Multiple regression

*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, 21 Nov 2009 07:51:23 -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/21/t1258815210flisvhs15u1w6uo.htm/, Retrieved Sat, 21 Nov 2009 15:53:42 +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/21/t1258815210flisvhs15u1w6uo.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 «

562000 4814 561000 3908 555000 5250 544000 3937 537000 4004 543000 5560 594000 3922 611000 3759 613000 4138 611000 4634 594000 3996 595000 4308 591000 4143 589000 4429 584000 5219 573000 4929 567000 5755 569000 5592 621000 4163 629000 4962 628000 5208 612000 4755 595000 4491 597000 5732 593000 5731 590000 5040 580000 6102 574000 4904 573000 5369 573000 5578 620000 4619 626000 4731 620000 5011 588000 5299 566000 4146 557000 4625 561000 4736 549000 4219 532000 5116 526000 4205 511000 4121 499000 5103 555000 4300 565000 4578 542000 3809 527000 5526 510000 4247 514000 3830 517000 4394 508000 4826 493000 4409 490000 4569 469000 4106 478000 4794 528000 3914 534000 3793 518000 4405 506000 4022 502000 4100 516000 4788

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 werkloos[t] = + 488516.201404741 + 15.3370721803531bouw[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) 488516.201404741 41966.856697 11.6405 0 0 bouw 15.3370721803531 8.962499 1.7112 0.092379 0.046189 Multiple Linear Regression - Regression Statistics Multiple R 0.219231804110551 R-squared 0.048062583933567 Adjusted R-squared 0.0316498698634563 F-TEST (value) 2.92837514430922 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.092378639331489 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 41300.4629313393 Sum Squared Residuals 98932237823.8902 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 562000 562348.866880961 -348.866880960755 2 561000 548453.479485561 12546.5205144391 3 555000 569035.830351595 -14035.8303515948 4 544000 548898.254578791 -4898.25457879115 5 537000 549925.838414875 -12925.8384148748 6 543000 573790.322727504 -30790.3227275043 7 594000 548668.198496086 45331.8015039141 8 611000 546168.255730688 64831.7442693117 9 613000 551981.006087042 61018.9939129579 10 611000 559588.193888497 51411.8061115027 11 594000 549803.141837432 44196.858162568 12 595000 554588.308357702 40411.6916422978 13 591000 552057.691447944 38942.3085520561 14 589000 556444.094091525 32555.9059084751 15 584000 568560.381114004 15439.6188859962 16 573000 564112.630181701 8887.36981829856 17 567000 576781.051802673 -9781.05180267312 18 569000 574281.109037276 -5281.10903727556 19 621000 552364.432891551 68635.567108449 20 629000 564618.753563653 64381.2464363469 21 628000 568391.67332002 59608.32667998 22 612000 561443.97962232 50556.02037768 23 595000 557394.992566707 37605.0074332932 24 597000 576428.299142525 20571.700857475 25 593000 576412.962070345 16587.0379296554 26 590000 565815.045193721 24184.9548062794 27 580000 582103.015849256 -2103.01584925565 28 574000 563729.203377193 10270.7966228074 29 573000 570860.941941057 2139.05805894318 30 573000 574066.390026751 -1066.39002675061 31 620000 559358.137805792 60641.862194208 32 626000 561075.889889991 64924.1101100085 33 620000 565370.27010049 54629.7298995096 34 588000 569787.346888432 18212.6531115679 35 566000 552103.702664485 13896.2973355150 36 557000 559450.160238874 -2450.16023887410 37 561000 561152.575250893 -152.575250893292 38 549000 553223.308933651 -4223.30893365073 39 532000 566980.662679428 -34980.6626794275 40 526000 553008.589923126 -27008.5899231258 41 511000 551720.275859976 -40720.2758599761 42 499000 566781.280741083 -67781.2807410829 43 555000 554465.611780259 534.388219740667 44 565000 558729.317846398 6270.6821536025 45 542000 546935.109339706 -4935.10933970595 46 527000 573268.862273372 -46268.8622733723 47 510000 553652.746954701 -43652.7469547006 48 514000 547257.187855493 -33257.1878554934 49 517000 555907.296565213 -38907.2965652125 50 508000 562532.911747125 -54532.9117471251 51 493000 556137.352647918 -63137.3526479178 52 490000 558591.284196774 -68591.2841967743 53 469000 551490.219777271 -82490.2197772708 54 478000 562042.125437354 -84042.1254373538 55 528000 548545.501918643 -20545.5019186430 56 534000 546689.71618482 -12689.7161848203 57 518000 556076.004359196 -38076.0043591964 58 506000 550201.905714121 -44201.9057141212 59 502000 551398.197344189 -49398.1973441887 60 516000 561950.103004272 -45950.1030042717 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0238612080185290 0.0477224160370579 0.976138791981471 6 0.00972799458309202 0.0194559891661840 0.990272005416908 7 0.0464965833602371 0.0929931667204743 0.953503416639763 8 0.098212520964649 0.196425041929298 0.901787479035351 9 0.144884927917828 0.289769855835656 0.855115072082172 10 0.19185243027512 0.38370486055024 0.80814756972488 11 0.143848268635712 0.287696537271425 0.856151731364288 12 0.111438789085268 0.222877578170536 0.888561210914732 13 0.0803994579707372 0.160798915941474 0.919600542029263 14 0.0566418802030706 0.113283760406141 0.94335811979693 15 0.0393140835397738 0.0786281670795475 0.960685916460226 16 0.0227052458460962 0.0454104916921924 0.977294754153904 17 0.0129673442263009 0.0259346884526017 0.9870326557737 18 0.00701518305867721 0.0140303661173544 0.992984816941323 19 0.0149572642986173 0.0299145285972346 0.985042735701383 20 0.0434624306471477 0.0869248612942953 0.956537569352852 21 0.0848439850356229 0.169687970071246 0.915156014964377 22 0.0985147187396507 0.197029437479301 0.90148528126035 23 0.0916069423934336 0.183213884786867 0.908393057606566 24 0.0705349837382687 0.141069967476537 0.929465016261731 25 0.0506045160752431 0.101209032150486 0.949395483924757 26 0.0391666901589556 0.0783333803179112 0.960833309841044 27 0.0250953133860427 0.0501906267720854 0.974904686613957 28 0.0180747671576925 0.0361495343153849 0.981925232842308 29 0.0118389664032760 0.0236779328065520 0.988161033596724 30 0.00739454594264101 0.0147890918852820 0.99260545405736 31 0.0208647843983368 0.0417295687966736 0.979135215601663 32 0.0854796096387801 0.170959219277560 0.91452039036122 33 0.265182206299276 0.530364412598552 0.734817793700724 34 0.382606670601138 0.765213341202276 0.617393329398862 35 0.459418522884119 0.918837045768239 0.540581477115881 36 0.524749839413454 0.950500321173091 0.475250160586546 37 0.624291002645896 0.751417994708209 0.375708997354104 38 0.687487492693247 0.625025014613507 0.312512507306753 39 0.73612854667853 0.527742906642941 0.263871453321471 40 0.766080047913982 0.467839904172036 0.233919952086018 41 0.805542454016674 0.388915091966652 0.194457545983326 42 0.853730220286336 0.292539559427328 0.146269779713664 43 0.890534400284593 0.218931199430814 0.109465599715407 44 0.968309175090245 0.063381649819511 0.0316908249097555 45 0.97712358748501 0.0457528250299821 0.0228764125149911 46 0.986985838383188 0.0260283232336243 0.0130141616168122 47 0.982004163128245 0.0359916737435094 0.0179958368717547 48 0.971899832111798 0.0562003357764031 0.0281001678882015 49 0.961652366175217 0.0766952676495656 0.0383476338247828 50 0.951538350789533 0.0969232984209348 0.0484616492104674 51 0.930093760011085 0.139812479977830 0.0699062399889152 52 0.89683133290427 0.206337334191461 0.103168667095730 53 0.97467438565755 0.0506512286849017 0.0253256143424509 54 0.981960317351218 0.0360793652975649 0.0180396826487824 55 0.94937784828764 0.101244303424722 0.050622151712361 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 14 0.274509803921569 NOK 10% type I error level 24 0.470588235294118 NOK

Charts produced by software:

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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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