*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, 12 Dec 2009 06:13:05 -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/12/t12606236469ljkkidb8d6js8u.htm/, Retrieved Sat, 12 Dec 2009 14:14:18 +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/12/t12606236469ljkkidb8d6js8u.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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30.3 122.5 19 80.2 29 122.4 18 74.8 30.3 121.9 19 77.8 32 122.2 19 73 30.3 123.7 22 72 28 122.6 23 75.8 27.7 115.7 20 72.6 27 116.1 14 71.9 28.7 120.5 14 74.8 29.7 122.6 14 72.9 23 119.9 15 72.9 28 120.7 11 79.9 32 120.2 17 74 27 122.1 16 76 27.7 119.3 20 69.6 30.7 121.7 24 77.3 33 113.5 23 75.2 34.3 123.7 20 75.8 26 123.4 21 77.6 30.3 126.4 19 76.7 37.7 124.1 23 77 36.3 125.6 23 77.9 36.3 124.8 23 76.7 36.7 123 23 71.9 33.7 126.9 27 73.4 33.7 127.3 26 72.5 32.7 129 17 73.7 37.3 126.2 24 69.5 37 125.4 26 74.7 37.3 126.3 24 72.5 41.7 126.3 27 72.1 40.7 128.4 27 70.7 38.7 127.2 26 71.4 38.3 128.5 24 69.5 38.3 129 23 73.5 36.7 128.9 23 72.4 37.3 128.3 24 74.5 36.7 124.6 17 72.2 36 126.2 21 73 33.3 129.1 19 73.3 28.7 127.3 22 71.3 33.7 129.2 22 73.6 31 130.4 18 71.3 29.3 125.9 16 71.2 27.3 135.8 14 81.4 30.3 126.4 12 76.1 16.7 129.5 14 71.1 14.7 128.4 16 75.7 13.3 125.6 8 70 12.3 127.7 3 68.5 10 126.4 0 56.7 1.7 124.2 5 57.9 2.3 126.4 1 58.8 2.7 123.7 1 59.3 0 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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation indcvtr[t] = + 13.4250498085512 + 0.578408538017413handel[t] -0.0691616293850647ntdzcg[t] -0.0423978091817987`dzcg `[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) 13.4250498085512 17.043953 0.7877 0.434152 0.217076 handel 0.578408538017413 0.059885 9.6587 0 0 ntdzcg -0.0691616293850647 0.11903 -0.581 0.563501 0.28175 `dzcg ` -0.0423978091817987 0.118185 -0.3587 0.721115 0.360557 Multiple Linear Regression - Regression Statistics Multiple R 0.884289513225906 R-squared 0.78196794320131 Adjusted R-squared 0.770492571790852 F-TEST (value) 68.1431489431977 F-TEST (DF numerator) 3 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.44092278375916 Sum Squared Residuals 674.877127416195 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 19 19.0782246144281 -0.0782246144281225 2 18 18.5621578475258 -0.562157847525757 3 19 19.2214763340955 -0.221476334095520 4 19 20.3875318439822 -1.38753184398224 5 22 19.3428926944568 2.65710730554316 6 23 17.9275191744495 5.07248082555048 7 20 18.366884845183 1.633115154817 8 14 17.9640126832440 -3.96401268324405 9 14 18.5200423819521 -4.52004238195215 10 14 19.0337673357063 -5.03376733570634 11 15 15.3451665303293 -0.345166530329350 12 11 17.8850952526358 -6.88509525263577 13 17 20.4834572935706 -3.48345729357057 14 16 17.3752118892883 -1.37521188928828 15 20 18.2450964069422 1.75490359305784 16 24 19.4878709797704 4.5121290202296 17 23 21.4743713774498 1.52562862255025 18 20 21.4954151716356 -1.49541517163565 19 21 16.6390567383794 4.36094326162059 20 19 18.9568865919627 0.0431134080372923 21 23 23.3834621781227 -0.383462178122674 22 23 22.4317897525571 0.568210247442923 23 23 22.5379964270833 0.462003572916713 24 23 23.097360259256 -0.0973602592560044 25 27 21.0288075768293 5.97119242317068 26 26 21.0393009533389 4.96069904666109 27 17 20.2924402743487 -3.29244027434873 28 24 23.3248429100706 0.675157089929441 29 26 22.9861810444280 3.01381895557197 30 24 23.1907333195867 0.809266680413343 31 27 25.752690010536 1.24730998946400 32 27 25.0883989836645 1.91160101633553 33 26 23.9848973964645 2.01510260353554 34 24 23.7441797005023 0.255820299497676 35 23 23.5400076490826 -0.540007649082596 36 23 22.6681077412932 0.331892258706777 37 24 22.9676144424529 1.03238555754707 38 17 22.9739823094854 -5.97398230948536 39 21 22.4245194785116 -1.42451947851163 