DJ

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 02:56:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227779825qd56a5ap1i32uq3.htm/, Retrieved Thu, 27 Nov 2008 09:57:15 +0000

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/2008/Nov/27/t1227779825qd56a5ap1i32uq3.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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9492.49 9682.35 9762.12 10124.63 10540.05 10601.61 10323.73 10418.4 10092.96 10364.91 10152.09 10032.8 10204.59 10001.6 10411.75 10673.38 10539.51 10723.78 10682.06 10283.19 10377.18 10486.64 10545.38 10554.27 10532.54 10324.31 10695.25 10827.81 10872.48 10971.19 11145.65 11234.68 11333.88 10997.97 11036.89 11257.35 11533.59 11963.12 12185.15 12377.62 12512.89 12631.48 12268.53 12754.8 13407.75 13480.21 13673.28 13239.71 13557.69 13901.28 13200.58 13406.97 12538.12 12419.57 12193.88 12656.63 12812.48 12056.67 11322.38 11530.75 11114.08

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation X[t] = + 9643.56940983607 + 55.4113939714437t + 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) 9643.56940983607 174.247532 55.3441 0 0 t 55.4113939714437 4.88758 11.3372 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.827880797071079 R-squared 0.685386614159045 Adjusted R-squared 0.680054183890554 F-TEST (value) 128.531753750064 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 672.108864694253 Sum Squared Residuals 26652089.2340352 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9492.49 9698.98080380749 -206.490803807487 2 9682.35 9754.39219777895 -72.0421977789542 3 9762.12 9809.8035917504 -47.6835917503972 4 10124.63 9865.21498572184 259.415014278158 5 10540.05 9920.62637969329 619.423620306714 6 10601.61 9976.03777366473 625.572226335272 7 10323.73 10031.4491676362 292.280832363827 8 10418.4 10086.8605616076 331.539438392383 9 10092.96 10142.2719555791 -49.3119555790608 10 10364.91 10197.6833495505 167.226650449496 11 10152.09 10253.0947435219 -101.004743521947 12 10032.8 10308.5061374934 -275.706137493392 13 10204.59 10363.9175314648 -159.327531464834 14 10001.6 10419.3289254363 -417.728925436278 15 10411.75 10474.7403194077 -62.9903194077217 16 10673.38 10530.1517133792 143.228286620834 17 10539.51 10585.5631073506 -46.0531073506088 18 10723.78 10640.9745013221 82.805498677948 19 10682.06 10696.3858952935 -14.3258952934968 20 10283.19 10751.7972892649 -468.607289264939 21 10377.18 10807.2086832364 -430.028683236383 22 10486.64 10862.6200772078 -375.980077207828 23 10545.38 10918.0314711793 -372.651471179272 24 10554.27 10973.4428651507 -419.172865150714 25 10532.54 11028.8542591222 -496.314259122157 26 10324.31 11084.2656530936 -759.955653093602 27 10695.25 11139.6770470650 -444.427047065045 28 10827.81 11195.0884410365 -367.278441036490 29 10872.48 11250.4998350079 -378.019835007933 30 10971.19 11305.9112289794 -334.721228979376 31 11145.65 11361.3226229508 -215.672622950820 32 11234.68 11416.7340169223 -182.054016922263 33 11333.88 11472.1454108937 -138.265410893708 34 10997.97 11527.5568048652 -529.586804865152 35 11036.89 11582.9681988366 -546.078198836595 36 11257.35 11638.3795928080 -381.029592808038 37 11533.59 11693.7909867795 -160.200986779482 38 11963.12 11749.2023807509 213.917619249075 39 12185.15 11804.6137747224 380.536225277631 40 12377.62 11860.0251686938 517.594831306188 41 12512.89 11915.4365626653 597.453437334743 42 12631.48 11970.8479566367 660.6320433633 43 12268.53 12026.2593506081 242.270649391857 44 12754.8 12081.6707445796 673.129255420412 45 13407.75 12137.0821385510 1270.66786144897 46 13480.21 12192.4935325225 1287.71646747752 47 13673.28 12247.9049264939 1425.37507350608 48 13239.71 12303.3163204654 936.393679534637 49 13557.69 12358.7277144368 1198.96228556319 50 13901.28 12414.1391084082 1487.14089159175 51 13200.58 12469.5505023797 731.029497620307 52 13406.97 12524.9618963511 882.008103648863 