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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 30 Dec 2009 04:46:58 -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/30/t1262173758zbw2gney4q4124r.htm/, Retrieved Wed, 30 Dec 2009 12:49:31 +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/30/t1262173758zbw2gney4q4124r.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 «

612613 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1 506174 1 501866 1 516141 1 528222 1 532638 1 536322 1 536535 1 523597 1 536214 1 586570 1 596594 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation wlh[t] = + 593211.196565783 -69585.655196409dummies[t] + 48.1465422612516t + 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) 593211.196565783 7221.910883 82.1405 0 0 dummies -69585.655196409 12981.857633 -5.3602 2e-06 1e-06 t 48.1465422612516 373.97218 0.1287 0.898014 0.449007 Multiple Linear Regression - Regression Statistics Multiple R 0.81014860836982 R-squared 0.656340767643556 Adjusted R-squared 0.644282548964383 F-TEST (value) 54.4309889467476 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 6.01740879346835e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25239.6592207947 Sum Squared Residuals 36311302662.1652 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 612613 593259.343108045 19353.6568919552 2 611324 593307.489650306 18016.5103496943 3 594167 593355.636192567 811.363807432979 4 595454 593403.782734828 2050.21726517172 5 590865 593451.929277090 -2586.92927708953 6 589379 593500.075819351 -4121.07581935078 7 584428 593548.222361612 -9120.22236161204 8 573100 593596.368903873 -20496.3689038733 9 567456 593644.515446134 -26188.5154461345 10 569028 593692.661988396 -24664.6619883958 11 620735 593740.808530657 26994.1914693430 12 628884 593788.955072918 35095.0449270817 13 628232 593837.10161518 34394.8983848205 14 612117 593885.248157441 18231.7518425592 15 595404 593933.394699702 1470.60530029795 16 597141 593981.541241963 3159.4587580367 17 593408 594029.687784225 -621.687784224551 18 590072 594077.834326486 -4005.8343264858 19 579799 594125.980868747 -14326.9808687471 20 574205 594174.127411008 -19969.1274110083 21 572775 594222.27395327 -21447.2739532696 22 572942 594270.420495531 -21328.4204955308 23 619567 594318.567037792 25248.4329622079 24 625809 594366.713580053 31442.2864199467 25 619916 594414.860122315 25501.1398776854 26 587625 594463.006664576 -6838.00666457582 27 565742 594511.153206837 -28769.1532068371 28 557274 594559.299749098 -37285.2997490983 29 560576 525021.79109495 35554.2089050494 30 548854 525069.937637212 23784.0623627882 31 531673 525118.084179473 6554.9158205269 32 525919 525166.230721734 752.769278265644 33 511038 525214.377263996 -14176.3772639956 34 498662 525262.523806257 -26600.5238062569 35 555362 525310.670348518 30051.3296514819 36 564591 525358.816890779 39232.1831092206 37 541657 525406.963433041 16250.0365669594 38 527070 525455.109975302 1614.89002469813 39 509846 525503.256517563 -15657.2565175631 40 514258 525551.403059824 -11293.4030598244 41 516922 525599.549602086 -8677.54960208562 42 507561 525647.696144347 -18086.6961443469 43 492622 525695.842686608 -33073.8426866081 44 490243 525743.989228869 -35500.9892288694 45 469357 525792.135771131 -56435.1357711306 46 477580 525840.282313392 -48260.2823133919 47 528379 525888.428855653 2490.57114434687 48 533590 525936.575397914 7653.42460208562 49 517945 525984.721940176 -8039.72194017564 50 506174 526032.868482437 -19858.8684824369 51 501866 526081.015024698 -24215.0150246981 52 516141 526129.161566959 -9988.1615669594 53 528222 526177.308109221 2044.69189077936 54 532638 526225.454651482 6412.5453485181 55 536322 526273.601193743 10048.3988062569 56 536535 526321.747736004 10213.2522639956 57 523597 526369.894278266 -2772.89427826565 58 536214 526418.040820527 9795.9591794731 59 586570 526466.187362788 60103.8126372118 60 596594 526514.333905049 70079.6660949506 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0116881636478217 0.0233763272956433 0.988311836352178 7 0.00214546189700008 0.00429092379400017 0.997854538103 8 0.000473313060766402 0.000946626121532803 0.999526686939234 9 9.06751635414292e-05 0.000181350327082858 0.999909324836459 10 2.13026085673464e-05 4.26052171346927e-05 0.999978697391433 11 0.115022841224952 0.230045682449904 0.884977158775048 12 0.293181040462376 0.586362080924752 0.706818959537624 13 0.351714778898510 0.703429557797021 0.64828522110149 14 0.280814533068622 0.561629066137245 0.719185466931378 15 0.213549168730537 0.427098337461074 0.786450831269463 16 0.154752217077126 0.309504434154252 0.845247782922874 17 0.110594869411479 0.221189738822958 0.889405130588521 18 0.078114220204682 0.156228440409364 0.921885779795318 19 0.0624677276479687 0.124935455295937 0.937532272352031 20 0.0526402237208441 0.105280447441688 0.947359776279156 21 0.0421543686245236 0.0843087372490473 0.957845631375476 22 0.0316814471843302 0.0633628943686605 0.96831855281567 23 0.045000896654084 0.090001793308168 0.954999103345916 24 0.0709728639265808 0.141945727853162 0.92902713607342 25 0.0866027562281708 0.173205512456342 0.913397243771829 26 0.068116201601728 0.136232403203456 0.931883798398272 27 0.0695056931514705 0.139011386302941 0.93049430684853 28 0.0754645992788615 0.150929198557723 0.924535400721138 29 0.0761942599373463 0.152388519874693 0.923805740062654 30 0.071869648790307 0.143739297580614 0.928130351209693 31 0.063183549232244 0.126367098464488 0.936816450767756 32 0.052511880308149 0.105023760616298 0.947488119691851 33 0.046880526093474 0.093761052186948 0.953119473906526 34 0.0483947607499057 0.0967895214998113 0.951605239250094 35 0.0765962740403482 0.153192548080696 0.923403725959652 36 0.218756915834312 0.437513831668625 0.781243084165688 37 0.315333206884396 0.630666413768792 0.684666793115604 38 0.379855427325376 0.759710854650753 0.620144572674624 39 0.392351764712110 0.784703529424221 0.60764823528789 40 0.428838985132774 0.857677970265548 0.571161014867226 41 0.51531463087489 0.969370738250221 0.484685369125110 42 0.567332633359442 0.865334733281117 0.432667366640558 43 0.55472084472074 0.890558310558519 0.445279155279259 44 0.516355235027764 0.967289529944473 0.483644764972236 45 0.566716183220733 0.866567633558533 0.433283816779266 46 0.57990423321638 0.84019153356724 0.42009576678362 47 0.608714281728958 0.782571436542085 0.391285718271042 48 0.75885315079308 0.482293698413841 0.241146849206921 49 0.77505026754431 0.449899464911381 0.224949732455690 50 0.697281222571394 0.605437554857211 0.302718777428606 51 0.578309243032331 0.843381513935338 0.421690756967669 52 0.456216345560693 0.912432691121385 0.543783654439307 53 0.382635319080676 0.765270638161353 0.617364680919324 54 0.336138054128371 0.672276108256743 0.663861945871629 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.0816326530612245 NOK 5% type I error level 5 0.102040816326531 NOK 10% type I error level 10 0.204081632653061 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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