Workshop 7

*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, 27 Nov 2009 03:40:15 -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/27/t1259319226tck27ljj6cx866u.htm/, Retrieved Fri, 27 Nov 2009 11:53:58 +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/27/t1259319226tck27ljj6cx866u.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:

» Textbox « » Textfile « » CSV «

627 0 696 0 825 0 677 0 656 0 785 0 412 0 352 0 839 0 729 0 696 0 641 0 695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 707 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 0 344 0 792 0 852 0 649 0 629 0 685 1 617 1 715 1 715 1 629 1 916 1 531 1 357 1 917 1 828 1 708 1 858 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 648.083333333333 + 58.25X[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) 648.083333333333 20.799884 31.158 0 0 X 58.25 46.509955 1.2524 0.215443 0.107722 Multiple Linear Regression - Regression Statistics Multiple R 0.162271210903277 R-squared 0.0263319458880159 Adjusted R-squared 0.00954456564470596 F-TEST (value) 1.56855599303586 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.215443415878782 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 144.105823982749 Sum Squared Residuals 1204456.33333333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 627 648.083333333334 -21.0833333333342 2 696 648.083333333333 47.9166666666667 3 825 648.083333333333 176.916666666667 4 677 648.083333333333 28.9166666666667 5 656 648.083333333333 7.91666666666669 6 785 648.083333333333 136.916666666667 7 412 648.083333333333 -236.083333333333 8 352 648.083333333333 -296.083333333333 9 839 648.083333333333 190.916666666667 10 729 648.083333333333 80.9166666666667 11 696 648.083333333333 47.9166666666667 12 641 648.083333333333 -7.08333333333331 13 695 648.083333333333 46.9166666666667 14 638 648.083333333333 -10.0833333333333 15 762 648.083333333333 113.916666666667 16 635 648.083333333333 -13.0833333333333 17 721 648.083333333333 72.9166666666667 18 854 648.083333333333 205.916666666667 19 418 648.083333333333 -230.083333333333 20 367 648.083333333333 -281.083333333333 21 824 648.083333333333 175.916666666667 22 687 648.083333333333 38.9166666666667 23 601 648.083333333333 -47.0833333333333 24 676 648.083333333333 27.9166666666667 25 740 648.083333333333 91.9166666666667 26 691 648.083333333333 42.9166666666667 27 683 648.083333333333 34.9166666666667 28 594 648.083333333333 -54.0833333333333 29 729 648.083333333333 80.9166666666667 30 731 648.083333333333 82.9166666666667 31 386 648.083333333333 -262.083333333333 32 331 648.083333333333 -317.083333333333 33 707 648.083333333333 58.9166666666667 34 715 648.083333333333 66.9166666666667 35 657 648.083333333333 8.91666666666669 36 653 648.083333333333 4.91666666666669 37 642 648.083333333333 -6.08333333333331 38 643 648.083333333333 -5.08333333333331 39 718 648.083333333333 69.9166666666667 40 654 648.083333333333 5.91666666666669 41 632 648.083333333333 -16.0833333333333 42 731 648.083333333333 82.9166666666667 43 392 648.083333333333 -256.083333333333 44 344 648.083333333333 -304.083333333333 45 792 648.083333333333 143.916666666667 46 852 648.083333333333 203.916666666667 47 649 648.083333333333 0.916666666666687 48 629 648.083333333333 -19.0833333333333 49 685 706.333333333333 -21.3333333333333 50 617 706.333333333333 -89.3333333333333 51 715 706.333333333333 8.66666666666666 52 715 706.333333333333 8.66666666666666 53 629 706.333333333333 -77.3333333333333 54 916 706.333333333333 209.666666666667 55 531 706.333333333333 -175.333333333333 56 357 706.333333333333 -349.333333333333 57 917 706.333333333333 210.666666666667 58 828 706.333333333333 121.666666666667 59 708 706.333333333333 1.66666666666666 60 858 706.333333333333 151.666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.213097395454698 0.426194790909395 0.786902604545302 6 0.149692049435052 0.299384098870105 0.850307950564948 7 0.568665741360022 0.862668517279956 0.431334258639978 8 0.835095199931883 0.329809600136235 0.164904800068118 9 0.86469608960581 0.270607820788381 0.135303910394190 10 0.81260599380856 