verbetering

*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: Thu, 26 Nov 2009 11:08:09 -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/26/t1259258941g4ra8qmrixahe5s.htm/, Retrieved Thu, 26 Nov 2009 19:09:12 +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/26/t1259258941g4ra8qmrixahe5s.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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7.6 4634 7.5 7.7 8.1 8 7.8 3996 7.6 7.5 7.7 8.1 7.8 4308 7.8 7.6 7.5 7.7 7.8 4143 7.8 7.8 7.6 7.5 7.5 4429 7.8 7.8 7.8 7.6 7.5 5219 7.5 7.8 7.8 7.8 7.1 4929 7.5 7.5 7.8 7.8 7.5 5755 7.1 7.5 7.5 7.8 7.5 5592 7.5 7.1 7.5 7.5 7.6 4163 7.5 7.5 7.1 7.5 7.7 4962 7.6 7.5 7.5 7.1 7.7 5208 7.7 7.6 7.5 7.5 7.9 4755 7.7 7.7 7.6 7.5 8.1 4491 7.9 7.7 7.7 7.6 8.2 5732 8.1 7.9 7.7 7.7 8.2 5731 8.2 8.1 7.9 7.7 8.2 5040 8.2 8.2 8.1 7.9 7.9 6102 8.2 8.2 8.2 8.1 7.3 4904 7.9 8.2 8.2 8.2 6.9 5369 7.3 7.9 8.2 8.2 6.7 5578 6.9 7.3 7.9 8.2 6.7 4619 6.7 6.9 7.3 7.9 6.9 4731 6.7 6.7 6.9 7.3 7 5011 6.9 6.7 6.7 6.9 7.1 5299 7 6.9 6.7 6.7 7.2 4146 7.1 7 6.9 6.7 7.1 4625 7.2 7.1 7 6.9 6.9 4736 7.1 7.2 7.1 7 7 4219 6.9 7.1 7.2 7.1 6.8 5116 7 6.9 7.1 7.2 6.4 4205 6.8 7 6.9 7.1 6.7 4121 6.4 6.8 7 6.9 6.6 5103 6.7 6.4 6.8 7 6.4 4300 6.6 6.7 6.4 6.8 6.3 4578 6.4 6.6 6.7 6.4 6.2 3809 6.3 6.4 6.6 6.7 6.5 5526 6.2 6.3 6.4 6.6 6.8 4247 6.5 6.2 6.3 6.4 6.8 3830 6.8 6.5 6.2 6.3 6.4 4394 6.8 6.8 6.5 6.2 6.1 48 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -0.153940288710229 -1.33201916470280e-05X[t] + 1.50648070929122Y1[t] -0.65589035973249Y2[t] -0.318048099574336Y3[t] + 0.479226132320903Y4[t] + 0.261087080885896M1[t] + 0.167093825083992M2[t] -0.0136708658093534M3[t] + 0.0604414740927271M4[t] + 0.119159398487352M5[t] -0.0631487681125825M6[t] -0.114763643209317M7[t] + 0.414158022941514M8[t] -0.309959829379935M9[t] -0.132693479589635M10[t] + 0.116449777839318M11[t] + 0.00303282565484625t + 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) -0.153940288710229 0.620335 -0.2482 0.805315 0.402658 X -1.33201916470280e-05 6.1e-05 -0.2186 0.828078 0.414039 Y1 1.50648070929122 0.144024 10.4599 0 0 Y2 -0.65589035973249 0.271473 -2.416 0.020472 0.010236 Y3 -0.318048099574336 0.271425 -1.1718 0.248397 0.124199 Y4 0.479226132320903 0.15291 3.134 0.003269 0.001635 M1 0.261087080885896 0.139492 1.8717 0.068763 0.034382 M2 0.167093825083992 0.148317 1.1266 0.266796 0.133398 M3 -0.0136708658093534 0.149317 -0.0916 0.927519 0.46376 M4 0.0604414740927271 0.147845 0.4088 0.68491 0.342455 M5 0.119159398487352 0.145601 0.8184 0.418103 0.209052 M6 -0.0631487681125825 0.144089 -0.4383 0.663613 0.331807 M7 -0.114763643209317 0.141841 -0.8091 0.423367 0.211683 M8 0.414158022941514 0.140606 2.9455 0.005414 0.002707 M9 -0.309959829379935 0.162573 -1.9066 0.063961 0.03198 M10 -0.132693479589635 0.174477 -0.7605 0.451516 0.225758 M11 0.116449777839318 0.155165 0.7505 0.457465 0.228732 t 0.00303282565484625 0.002601 1.1661 0.250662 0.125331 Multiple Linear Regression - Regression Statistics Multiple R 0.965407731466025 R-squared 0.932012087974376 Adjusted R-squared 0.902376331450387 F-TEST (value) 31.4489048801546 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.205821064783154 Sum Squared Residuals 1.65213011763038 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.6 7.55432285149729 0.0456771485027087 2 7.8 7.92882869955848 -0.128828699558484 3 7.8 7.85456720739761 -0.0545672073976106 4 7.8 