53 12538.12 12580.3732903226 -42.2532903225791 54 12419.57 12635.7846842940 -216.214684294024 55 12193.88 12691.1960782655 -497.316078265468 56 12656.63 12746.6074722369 -89.9774722369118 57 12812.48 12802.0188662084 10.4611337916450 58 12056.67 12857.4302601798 -800.760260179798 59 11322.38 12912.8416541512 -1590.46165415124 60 11530.75 12968.2530481227 -1437.50304812269 61 11114.08 13023.6644420941 -1909.58444209413 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00783245736527133 0.0156649147305427 0.992167542634729 6 0.00131828042176721 0.00263656084353442 0.998681719578233 7 0.00623840519540221 0.0124768103908044 0.993761594804598 8 0.0041729606234953 0.0083459212469906 0.995827039376505 9 0.0102897713874373 0.0205795427748745 0.989710228612563 10 0.0049201797103459 0.0098403594206918 0.995079820289654 11 0.00396698005960183 0.00793396011920366 0.996033019940398 12 0.00349570975200275 0.0069914195040055 0.996504290247997 13 0.00163528560550213 0.00327057121100427 0.998364714394498 14 0.00111981322253357 0.00223962644506713 0.998880186777466 15 0.000435939584492308 0.000871879168984615 0.999564060415508 16 0.000221729112165620 0.000443458224331239 0.999778270887834 17 8.07413066938636e-05 0.000161482613387727 0.999919258693306 18 3.29490081128871e-05 6.58980162257742e-05 0.999967050991887 19 1.13479121562792e-05 2.26958243125583e-05 0.999988652087844 20 7.65101645783749e-06 1.53020329156750e-05 0.999992348983542 21 3.51012933555564e-06 7.02025867111129e-06 0.999996489870664 22 1.26620246869416e-06 2.53240493738832e-06 0.999998733797531 23 4.24881706511833e-07 8.49763413023665e-07 0.999999575118294 24 1.43414333002648e-07 2.86828666005296e-07 0.999999856585667 25 5.21974586160344e-08 1.04394917232069e-07 0.999999947802541 26 4.21568202292563e-08 8.43136404585126e-08 0.99999995784318 27 1.51941767183572e-08 3.03883534367144e-08 0.999999984805823 28 6.0817717678965e-09 1.2163543535793e-08 0.999999993918228 29 2.56721362670328e-09 5.13442725340656e-09 0.999999997432786 30 1.25620926594589e-09 2.51241853189178e-09 0.999999998743791 31 8.89294392982477e-10 1.77858878596495e-09 0.999999999110706 32 7.0843811007297e-10 1.41687622014594e-09 0.999999999291562 33 6.53921154617926e-10 1.30784230923585e-09 0.999999999346079 34 6.04261919038174e-10 1.20852383807635e-09 0.999999999395738 35 9.67874665915447e-10 1.93574933183089e-09 0.999999999032125 36 2.38621104531437e-09 4.77242209062874e-09 0.999999997613789 37 1.38109060872344e-08 2.76218121744688e-08 0.999999986189094 38 3.18065074144242e-07 6.36130148288484e-07 0.999999681934926 39 7.1394481359326e-06 1.42788962718652e-05 0.999992860551864 40 0.000106246387377072 0.000212492774754145 0.999893753612623 41 0.000921909080937425 0.00184381816187485 0.999078090919063 42 0.00528323905524061 0.0105664781104812 0.99471676094476 43 0.0659835084380512 0.131967016876102 0.934016491561949 44 0.361987960707237 0.723975921414475 0.638012039292763 45 0.626266801259982 0.747466397480036 0.373733198740018 46 0.763693406832421 0.472613186335158 0.236306593167579 47 0.798072998475377 0.403854003049246 0.201927001524623 48 0.863037449799316 0.273925100401367 0.136962550200684 49 0.840250096074944 0.319499807850112 0.159749903925056 50 0.847412729147662 0.305174541704675 0.152587270852338 51 0.773769617333497 0.452460765333007 0.226230382666503 52 0.735538385222199 0.528923229555603 0.264461614777801 53 0.687011312825181 0.625977374349638 0.312988687174819 54 0.670626721082612 0.658746557834777 0.329373278917388 55 0.86175807136695 0.276483857266101 0.138241928633050 56 0.766459463771125 0.46708107245775 0.233540536228875 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 34 0.653846153846154 NOK 5% type I error level 38 0.730769230769231 NOK 10% type I error level 38 0.730769230769231 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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