*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, 20 Nov 2009 07:57:48 -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/20/t1258729114h4rh5gotdzuhttx.htm/, Retrieved Fri, 20 Nov 2009 15:58:46 +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/20/t1258729114h4rh5gotdzuhttx.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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22 0 22 20 0 22 21 0 20 20 0 21 21 0 20 21 0 21 21 0 21 19 0 21 21 0 19 21 0 21 22 0 21 19 0 22 24 0 19 22 0 24 22 0 22 22 0 22 24 0 22 22 0 24 23 0 22 24 0 23 21 0 24 20 0 21 22 0 20 23 0 22 23 0 23 22 0 23 20 0 22 21 1 20 21 1 21 20 1 21 20 1 20 17 1 20 18 1 17 19 1 18 19 1 19 20 1 19 21 1 20 20 1 21 21 1 20 19 1 21 22 1 19 20 1 22 18 1 20 16 1 18 17 1 16 18 1 17 19 1 18 18 1 19 20 1 18 21 1 20 18 1 21 19 1 18 19 1 19 19 1 19 21 1 19 19 1 21 19 1 19 17 1 19 16 1 17 16 1 16 17 1 16 16 1 17 15 1 16 16 1 15 16 1 16 16 1 16 18 1 16 19 1 18 16 1 19 16 1 16 16 1 16

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] = + 10.0677699988789 -0.472058006916226X[t] + 0.531978236551268Y1[t] + 1.74353611810301M1[t] -0.0263393303035021M2[t] -0.132935853998509M3[t] + 0.328484544608762M4[t] + 1.35657645102915M5[t] + 0.0193567875649408M6[t] + 0.990763891111386M7[t] -0.413799987410524M8[t] -0.0984001383469897M9[t] -0.059648819742844M10[t] + 0.557106126102756M11[t] -0.0280919064203895t + 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) 10.0677699988789 2.61959 3.8433 0.000312 0.000156 X -0.472058006916226 0.626745 -0.7532 0.454491 0.227245 Y1 0.531978236551268 0.113645 4.6811 1.9e-05 9e-06 M1 1.74353611810301 0.812681 2.1454 0.036271 0.018135 M2 -0.0263393303035021 0.823564 -0.032 0.9746 0.4873 M3 -0.132935853998509 0.812266 -0.1637 0.870588 0.435294 M4 0.328484544608762 0.81384 0.4036 0.688027 0.344014 M5 1.35657645102915 0.81273 1.6692 0.100668 0.050334 M6 0.0193567875649408 0.819414 0.0236 0.981238 0.490619 M7 0.990763891111386 0.811743 1.2205 0.227375 0.113687 M8 -0.413799987410524 0.815706 -0.5073 0.613943 0.306971 M9 -0.0984001383469897 0.81226 -0.1211 0.904011 0.452005 M10 -0.059648819742844 0.814731 -0.0732 0.941898 0.470949 M11 0.557106126102756 0.816485 0.6823 0.497848 0.248924 t -0.0280919064203895 0.015916 -1.765 0.083022 0.041511 Multiple Linear Regression - Regression Statistics Multiple R 0.853205467466476 R-squared 0.727959569714688 Adjusted R-squared 0.65994946214336 F-TEST (value) 10.7036967843524 F-TEST (DF numerator) 14 F-TEST (DF denominator) 56 p-value 3.20220516769609e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.33914328879777 Sum Squared Residuals 100.425065884198 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 22 23.4867354146894 -1.48673541468945 2 20 21.6887680598625 -1.68876805986253 3 21 20.4901231566446 0.509876843355412 4 20 21.4554298853827 -1.45542988538274 5 21 21.9234516488315 -0.92345164883147 6 21 21.0901183154981 -0.0901183154981386 7 21 22.0334335126242 -1.03343351262419 8 19 20.6007777276819 -1.60077772768189 9 21 19.8241291972225 1.17587080277750 10 21 20.8987450825088 0.101254917491207 11 22 21.487408121934 0.512591878065995 12 19 21.4341883259621 -2.43418832596213 13 24 21.5536978279909 2.44630217200906 14 22 22.4156216559204 -0.41562165592038 15 22 21.2169767527025 0.78302324729755 16 22 21.6503052448893 0.349694755110669 17 24 22.6503052448893 1.34969475511067 18 22 22.3489501481073 -0.348950148107265 19 23 22.2283088721308 0.771691127869213 20 24 21.3276313237398 2.67236867626025 21 21 22.1469175029342 -1.14691750293417 22 20 20.5616422054641 -0.561642205464119 23 22 20.6183270083381 1.38167299166194 24 23 21.0970854489175 1.90291455108255 25 23 23.3445078971513 -0.344507897151338 26 22 21.5465405423244 0.453459457675561 27 20 20.8798738756578 -0.879873875657774 28 21 19.7771878878259 1.22281211217410 29 21 21.3091661243772 -0.309166124377163 30 20 19.9438545544926 