Q3

*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: Mon, 01 Dec 2008 11:46:16 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/01/t1228157236ac5clq6c67mz8sg.htm/, Retrieved Mon, 01 Dec 2008 18:47:16 +0000

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/2008/Dec/01/t1228157236ac5clq6c67mz8sg.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

12192.5 0 11268.8 0 9097.4 0 12639.8 0 13040.1 0 11687.3 0 11191.7 0 11391.9 0 11793.1 0 13933.2 0 12778.1 0 11810.3 0 13698.4 0 11956.6 0 10723.8 0 13938.9 0 13979.8 0 13807.4 0 12973.9 0 12509.8 0 12934.1 0 14908.3 0 13772.1 0 13012.6 0 14049.9 0 11816.5 0 11593.2 0 14466.2 0 13615.9 0 14733.9 0 13880.7 0 13527.5 0 13584 0 16170.2 0 13260.6 0 14741.9 0 15486.5 0 13154.5 0 12621.2 0 15031.6 0 15452.4 0 15428 0 13105.9 0 14716.8 1 14180 1 16202.2 1 14392.4 1 15140.6 1 15960.1 1 14351.3 1 13230.2 1 15202.1 1 17157.3 1 16159.1 1 13405.7 1 17224.7 1 17338.4 1 17370.6 1 18817.8 1 16593.2 1 17979.5 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 13180.4767441860 + 2676.30103359173x[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) 13180.4767441860 229.938374 57.3218 0 0 x 2676.30103359173 423.292059 6.3226 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.635523832389632 R-squared 0.403890541535205 Adjusted R-squared 0.393786991391734 F-TEST (value) 39.9751113024562 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 3.74717391560253e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1507.80675226205 Sum Squared Residuals 134135390.927855 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12192.5 13180.4767441860 -987.976744186035 2 11268.8 13180.4767441860 -1911.67674418605 3 9097.4 13180.4767441860 -4083.07674418605 4 12639.8 13180.4767441860 -540.676744186047 5 13040.1 13180.4767441860 -140.376744186046 6 11687.3 13180.4767441860 -1493.17674418605 7 11191.7 13180.4767441860 -1988.77674418605 8 11391.9 13180.4767441860 -1788.57674418605 9 11793.1 13180.4767441860 -1387.37674418605 10 13933.2 13180.4767441860 752.723255813954 11 12778.1 13180.4767441860 -402.376744186046 12 11810.3 13180.4767441860 -1370.17674418605 13 13698.4 13180.4767441860 517.923255813953 14 11956.6 13180.4767441860 -1223.87674418605 15 10723.8 13180.4767441860 -2456.67674418605 16 13938.9 13180.4767441860 758.423255813953 17 13979.8 13180.4767441860 799.323255813953 18 13807.4 13180.4767441860 626.923255813953 19 12973.9 13180.4767441860 -206.576744186047 20 12509.8 13180.4767441860 -670.676744186047 21 12934.1 13180.4767441860 -246.376744186046 22 14908.3 13180.4767441860 1727.82325581395 23 13772.1 13180.4767441860 591.623255813954 24 13012.6 13180.4767441860 -167.876744186046 25 14049.9 13180.4767441860 869.423255813953 26 11816.5 13180.4767441860 -1363.97674418605 27 11593.2 13180.4767441860 -1587.27674418605 28 14466.2 13180.4767441860 1285.72325581395 29 13615.9 13180.4767441860 435.423255813953 30 14733.9 13180.4767441860 1553.42325581395 31 13880.7 13180.4767441860 700.223255813954 32 13527.5 13180.4767441860 347.023255813953 33 13584 13180.4767441860 403.523255813953 34 16170.2 13180.4767441860 2989.72325581395 35 13260.6 13180.4767441860 80.1232558139536 36 14741.9 13180.4767441860 1561.42325581395 37 15486.5 13180.4767441860 2306.02325581395 38 13154.5 13180.4767441860 -25.9767441860467 39 12621.2 13180.4767441860 -559.276744186046 40 15031.6 13180.4767441860 1851.12325581395 41 15452.4 13180.4767441860 2271.92325581395 42 15428 13180.4767441860 2247.52325581395 43 13105.9 13180.4767441860 -74.576744186047 44 14716.8 15856.7777777778 -1139.97777777778 45 14180 15856.7777777778 -1676.77777777778 46 16202.2 15856.7777777778 345.422222222223 47 14392.4 15856.7777777778 -1464.37777777778 48 15140.6 