Model 5

*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: Fri, 20 Nov 2009 12:50:08 -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/20/t12587466686ziy1ee9mkcbgfr.htm/, Retrieved Fri, 20 Nov 2009 20:51:20 +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/20/t12587466686ziy1ee9mkcbgfr.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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96.9 8.6 8.4 8.4 95.1 8.9 8.6 8.4 97 8.8 8.9 8.6 112.7 8.3 8.8 8.9 102.9 7.5 8.3 8.8 97.4 7.2 7.5 8.3 111.4 7.4 7.2 7.5 87.4 8.8 7.4 7.2 96.8 9.3 8.8 7.4 114.1 9.3 9.3 8.8 110.3 8.7 9.3 9.3 103.9 8.2 8.7 9.3 101.6 8.3 8.2 8.7 94.6 8.5 8.3 8.2 95.9 8.6 8.5 8.3 104.7 8.5 8.6 8.5 102.8 8.2 8.5 8.6 98.1 8.1 8.2 8.5 113.9 7.9 8.1 8.2 80.9 8.6 7.9 8.1 95.7 8.7 8.6 7.9 113.2 8.7 8.7 8.6 105.9 8.5 8.7 8.7 108.8 8.4 8.5 8.7 102.3 8.5 8.4 8.5 99 8.7 8.5 8.4 100.7 8.7 8.7 8.5 115.5 8.6 8.7 8.7 100.7 8.5 8.6 8.7 109.9 8.3 8.5 8.6 114.6 8 8.3 8.5 85.4 8.2 8 8.3 100.5 8.1 8.2 8 114.8 8.1 8.1 8.2 116.5 8 8.1 8.1 112.9 7.9 8 8.1 102 7.9 7.9 8 106 8 7.9 7.9 105.3 8 8 7.9 118.8 7.9 8 8 106.1 8 7.9 8 109.3 7.7 8 7.9 117.2 7.2 7.7 8 92.5 7.5 7.2 7.7 104.2 7.3 7.5 7.2 112.5 7 7.3 7.5 122.4 7 7 7.3 113.3 7 7 7 100 7.2 7 7 110.7 7.3 7.2 7 112.8 7.1 7.3 7.2 109.8 6.8 7.1 7.3 117.3 6.4 6.8 7.1 109.1 6.1 6.4 6.8 115.9 6.5 6.1 6.4 96 7.7 6.5 6.1 99.8 7.9 7.7 6.5 116.8 7.5 7.9 7.7 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation X[t] = + 2.91905237632963 -0.00453242253479385Y[t] + 1.41540921091640Y2[t] -0.690016330933515Y3[t] + 0.137104573754478M1[t] + 0.0607064192686293M2[t] -0.137858049153742M3[t] -0.124199435265789M4[t] -0.161449243535398M5[t] -0.126372602670887M6[t] -0.0213838761519172M7[t] + 0.575373145223861M8[t] -0.398167433129223M9[t] -0.080157117956941M10[t] -0.105845708602752M11[t] -0.00769637743671768t + 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) 2.91905237632963 1.021101 2.8587 0.006534 0.003267 Y -0.00453242253479385 0.007543 -0.6009 0.551062 0.275531 Y2 1.41540921091640 0.113061 12.519 0 0 Y3 -0.690016330933515 0.112329 -6.1428 0 0 M1 0.137104573754478 0.146224 0.9376 0.353668 0.176834 M2 0.0607064192686293 0.150161 0.4043 0.688015 0.344007 M3 -0.137858049153742 0.147784 -0.9328 0.356114 0.178057 M4 -0.124199435265789 0.133191 -0.9325 0.356289 0.178144 M5 -0.161449243535398 0.132865 -1.2151 0.230945 0.115473 M6 -0.126372602670887 0.137069 -0.922 0.361691 0.180845 M7 -0.0213838761519172 0.138145 -0.1548 0.877709 0.438854 M8 0.575373145223861 0.217551 2.6448 0.011367 0.005684 M9 -0.398167433129223 0.192458 -2.0689 0.044605 0.022303 M10 -0.080157117956941 0.137849 -0.5815 0.56395 0.281975 M11 -0.105845708602752 0.133625 -0.7921 0.432643 0.216322 t -0.00769637743671768 0.002721 -2.8281 0.007084 0.003542 Multiple Linear Regression - Regression Statistics Multiple R 0.972918106226033 R-squared 0.946569641422451 Adjusted R-squared 0.927931144244237 F-TEST (value) 50.7857276459411 F-TEST (DF numerator) 15 F-TEST (DF denominator) 43 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.193728062396361 Sum Squared Residuals 1.61381417287347 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.6 8.70256902088208 -0.102569020882076 2 8.9 8.90971469170541 -0.00971469170541226 3 8.8 8.98146174011844 -0.181461740118434 4 8.3 8.56771912240171 -0.267719122401711 5 7.5 7.92848770517152 -0.428487705171517 6 7.2 7.19347708927432 0.00652291072568439 7 7.4 7.35470582434135 0.0452941756586532 8 8.8 8.5426313505788 0.257368649421206 9 9.3 9.36235925205818 -0.0623592520581825 10 9.3 9.33594402209309 -0.0359440220930902 11 8.7 8.97477409417602 -0.274774094176023 