0.374788012382882 0.187394006191441 11 0.739191645652075 0.52161670869585 0.260808354347925 12 0.652008140887032 0.695983718225935 0.347991859112968 13 0.563121272315102 0.873757455369796 0.436878727684898 14 0.469605246252464 0.939210492504927 0.530394753747536 15 0.421971716623084 0.843943433246169 0.578028283376916 16 0.338309452993678 0.676618905987357 0.661690547006322 17 0.27365347649963 0.54730695299926 0.72634652350037 18 0.332070065671589 0.664140131343178 0.667929934328411 19 0.482514846138422 0.965029692276845 0.517485153861578 20 0.694240635006335 0.61151872998733 0.305759364993665 21 0.71714982082817 0.565700358343659 0.282850179171830 22 0.650427989577829 0.699144020844343 0.349572010422171 23 0.583679100261713 0.832641799476575 0.416320899738287 24 0.508309047225072 0.983381905549856 0.491690952774928 25 0.459447886919193 0.918895773838385 0.540552113080807 26 0.389860769790743 0.779721539581486 0.610139230209257 27 0.322342391110202 0.644684782220404 0.677657608889798 28 0.266050504005632 0.532101008011264 0.733949495994368 29 0.224944099768100 0.449888199536199 0.7750559002319 30 0.189546590702056 0.379093181404112 0.810453409297944 31 0.319383026178417 0.638766052356834 0.680616973821583 32 0.582644265001128 0.834711469997744 0.417355734998872 33 0.518382286984269 0.963235426031462 0.481617713015731 34 0.4576565235588 0.9153130471176 0.5423434764412 35 0.382431141110678 0.764862282221355 0.617568858889322 36 0.310918422343325 0.62183684468665 0.689081577656675 37 0.245447541312115 0.49089508262423 0.754552458687885 38 0.187882472275064 0.375764944550128 0.812117527724936 39 0.150678264648880 0.301356529297759 0.84932173535112 40 0.109232702885476 0.218465405770951 0.890767297114524 41 0.076221055346219 0.152442110692438 0.923778944653781 42 0.0606108132704026 0.121221626540805 0.939389186729597 43 0.109919774524394 0.219839549048788 0.890080225475606 44 0.33450827191118 0.66901654382236 0.66549172808882 45 0.2898114626117 0.5796229252234 0.7101885373883 46 0.324839429570641 0.649678859141283 0.675160570429359 47 0.245845296811658 0.491690593623316 0.754154703188342 48 0.176878057249624 0.353756114499247 0.823121942750376 49 0.120827171477645 0.24165434295529 0.879172828522355 50 0.0879536778627967 0.175907355725593 0.912046322137203 51 0.0534413782754709 0.106882756550942 0.94655862172453 52 0.0296614496878911 0.0593228993757822 0.97033855031211 53 0.0175548174306988 0.0351096348613977 0.982445182569301 54 0.0216013393094702 0.0432026786189405 0.97839866069053 55 0.0203794627474820 0.0407589254949641 0.979620537252518 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 3 0.0588235294117647 NOK 10% type I error level 4 0.0784313725490196 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/10jnxq1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/10jnxq1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/1hf901259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/1hf901259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/2gf1g1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/2gf1g1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/312se1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/312se1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/4bcxu1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/4bcxu1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/5tpk91259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/5tpk91259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/6f2lh1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/6f2lh1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/78ysh1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/78ysh1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/8jsok1259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/8jsok1259318410.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/9k2731259318410.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259319226tck27ljj6cx866u/9k2731259318410.ps (open in new window)

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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