: Tue, 17 Nov 2009 12:32:14 -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/17/t125848638546rf8la7uk61vn2.htm/, Retrieved Tue, 17 Nov 2009 20:33:17 +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/17/t125848638546rf8la7uk61vn2.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:

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No (this computation is public)

User-defined keywords:

JSSHWWS7P2

Dataseries X:

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8 11.1 8.1 10.9 7.7 10 7.5 9.2 7.6 9.2 7.8 9.5 7.8 9.6 7.8 9.5 7.5 9.1 7.5 8.9 7.1 9 7.5 10.1 7.5 10.3 7.6 10.2 7.7 9.6 7.7 9.2 7.9 9.3 8.1 9.4 8.2 9.4 8.2 9.2 8.2 9 7.9 9 7.3 9 6.9 9.8 6.6 10 6.7 9.8 6.9 9.3 7 9 7.1 9 7.2 9.1 7.1 9.1 6.9 9.1 7 9.2 6.8 8.8 6.4 8.3 6.7 8.4 6.6 8.1 6.4 7.7 6.3 7.9 6.2 7.9 6.5 8 6.8 7.9 6.8 7.6 6.4 7.1 6.1 6.8 5.8 6.5 6.1 6.9 7.2 8.2 7.3 8.7 6.9 8.3 6.1 7.9 5.8 7.5 6.2 7.8 7.1 8.3 7.7 8.4 7.9 8.2 7.7 7.7 7.4 7.2 7.5 7.3 8 8.1