12 8.2 8.2526854030149 -0.0526854030148971 13 8.3 8.0988233642646 0.201176635735407 14 8.5 8.53300487664398 -0.0330048766439838 15 8.6 8.53493209057959 0.0650679094204113 16 8.5 8.50454666362957 -0.00454666362957453 17 8.2 8.25766952655437 -0.0576695265543664 18 8.1 7.95073104571412 0.149268954285878 19 7.9 8.04187509693505 -0.141875096935046 20 8.6 8.56642547543238 0.0335745245676221 21 8.7 8.6468983799558 0.0531016200441935 22 8.7 8.53642441277066 0.163575587229343 23 8.5 8.46712449609877 0.0328755039012277 24 8.4 8.26904795973063 0.130952040269375 25 8.5 8.42437924761961 0.0756207523803906 26 8.7 8.56578426424685 0.134215735753146 27 8.7 8.56589850916854 0.134101490831458 28 8.6 8.36677762591813 0.233222374081874 29 8.5 8.2473703726351 0.252629627364891 30 8.3 8.16051306074451 0.13948693925549 31 8 8.0224228148233 -0.0224228148233045 32 8.2 8.45721069969013 -0.257210699690129 33 8.1 7.89762090508827 0.202379094911727 34 8.1 7.86357701329794 0.236422986702057 35 8 7.89148855999962 0.108511440000383 36 7.9 7.86441369119927 0.0355863088007312 37 7.9 7.970686005148 -0.0706860051479941 38 8 7.9374634161796 0.0625365838203962 39 8 7.87591618718651 0.124083812813491 40 7.9 7.75168908632468 0.148310913675323 41 8 7.62276374571859 0.377236254281407 42 7.7 7.84618281122004 -0.146182811220036 43 7.2 7.41404462590915 -0.214044625909147 44 7.5 7.61435640027947 -0.114356400279472 45 7.3 7.34972102957426 -0.0497210295742588 46 7 7.1323291188077 -0.132329118807700 47 7 6.7674536705425 0.232546329457503 48 7 7.11385294605521 -0.113852946055209 49 7.2 7.30354236208573 -0.103542362085727 50 7.3 7.45403275122415 -0.154032751224146 51 7.1 7.24179147294693 -0.141791472946926 52 6.8 6.90926750172591 -0.109267501725913 53 6.4 6.54370864992042 -0.143708649920416 54 6.1 6.24909599304702 -0.149095993047016 55 6.5 6.16695163799116 0.333048362008845 56 7.7 7.61937607401923 0.0806239259807724 57 7.9 8.04340043332348 -0.143400433323479 58 7.5 7.73172543303061 -0.231725433030609 59 6.9 6.9991591791831 -0.0991591791830919 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.549529623176074 0.900940753647853 0.450470376823926 20 0.389849387565171 0.779698775130342 0.610150612434829 21 0.296836948123029 0.593673896246057 0.703163051876971 22 0.193698959118506 0.387397918237011 0.806301040881494 23 0.155426272334262 0.310852544668524 0.844573727665738 24 0.143456364331348 0.286912728662695 0.856543635668652 25 0.141087436726785 0.282174873453569 0.858912563273215 26 0.0829901971504919 0.165980394300984 0.917009802849508 27 0.0464348004442418 0.0928696008884837 0.953565199555758 28 0.0393116977762414 0.0786233955524828 0.960688302223759 29 0.0802396876416093 0.160479375283219 0.91976031235839 30 0.0621945143092876 0.124389028618575 0.937805485690712 31 0.0396156494741542 0.0792312989483084 0.960384350525846 32 0.221079219461420 0.442158438922839 0.77892078053858 33 0.177487635271593 0.354975270543185 0.822512364728407 34 0.182218913083658 0.364437826167316 0.817781086916342 35 0.265419641393698 0.530839282787397 0.734580358606302 36 0.294500974875637 0.589001949751275 0.705499025124363 37 0.314284998854232 0.628569997708464 0.685715001145768 38 0.230357251816582 0.460714503633165 0.769642748183418 39 0.138761099948727 0.277522199897454 0.861238900051273 40 0.154873972249608 0.309747944499216 0.845126027750392 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 0 0 OK 10% type I error level 3 0.136363636363636 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = 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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