model 3

*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: Sat, 05 Dec 2009 07:58:14 -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/Dec/05/t12600251631k0xpqazdrr5cmu.htm/, Retrieved Sat, 05 Dec 2009 15:59:35 +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/Dec/05/t12600251631k0xpqazdrr5cmu.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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6.3 2.7 6.1 2.5 6.1 2.2 6.3 2.9 6.3 3.1 6 3 6.2 2.8 6.4 2.5 6.8 1.9 7.5 1.9 7.5 1.8 7.6 2 7.6 2.6 7.4 2.5 7.3 2.5 7.1 1.6 6.9 1.4 6.8 0.8 7.5 1.1 7.6 1.3 7.8 1.2 8 1.3 8.1 1.1 8.2 1.3 8.3 1.2 8.2 1.6 8 1.7 7.9 1.5 7.6 0.9 7.6 1.5 8.3 1.4 8.4 1.6 8.4 1.7 8.4 1.4 8.4 1.8 8.6 1.7 8.9 1.4 8.8 1.2 8.3 1 7.5 1.7 7.2 2.4 7.4 2 8.8 2.1 9.3 2 9.3 1.8 8.7 2.7 8.2 2.3 8.3 1.9 8.5 2 8.6 2.3 8.5 2.8 8.2 2.4 8.1 2.3 7.9 2.7 8.6 2.7 8.7 2.9 8.7 3 8.5 2.2 8.4 2.3 8.5 2.8 8.7 2.8

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 Werkl[t] = + 7.62177873039487 -0.406930054325027Infl[t] + 0.0774000839023803M1[t] + 0.00357261962257999M2[t] -0.207390600818577M3[t] -0.494631023432735M4[t] -0.713732844960393M5[t] -0.840973267574551M6[t] -0.131936488015708M7[t] + 0.0452388926296351M8[t] + 0.0691668634964734M9[t] + 0.041926440882315M10[t] -0.113452582818344M11[t] + 0.0391018215276578t + 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) 7.62177873039487 0.23046 33.072 0 0 Infl -0.406930054325027 0.076462 -5.322 3e-06 1e-06 M1 0.0774000839023803 0.219341 0.3529 0.725759 0.36288 M2 0.00357261962257999 0.229868 0.0155 0.987666 0.493833 M3 -0.207390600818577 0.229628 -0.9032 0.371047 0.185523 M4 -0.494631023432735 0.229279 -2.1573 0.036124 0.018062 M5 -0.713732844960393 0.229031 -3.1163 0.00312 0.00156 M6 -0.840973267574551 0.228762 -3.6762 0.000607 0.000303 M7 -0.131936488015708 0.228629 -0.5771 0.566642 0.283321 M8 0.0452388926296351 0.2286 0.1979 0.84398 0.42199 M9 0.0691668634964734 0.228237 0.303 0.76319 0.381595 M10 0.041926440882315 0.22817 0.1838 0.854999 0.4275 M11 -0.113452582818344 0.228184 -0.4972 0.621367 0.310684 t 0.0391018215276578 0.002692 14.5258 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.927148263206159 R-squared 0.859603901966197 Adjusted R-squared 0.820770938680252 F-TEST (value) 22.1359337333216 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 9.9920072216264e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.360652671465877 Sum Squared Residuals 6.11330642346728 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 6.63956948914732 -0.339569489147325 2 6.1 6.6862298572602 -0.586229857260202 3 6.1 6.63644747464421 -0.536447474644211 4 6.3 6.10345783553019 0.196542164469811 5 6.3 5.84207182466518 0.457928175334816 6 6 5.79462622901119 0.205373770988814 7 6.2 6.6241508409627 -0.424150840962692 8 6.4 6.9625070594332 -0.562507059433201 9 6.8 7.26969488442271 -0.469694884422714 10 7.5 7.28155628333621 0.218443716663787 11 7.5 7.20597208659571 0.294027913404286 12 7.6 7.27714048007671 0.322859519923289 13 7.6 7.14948435291173 0.450515647088268 14 7.4 7.15545171559209 0.244548284407908 15 7.3 6.9835903166786 0.316409683321406 16 7.1 7.10168876448462 -0.00168876448461783 17 6.9 7.00307477534962 -0.103074775349623 18 6.8 7.15909420685814 -0.359094206858138 19 7.5 7.78515379164713 -0.285153791647131 20 7.6 7.92004498295513 -0.320044982955127 21 7.8 8.02376778078212 -0.223767780782126 22 8 7.99493617426312 0.00506382573687796 23 8.1 7.96004498295513 0.139955017044873 24 8.2 