0.0561454455074385 31 20 20.3551915150674 -0.35519151506735 32 17 18.9225357301251 -1.92253573012505 33 18 17.6139089631144 0.386091036885607 34 19 18.1565466118494 0.843453388150584 35 19 19.2771878878259 -0.277187887825895 36 20 18.6919898553027 1.30801014469725 37 21 20.9394123035366 0.0605876964633657 38 20 19.673423185261 0.326576814738997 39 21 19.0067565185943 1.99324348140566 40 19 19.9720632473325 -0.972063247332488 41 22 19.9081067742300 2.09189322577005 42 20 20.1387299139992 -0.138729913999155 43 18 20.0180886380227 -2.01808863802268 44 16 17.5214763799778 -1.52147637997784 45 17 16.7448278495185 0.255172150481548 46 18 17.2874654982535 0.712534501746525 47 19 18.4081067742300 0.591893225770047 48 18 18.3548869782581 -0.354886978258075 49 20 19.5383529533894 0.461647046610574 50 21 18.8043420716651 2.19565792833494 51 18 19.2016318781009 -1.20163187810093 52 19 18.039025660634 0.960974339365988 53 19 19.5710038971853 -0.57100389718528 54 19 18.2056923273007 0.794307672699321 55 21 19.1490075244267 1.85099247557326 56 19 18.7803082125870 0.21969178741303 57 19 18.0036596821276 0.99634031787242 58 17 18.0143190943113 -1.01431909431134 59 16 17.539025660634 -1.53902566063401 60 16 16.4218493915596 -0.4218493915596 61 17 18.1372936032422 -1.13729360324222 62 16 16.8713044849666 -0.871304484966586 63 15 16.2046378182999 -1.20463781829992 64 16 16.1059880739355 -0.105988073935537 65 16 17.6379663104868 -1.63796631048680 66 16 16.2726547406022 -0.272654740602203 67 18 17.2159699377283 0.784030062271741 68 19 16.8472706258885 2.15272937411151 69 16 17.6665568050829 -1.66655680508291 70 16 16.0812815076129 -0.0812815076128598 71 16 16.6699445470381 -0.669944547038071 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.150678253935444 0.301356507870889 0.849321746064556 19 0.0610202015740142 0.122040403148028 0.938979798425986 20 0.377111645621302 0.754223291242605 0.622888354378698 21 0.383710211691481 0.767420423382961 0.616289788308519 22 0.575347474139889 0.849305051720223 0.424652525860111 23 0.55144900711186 0.897101985776279 0.448550992888139 24 0.607341139264424 0.785317721471151 0.392658860735576 25 0.652038342865371 0.695923314269259 0.347961657134629 26 0.586078614288065 0.82784277142387 0.413921385711935 27 0.707511456265643 0.584977087468713 0.292488543734356 28 0.62991538891208 0.74016922217584 0.37008461108792 29 0.563406635490622 0.873186729018756 0.436593364509378 30 0.478908669742914 0.957817339485828 0.521091330257086 31 0.41229153494486 0.82458306988972 0.58770846505514 32 0.577351901919543 0.845296196160915 0.422648098080457 33 0.497396649130457 0.994793298260914 0.502603350869543 34 0.41578634005736 0.83157268011472 0.58421365994264 35 0.347533118048977 0.695066236097955 0.652466881951023 36 0.303774971368919 0.607549942737838 0.696225028631081 37 0.232880581824874 0.465761163649748 0.767119418175126 38 0.175587396079851 0.351174792159702 0.824412603920149 39 0.22095670575049 0.44191341150098 0.77904329424951 40 0.224268803528788 0.448537607057576 0.775731196471212 41 0.279770989797058 0.559541979594116 0.720229010202942 42 0.218232578710617 0.436465157421234 0.781767421289383 43 0.539606909584226 0.920786180831548 0.460393090415774 44 0.853029762630654 0.293940474738693 0.146970237369346 45 0.828898071903608 0.342203856192785 0.171101928096392 46 0.770460078546877 0.459079842906246 0.229539921453123 47 0.680916393432516 0.638167213134969 0.319083606567484 48 0.593699594028872 0.812600811942255 0.406300405971128 49 0.494747405608444 0.989494811216888 0.505252594391556 50 0.638363157805637 0.723273684388727 0.361636842194363 51 0.545008134216622 0.909983731566755 0.454991865783378 52 0.435030829534142 0.870061659068284 0.564969170465858 53 0.356297295839447 0.712594591678894 0.643702704160553 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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