7.67508209620819 0.124917903791812 5 7.5 7.71733626476383 -0.217336264763833 6 7.5 7.1714389860944 0.328561013905595 7 7.1 7.3234869001499 -0.223486900149903 8 7.5 7.33726105981095 0.162738940189054 9 7.5 7.33952781229602 0.160472187703976 10 7.6 7.40372463754151 0.196275362458489 11 7.7 7.47699626567036 0.223003734329639 12 7.7 7.63705203422496 0.0629479657750442 13 7.9 7.80981214165112 0.0901878583488803 14 8.1 8.03978218723178 0.0602178127682218 15 8.2 8.06356064730315 0.136439352696846 16 8.2 8.09657951211948 0.103420487880515 17 8.2 8.13418108517312 0.0658189148268819 18 7.9 8.00480011720563 -0.104800117205631 19 7.3 7.5681540578016 -0.268154057801608 20 6.9 7.38679334283643 -0.486793342836429 21 6.7 6.5492807581109 0.150719241889097 22 6.7 6.75047501942863 -0.0504750194286303 23 6.9 6.97202087343165 -0.0720208734316533 24 7 7.02808957643076 -0.0280895764307648 25 7.1 7.2119980402956 -0.111998040295607 26 7.2 7.15784520615858 0.0421547938414226 27 7.1 7.12283242058377 -0.0228324205837740 28 6.9 6.99837974124016 -0.098379741240164 29 7 6.84742772776081 0.152572272239188 30 6.8 7.01775774097348 -0.217757740973483 31 6.4 6.63011221497332 -0.230112214973319 32 6.7 6.56412135468574 0.135878645314257 33 6.6 6.65578848964908 -0.0557884896490787 34 6.4 6.53074261350347 -0.130742613503471 35 6.3 6.25640369462374 0.0435963053762581 36 6.2 6.30933262048691 -0.109332620486913 37 6.5 6.48120972969661 0.0187902703033876 38 6.8 6.86077865691997 -0.0607786569199721 39 6.8 6.92766061319125 -0.127660613191246 40 6.4 6.65718903963511 -0.257189039635111 41 6.1 6.15894659300055 -0.0589465930005492 42 5.8 5.93940554277417 -0.139405542774169 43 6.1 5.76073439763087 0.339265602369128 44 7.2 6.85129143582018 0.348708564179824 45 7.3 7.53305037977705 -0.233050379777047 46 6.9 6.91505772952639 -0.0150577295263880 47 6.1 6.29457916627424 -0.194579166274244 48 5.8 5.72552576885737 0.0744742311426342 49 6.2 6.24265723685937 -0.0426572368593701 50 7.1 7.01276525013119 0.0872347498688113 51 7.7 7.63137911152422 0.0686208884757846 52 7.9 7.77276961079705 0.127230389202949 53 7.7 7.64210832930169 0.0578916706983125 54 7.4 7.26659761295231 0.133402387047689 55 7.5 7.1175124294443 0.382487570555702 56 8 8.1605328068467 -0.160532806846705 57 8.1 8.12235256016695 -0.0223525601669478 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.593275715207907 0.813448569584186 0.406724284792093 22 0.474080237815703 0.948160475631406 0.525919762184297 23 0.345723187406401 0.691446374812803 0.654276812593598 24 0.220763749575815 0.441527499151631 0.779236250424185 25 0.316881934505349 0.633763869010698 0.683118065494651 26 0.228399821903582 0.456799643807164 0.771600178096418 27 0.160787894853512 0.321575789707023 0.839212105146488 28 0.100269539388075 0.200539078776149 0.899730460611925 29 0.237819649524832 0.475639299049663 0.762180350475168 30 0.153186097428748 0.306372194857496 0.846813902571252 31 0.215791906412596 0.431583812825192 0.784208093587404 32 0.297371763921559 0.594743527843119 0.70262823607844 33 0.325620282693481 0.651240565386962 0.674379717306519 34 0.286159262927561 0.572318525855122 0.713840737072439 35 0.418092048661877 0.836184097323755 0.581907951338122 36 0.554093298880808 0.891813402238383 0.445906701119192 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 = 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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