40 19 20.6495283578934 -1.64952835789339 41 22 18.19813563427 3.80186436573 42 22 20.8612562674073 1.13874373259269 43 18 19.3140742206164 -1.31407422061635 44 16 18.6462468191377 -2.64624681913772 45 14 16.3722719585364 -2.37227195853641 46 12 18.9823252774718 -6.98232527747179 47 14 11.1135571552503 2.88644284474973 48 16 9.83778794930274 6.16221205069726 49 8 9.4633360706928 -1.46333607069279 50 3 8.80328482473944 -5.80328482473944 51 0 8.0631494538452 -8.0631494538452 52 5 3.36363680192966 1.63636319807034 53 1 3.52036831182935 -2.52036831182935 54 1 3.91726922178509 -2.91726922178509 55 3 2.63354106181306 0.366458938186937 56 6 5.7104776491743 0.289522350825702 57 7 6.44239301916499 0.557606980835009 58 8 8.78428419829928 -0.784284198299278 59 14 8.94536976055816 5.05463023944184 60 14 7.06324668620928 6.93675331379072 61 13 9.06500890547162 3.93499109452838 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.178841008371931 0.357682016743862 0.82115899162807 8 0.378796248757972 0.757592497515943 0.621203751242028 9 0.524259154958133 0.951481690083733 0.475740845041867 10 0.657024058325499 0.685951883349002 0.342975941674501 11 0.557739304784042 0.884521390431915 0.442260695215958 12 0.74672571776533 0.50654856446934 0.25327428223467 13 0.704610952642155 0.59077809471569 0.295389047357845 14 0.63139807923657 0.73720384152686 0.36860192076343 15 0.558045635341793 0.883908729316413 0.441954364658207 16 0.689714524744369 0.620570950511263 0.310285475255631 17 0.673302173552315 0.65339565289537 0.326697826447685 18 0.619749988482496 0.760500023035009 0.380250011517504 19 0.656326621147578 0.687346757704845 0.343673378852422 20 0.575917030023166 0.848165939953669 0.424082969976834 21 0.50300559093309 0.99398881813382 0.49699440906691 22 0.425806848639789 0.851613697279577 0.574193151360211 23 0.3532186724294 0.7064373448588 0.6467813275706 24 0.289372590097419 0.578745180194838 0.710627409902581 25 0.375511272325938 0.751022544651876 0.624488727674062 26 0.388467294380137 0.776934588760273 0.611532705619863 27 0.447445110438214 0.894890220876428 0.552554889561786 28 0.374955138117742 0.749910276235484 0.625044861882258 29 0.328214187302567 0.656428374605134 0.671785812697433 30 0.261957877527423 0.523915755054846 0.738042122472577 31 0.206247386670742 0.412494773341483 0.793752613329258 32 0.176479024423948 0.352958048847897 0.823520975576052 33 0.148872545814422 0.297745091628843 0.851127454185578 34 0.127675044691701 0.255350089383401 0.872324955308299 35 0.100710323222128 0.201420646444256 0.899289676777872 36 0.0817701710174676 0.163540342034935 0.918229828982532 37 0.0660141086923885 0.132028217384777 0.933985891307612 38 0.129162521300127 0.258325042600253 0.870837478699873 39 0.0973358725814678 0.194671745162936 0.902664127418532 40 0.0729426735928428 0.145885347185686 0.927057326407157 41 0.0878783459938531 0.175756691987706 0.912121654006147 42 0.0879620001871705 0.175924000374341 0.91203799981283 43 0.110211156780190 0.220422313560379 0.88978884321981 44 0.0897337604346815 0.179467520869363 0.910266239565318 45 0.0700795675053548 0.140159135010710 0.929920432494645 46 0.200084026072857 0.400168052145715 0.799915973927143 47 0.240212070148947 0.480424140297895 0.759787929851053 48 0.560899883406796 0.878200233186407 0.439100116593204 49 0.466988038826194 0.933976077652388 0.533011961173806 50 0.428321220573537 0.856642441147073 0.571678779426463 51 0.658192432174016 0.683615135651969 0.341807567825984 52 0.580146977210436 0.839706045579128 0.419853022789564 53 0.443960587780066 0.887921175560132 0.556039412219934 54 0.446745111895736 0.893490223791471 0.553254888104264 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 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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