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: Sat, 22 Nov 2008 04:07:40 -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/Nov/22/t1227352104wr0q1ue2rfkq25g.htm/, Retrieved Sat, 22 Nov 2008 11:08:25 +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/Nov/22/t1227352104wr0q1ue2rfkq25g.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}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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15859,4 0 15258,9 0 15498,6 0 15106,5 0 15023,6 0 12083 0 15761,3 0 16942,6 0 15070,3 0 13659,6 0 14768,9 0 14725,1 0 15998,1 0 15370,6 0 14956,9 0 15469,7 0 15101,8 0 11703,7 0 16283,6 0 16726,5 0 14968,9 0 14861 0 14583,3 0 15305,8 0 17903,9 0 16379,4 0 15420,3 0 17870,5 0 15912,8 0 13866,5 0 17823,2 0 17872 0 17422 0 16704,5 0 15991,2 0 16583,6 0 19123,5 0 17838,7 0 17209,4 0 18586,5 0 16258,1 0 15141,6 1 19202,1 1 17746,5 1 19090,1 1 18040,3 1 17515,5 1 17751,8 1 21072,4 1 17170 1 19439,5 1 19795,4 1 17574,9 1 16165,4 1 19464,6 1 19932,1 1 19961,2 1 17343,4 1 18924,2 1 18574,1 1 21350,6 1 18594,6 1 19823,1 1 20844,4 1 19640,2 1 17735,4 1 19813,6 1 22238,5 1 20682,2 1 17818,6 1 21872,1 1 22117 1 21865,9 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 15850.0926829268 + 3346.82294207317x[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) 15850.0926829268 258.070079 61.4178 0 0 x 3346.82294207317 389.784079 8.5864 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.713733736147193 R-squared 0.509415846114632 Adjusted R-squared 0.502506210144415 F-TEST (value) 73.7254246548496 F-TEST (DF numerator) 1 F-TEST (DF denominator) 71 p-value 1.36779476633819e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1652.45477903647 Sum Squared Residuals 193873082.569992 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15859.4 15850.0926829268 9.30731707316702 2 15258.9 15850.0926829268 -591.192682926832 3 15498.6 15850.0926829268 -351.492682926829 4 15106.5 15850.0926829268 -743.59268292683 5 15023.6 15850.0926829268 -826.492682926829 6 12083 15850.0926829268 -3767.09268292683 7 15761.3 15850.0926829268 -88.7926829268298 8 16942.6 15850.0926829268 1092.50731707317 9 15070.3 15850.0926829268 -779.79268292683 10 13659.6 15850.0926829268 -2190.49268292683 11 14768.9 15850.0926829268 -1081.19268292683 12 14725.1 15850.0926829268 -1124.99268292683 13 15998.1 15850.0926829268 148.007317073171 14 15370.6 15850.0926829268 -479.492682926829 15 14956.9 15850.0926829268 -893.19268292683 16 15469.7 15850.0926829268 -380.392682926828 17 15101.8 15850.0926829268 -748.29268292683 18 11703.7 15850.0926829268 -4146.39268292683 19 16283.6 15850.0926829268 433.507317073171 20 16726.5 15850.0926829268 876.40731707317 21 14968.9 15850.0926829268 -881.19268292683 22 14861 15850.0926829268 -989.09268292683 23 14583.3 15850.0926829268 -1266.79268292683 24 15305.8 15850.0926829268 -544.29268292683 25 17903.9 15850.0926829268 2053.80731707317 26 16379.4 15850.0926829268 529.307317073171 27 15420.3 15850.0926829268 -429.79268292683 28 17870.5 15850.0926829268 2020.40731707317 29 15912.8 15850.0926829268 62.7073170731702 30 13866.5 15850.0926829268 -1983.59268292683 31 17823.2 15850.0926829268 1973.10731707317 32 17872 15850.0926829268 2021.90731707317 33 17422 15850.0926829268 1571.90731707317 34 16704.5 15850.0926829268 854.40731707317 35 15991.2 15850.0926829268 141.107317073172 36 16583.6 15850.0926829268 733.50731707317 37 19123.5 15850.0926829268 3273.40731707317 38 17838.7 15850.0926829268 1988.60731707317 39 17209.4 15850.0926829268 1359.30731707317 40 18586.5 15850.0926829268 2736.40731707317 41 16258.1 15850.0926829268 408.007317073171 42 15141.6 19196.915625 -4055.315625 43 19202.1 19196.915625 5.18437499999872 44 17746.5 19196.915625 -1450.415625 45 19090.1 19196.915625 -106.815625000001 46 18040.3 19196.915625 -1156.615625 47 17515.5 19196.915625 -1681.415625 48 17751.8 19196.915625 -1445.115625 49 21072.4 19196.915625 1875.484375 50 17170 19196.915625 -2026.915625 51 19439.5 19196.915625 242.584375 52 19795.4 19196.915625 598.484375000001 53 17574.9 19196.915625 -1622.01562500000 54 16165.4 19196.915625 -3031.515625 55 19464.6 19196.915625 267.684374999999 56 19932.1 19196.915625 735.184374999998 57 19961.2 19196.915625 764.284375 58 17343.4 19196.915625 -1853.515625 59 18924.2 19196.915625 -272.715624999999 60 18574.1 19196.915625 -622.815625000001 61 21350.6 