15856.7777777778 -716.177777777777 49 15960.1 15856.7777777778 103.322222222222 50 14351.3 15856.7777777778 -1505.47777777778 51 13230.2 15856.7777777778 -2626.57777777778 52 15202.1 15856.7777777778 -654.677777777777 53 17157.3 15856.7777777778 1300.52222222222 54 16159.1 15856.7777777778 302.322222222222 55 13405.7 15856.7777777778 -2451.07777777778 56 17224.7 15856.7777777778 1367.92222222222 57 17338.4 15856.7777777778 1481.62222222222 58 17370.6 15856.7777777778 1513.82222222222 59 18817.8 15856.7777777778 2961.02222222222 60 16593.2 15856.7777777778 736.422222222223 61 17979.5 15856.7777777778 2122.72222222222 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.800014570117843 0.399970859764314 0.199985429882157 6 0.682667212379944 0.634665575240112 0.317332787620056 7 0.582240661556846 0.835518676886309 0.417759338443154 8 0.477773019105055 0.95554603821011 0.522226980894945 9 0.377249054384332 0.754498108768665 0.622750945615668 10 0.530862708551112 0.938274582897777 0.469137291448888 11 0.466245287987984 0.932490575975968 0.533754712012016 12 0.390443985153732 0.780887970307464 0.609556014846268 13 0.423628160856432 0.847256321712863 0.576371839143568 14 0.357165990482447 0.714331980964893 0.642834009517553 15 0.424296349790759 0.848592699581517 0.575703650209241 16 0.480403332345143 0.960806664690286 0.519596667654857 17 0.513598562117996 0.972802875764007 0.486401437882004 18 0.508556047731945 0.98288790453611 0.491443952268055 19 0.448330921118741 0.896661842237483 0.551669078881259 20 0.391745568980629 0.783491137961258 0.608254431019371 21 0.337666247178069 0.675332494356137 0.662333752821932 22 0.445698435466904 0.891396870933808 0.554301564533096 23 0.41021635394086 0.82043270788172 0.58978364605914 24 0.352529124265739 0.705058248531479 0.647470875734261 25 0.331449826128627 0.662899652257254 0.668550173871373 26 0.340164073563357 0.680328147126713 0.659835926436643 27 0.390756966871206 0.781513933742413 0.609243033128794 28 0.398872269927638 0.797744539855275 0.601127730072362 29 0.354493821969115 0.70898764393823 0.645506178030885 30 0.371065816476867 0.742131632953734 0.628934183523133 31 0.32807189926234 0.65614379852468 0.67192810073766 32 0.281714253078811 0.563428506157621 0.71828574692119 33 0.239884462840986 0.479768925681972 0.760115537159014 34 0.399209388073467 0.798418776146934 0.600790611926533 35 0.348651399843662 0.697302799687323 0.651348600156338 36 0.327856549772724 0.655713099545449 0.672143450227276 37 0.368082750962315 0.736165501924631 0.631917249037685 38 0.317429098603845 0.634858197207691 0.682570901396155 39 0.316088985633628 0.632177971267256 0.683911014366372 40 0.294197304688033 0.588394609376066 0.705802695311967 41 0.301033474960008 0.602066949920015 0.698966525039992 42 0.33297511962961 0.66595023925922 0.66702488037039 43 0.261330764740277 0.522661529480555 0.738669235259723 44 0.219738158333872 0.439476316667744 0.780261841666128 45 0.213039905418810 0.426079810837619 0.78696009458119 46 0.168703483274228 0.337406966548456 0.831296516725772 47 0.158186300969795 0.31637260193959 0.841813699030205 48 0.122546437787021 0.245092875574043 0.877453562212979 49 0.0851356235030285 0.170271247006057 0.914864376496971 50 0.0886586844442925 0.177317368888585 0.911341315555708 51 0.253056968747921 0.506113937495842 0.746943031252079 52 0.245791477275017 0.491582954550034 0.754208522724983 53 0.188643042246242 0.377286084492484 0.811356957753758 54 0.131289580848299 0.262579161696598 0.868710419151701 55 0.833444196653954 0.333111606692091 0.166555803346046 56 0.71679509370519 0.566409812589619 0.283204906294809 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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