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 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.81400771388499 + 0.978786816269285X[t] + 0.778727208976158M1[t] + 0.577454417952314M2[t] + 0.333211781206171M3[t] + 0.0510904628330994M4[t] -0.0642426367461433M5[t] -0.2170301542777M6[t] -0.354484572230014M7[t] -0.476181626928472M8[t] -0.599151472650772M9[t] -0.663818373071529M10[t] -0.448061009817672M11[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) 1.81400771388499 1.1641 1.5583 0.125873 0.062936 X 0.978786816269285 0.153824 6.363 0 0 M1 0.778727208976158 0.464792 1.6754 0.100491 0.050246 M2 0.577454417952314 0.465067 1.2417 0.220524 0.110262 M3 0.333211781206171 0.4673 0.7131 0.479336 0.239668 M4 0.0510904628330994 0.46917 0.1089 0.913749 0.456875 M5 -0.0642426367461433 0.465718 -0.1379 0.890875 0.445437 M6 -0.2170301542777 0.465199 -0.4665 0.64299 0.321495 M7 -0.354484572230014 0.466418 -0.76 0.451042 0.225521 M8 -0.476181626928472 0.465525 -1.0229 0.311595 0.155798 M9 -0.599151472650772 0.464741 -1.2892 0.203632 0.101816 M10 -0.663818373071529 0.465525 -1.426 0.160489 0.080245 M11 -0.448061009817672 0.468362 -0.9567 0.343637 0.171818 Multiple Linear Regression - Regression Statistics Multiple R 0.75488037601094 R-squared 0.569844382086419 Adjusted R-squared 0.460017415810612 F-TEST (value) 5.18856526233614 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.87317418973709e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.734756187946033 Sum Squared Residuals 25.3737328190743 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11.1 10.4230294530154 0.676970546984578 2 10.9 10.3196353436185 0.580364656381486 3 10 9.68387798036466 0.316122019635345 4 9.2 9.20599929873773 -0.00599929873772784 5 9.2 9.18854488078541 0.0114551192145857 6 9.5 9.23151472650771 0.268485273492286 7 9.6 9.0940603085554 0.5059396914446 8 9.5 8.97236325385694 0.527636746143058 9 9.1 8.55575736325386 0.544242636746143 10 8.9 8.4910904628331 0.4089095371669 11 9 8.31533309957924 0.684666900420758 12 10.1 9.15490883590463 0.94509116409537 13 10.3 9.93363604488079 0.366363955119214 14 10.2 9.83024193548387 0.369758064516129 15 9.6 9.68387798036466 -0.0838779803646572 16 9.2 9.40175666199159 -0.201756661991586 17 9.3 9.4821809256662 -0.182180925666199 18 9.4 9.5251507713885 -0.125150771388499 19 9.4 9.48557503506311 -0.0855750350631127 20 9.2 9.36387798036466 -0.163877980364656 21 9 9.24090813464236 -0.240908134642356 22 9 8.88260518934081 0.117394810659186 23 9 8.5110904628331 0.4889095371669 24 9.8 8.56763674614306 1.23236325385694 25 10 9.05272791023843 0.94727208976157 26 9.8 8.94933380084152 0.850666199158486 27 9.3 8.90084852734923 0.399151472650771 28 9 8.71660589060309 0.283394109396914 29 9 8.69915147265077 0.300848527349229 30 9.1 8.64424263674614 0.455757363253856 31 9.1 8.4089095371669 0.691090462833099 32 9.1 8.09145511921459 1.00854488078541 33 9.2 8.06636395511921 1.13363604488078 34 8.8 7.8059396914446 0.9940603085554 35 8.3 7.63018232819074 0.669817671809257 36 8.4 8.3718793828892 0.0281206171107995 37 8.1 9.05272791023843 -0.95272791023843 38 7.7 8.65569775596073 -0.955697755960729 39 7.9 8.31357643758766 -0.413576437587657 40 7.9 7.93357643758766 -0.0335764375876577 41 8 8.1118793828892 -0.111879382889200 42 7.9 8.25272791023843 -0.352727910238429 43 7.6 8.11527349228611 -0.515273492286115 44 7.1 7.60206171107994 -0.502061711079944 45 6.8 7.18545582047686 -0.385455820476858 46 6.5 6.82715287517532 -0.327152875175315 47 6.9 7.33654628330996 -0.436546283309958 48 8.2 8.86127279102384 -0.661272791023844 49 8.7 9.73787868162693 -1.03787868162693 50 8.3 9.14509116409537 -0.845091164095371 51 7.9 8.1178190743338 -0.217819074333801 52 7.5 7.54206171107994 -0.0420617110799438 53 7.8 7.81824333800841 -0.0182433380084153 54 8.3 8.54636395511922 -0.246363955119214 55 8.4 8.99618162692847 -0.596181626928471 56 8.2 9.07024193548387 -0.870241935483872 57 7.7 8.75151472650771 -1.05151472650771 58 7.2 8.39321178120617 -1.19321178120617 59 7.3 8.70684782608696 -1.40684782608696 60 8.1 9.64430224403927 -1.54430224403927 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0223180733084264 0.0446361466168528 0.977681926691574 17 0.00797515577441008 0.0159503115488202 0.99202484422559 18 0.00495186245676104 0.00990372491352208 0.995048137543239 19 0.00431093396964533 0.00862186793929065 0.995689066030355 20 0.00322039837362435 0.00644079674724871 0.996779601626376 21 0.00148859620689248 0.00297719241378496 0.998511403793108 22 0.00047365650794482 0.00094731301588964 0.999526343492055 23 0.000168473080606498 0.000336946161212997 0.999831526919393 24 9.48392211469318e-05 0.000189678442293864 0.999905160778853 25 7.60179189020013e-05 0.000152035837804003 0.999923982081098 26 6.69114849297619e-05 0.000133822969859524 0.99993308851507 27 2.87649992461353e-05 5.75299984922706e-05 0.999971235000754 28 1.12762543146486e-05 2.25525086292971e-05 0.999988723745685 29 4.17865511147363e-06 8.35731022294727e-06 0.999995821344889 30 1.67117340492875e-06 3.3423468098575e-06 0.999998328826595 31 9.68147344373713e-07 1.93629468874743e-06 0.999999031852656 32 2.41655043075104e-06 4.83310086150207e-06 0.99999758344957 33 0.00010597357759822 0.00021194715519644 0.999894026422402 34 0.0071557671240856 0.0143115342481712 0.992844232875914 35 0.283811152910054 0.567622305820107 0.716188847089946 36 0.937833041187647 0.124333917624705 0.0621669588123527 37 0.994658259907706 0.0106834801845872 0.00534174009229360 38 0.998312342743936 0.00337531451212886 0.00168765725606443 39 0.996153622103638 0.00769275579272377 0.00384637789636188 40 0.990915548817743 0.0181689023645131 0.00908445118225655 41 0.976277210042818 0.0474455799143632 0.0237227899571816 42 0.955275064984645 0.0894498700307102 0.0447249350153551 43 0.93679429005019 0.126411419899620 0.0632057099498102 44 0.930010696347068 0.139978607305864 0.0699893036529321 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.620689655172414 NOK 5% type I error level 24 0.827586206896552 NOK 10% type I error level 25 0.862068965517241 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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