19196.915625 2153.684375 62 18594.6 19196.915625 -602.315625000001 63 19823.1 19196.915625 626.184374999998 64 20844.4 19196.915625 1647.484375 65 19640.2 19196.915625 443.284375000001 66 17735.4 19196.915625 -1461.51562500000 67 19813.6 19196.915625 616.684374999998 68 22238.5 19196.915625 3041.584375 69 20682.2 19196.915625 1485.284375 70 17818.6 19196.915625 -1378.315625 71 21872.1 19196.915625 2675.184375 72 22117 19196.915625 2920.084375 73 21865.9 19196.915625 2668.984375 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0158817140123052 0.0317634280246103 0.984118285987695 6 0.506530966952173 0.986938066095654 0.493469033047827 7 0.399019602758041 0.798039205516082 0.600980397241959 8 0.436705389224376 0.873410778448752 0.563294610775624 9 0.320467670095285 0.640935340190569 0.679532329904715 10 0.317218861004779 0.634437722009557 0.682781138995221 11 0.232190775742096 0.464381551484192 0.767809224257904 12 0.165442541139599 0.330885082279199 0.8345574588604 13 0.129892270981919 0.259784541963838 0.870107729018081 14 0.086708947923399 0.173417895846798 0.913291052076601 15 0.0564153905601615 0.112830781120323 0.943584609439838 16 0.0359161260175171 0.0718322520350342 0.964083873982483 17 0.0219305424881358 0.0438610849762716 0.978069457511864 18 0.193416285477887 0.386832570955773 0.806583714522113 19 0.175780887284238 0.351561774568475 0.824219112715762 20 0.179191448622643 0.358382897245286 0.820808551377357 21 0.142064719794942 0.284129439589885 0.857935280205058 22 0.114266878038460 0.228533756076919 0.88573312196154 23 0.0988868295203956 0.197773659040791 0.901113170479604 24 0.0773544824404538 0.154708964880908 0.922645517559546 25 0.147088944191296 0.294177888382592 0.852911055808704 26 0.127423457272499 0.254846914544999 0.8725765427275 27 0.102938903366966 0.205877806733932 0.897061096633034 28 0.151096350523886 0.302192701047771 0.848903649476114 29 0.122485854441537 0.244971708883074 0.877514145558463 30 0.172114956191379 0.344229912382758 0.827885043808621 31 0.212867394292265 0.425734788584531 0.787132605707735 32 0.248370478104585 0.49674095620917 0.751629521895415 33 0.245608042270772 0.491216084541544 0.754391957729228 34 0.213961489091492 0.427922978182984 0.786038510908508 35 0.184980974928934 0.369961949857869 0.815019025071066 36 0.160665082039873 0.321330164079745 0.839334917960127 37 0.262232385950252 0.524464771900503 0.737767614049748 38 0.258799524815821 0.517599049631642 0.741200475184179 39 0.227154678118856 0.454309356237712 0.772845321881144 40 0.274927649106148 0.549855298212295 0.725072350893852 41 0.221895861907239 0.443791723814478 0.778104138092761 42 0.352310456381015 0.704620912762031 0.647689543618985 43 0.375319053863291 0.750638107726583 0.624680946136709 44 0.347530501344624 0.695061002689248 0.652469498655376 45 0.30679260126306 0.61358520252612 0.69320739873694 46 0.271099639584496 0.542199279168991 0.728900360415505 47 0.262565702166336 0.525131404332672 0.737434297833664 48 0.247100917190617 0.494201834381233 0.752899082809383 49 0.295953806474731 0.591907612949463 0.704046193525269 50 0.328442078407223 0.656884156814446 0.671557921592777 51 0.277082133894998 0.554164267789996 0.722917866105002 52 0.233017622295076 0.466035244590151 0.766982377704924 53 0.241478571466136 0.482957142932271 0.758521428533864 54 0.462537208841339 0.925074417682678 0.537462791158661 55 0.400976909601838 0.801953819203675 0.599023090398162 56 0.342702842531805 0.685405685063611 0.657297157468195 57 0.284516423106932 0.569032846213863 0.715483576893068 58 0.377811404695575 0.75562280939115 0.622188595304425 59 0.335682480362823 0.671364960725646 0.664317519637177 60 0.326873001540026 0.653746003080052 0.673126998459974 61 0.316092563425799 0.632185126851598 0.683907436574201 62 0.308900058898368 0.617800117796736 0.691099941101632 63 0.239340859212381 0.478681718424763 0.760659140787619 64 0.183016491650887 0.366032983301774 0.816983508349113 65 0.129979613697236 0.259959227394472 0.870020386302764 66 0.258715987846663 0.517431975693326 0.741284012153337 67 0.20153177315729 0.40306354631458 0.79846822684271 68 0.170119263382948 0.340238526765896 0.829880736617052 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 2 0.03125 OK 10% type I error level 3 0.046875 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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