8.03121337643612 0.168786623563876 25 8.3 8.18840828729866 0.111591712701338 26 8.2 7.99091062281651 0.209089377183488 27 8 7.77835621847051 0.221643781529491 28 7.9 7.61160362824901 0.288396371750987 29 7.6 7.67576166084403 -0.0757616608440296 30 7.6 7.34346502716251 0.256534972837486 31 8.3 8.13229663368152 0.167703366318484 32 8.4 8.26718782498951 0.132812175010488 33 8.4 8.2895246119515 0.110475388048495 34 8.4 8.42346502716251 -0.0234650271625128 35 8.4 8.1444158032595 0.255584196740499 36 8.6 8.337663213038 0.262336786961994 37 8.9 8.57624413476555 0.323755865234449 38 8.8 8.62290450287841 0.177095497121586 39 8.3 8.53242911482992 -0.23242911482992 40 7.5 7.9994394757159 -0.499439475715902 41 7.2 7.53458843768838 -0.334588437688383 42 7.4 7.60922185833189 -0.209221858331893 43 8.8 8.3166674539859 0.483332546014109 44 9.3 8.5736376615914 0.726362338408605 45 9.3 8.7180534648509 0.581946535149104 46 8.7 8.36367781487187 0.336322185128127 47 8.2 8.41017263442888 -0.210172634428883 48 8.3 8.7254990605049 -0.425499060504893 49 8.5 8.80130796050243 -0.301307960502429 50 8.6 8.64450330145278 -0.0445033014527798 51 8.5 8.26917687537677 0.230823124623233 52 8.2 8.18381029602028 0.0161897039797223 53 8.1 8.04450330145278 0.0554966985472196 54 7.9 7.79359267863627 0.106407321363731 55 8.6 8.54173127972277 0.0582687202772301 56 8.7 8.67662247103076 0.0233775289692344 57 8.7 8.69895925799276 0.00104074200724086 58 8.5 9.03636470036628 -0.53636470036628 59 8.4 8.87939449276078 -0.479394492760775 60 8.5 8.82848386994426 -0.328483869944264 61 8.7 8.9449857753743 -0.244985775374302 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0176743188398783 0.0353486376797566 0.982325681160122 18 0.0201666676766116 0.0403333353532233 0.979833332323388 19 0.096236739087901 0.192473478175802 0.903763260912099 20 0.089673789175368 0.179347578350736 0.910326210824632 21 0.0743697366288306 0.148739473257661 0.92563026337117 22 0.218651589089328 0.437303178178656 0.781348410910672 23 0.232216131699221 0.464432263398442 0.767783868300779 24 0.220374623161972 0.440749246323943 0.779625376838028 25 0.149032220401235 0.29806444080247 0.850967779598765 26 0.0993136760177952 0.198627352035590 0.900686323982205 27 0.0696569937456013 0.139313987491203 0.930343006254399 28 0.054529322211934 0.109058644423868 0.945470677788066 29 0.0496819993099501 0.0993639986199003 0.95031800069005 30 0.0335202056155961 0.0670404112311921 0.966479794384404 31 0.0217194214010752 0.0434388428021504 0.978280578598925 32 0.0183533758734193 0.0367067517468386 0.98164662412658 33 0.0266164235106769 0.0532328470213537 0.973383576489323 34 0.070325973809434 0.140651947618868 0.929674026190566 35 0.100102788031697 0.200205576063395 0.899897211968303 36 0.102265257389802 0.204530514779604 0.897734742610198 37 0.0869301760937956 0.173860352187591 0.913069823906204 38 0.0565825683738639 0.113165136747728 0.943417431626136 39 0.0572709320803939 0.114541864160788 0.942729067919606 40 0.252823585105221 0.505647170210443 0.747176414894779 41 0.500788313544133 0.998423372911733 0.499211686455867 42 0.629424255888555 0.74115148822289 0.370575744111445 43 0.504213136375013 0.991573727249974 0.495786863624987 44 0.542181373296135 0.91563725340773 0.457818626703865 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 0.142857142857143 NOK 10% type I error level 7 0.25 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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