W8

*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, 26 Nov 2010 13:09:12 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/26/t1290777592mnqo2dzsei0do1e.htm/, Retrieved Fri, 26 Nov 2010 14:19:52 +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/2010/Nov/26/t1290777592mnqo2dzsei0do1e.htm/}, year = {2010}, } @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 = {2010}, 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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13768040,14 14731798,37 17487530,67 16471559,62 16198106,13 15213975,95 17535166,38 17637387,4 16571771,60 17972385,83 16198892,67 16896235,55 16554237,93 16697955,94 19554176,37 19691579,52 15903762,33 15930700,75 18003781,65 17444615,98 18329610,38 17699369,88 16260733,42 15189796,81 14851949,20 15672722,75 18174068,44 17180794,3 18406552,23 17664893,45 18466459,42 17862884,98 16016524,60 16162288,88 17428458,32 17463628,82 17167191,42 16772112,17 19629987,60 19106861,48 17183629,01 16721314,25 18344657,85 18161267,85 19301440,71 18509941,2 18147463,68 17802737,97 16192909,22 16409869,75 18374420,60 17967742,04 20515191,95 20286602,27 18957217,20 19537280,81 16471529,53 18021889,62 18746813,27 20194317,23 19009453,59 19049596,62 19211178,55 20244720,94 20547653,75 21473302,24 19325754,03 19673603,19 20605542,58 21053177,29 20056915,06 20159479,84 16141449,72 18203628,31 20359793,22 21289464,94 19711553,27 20432335,71 15638580,70 17180395,07 14384486,00 15816786,32 13 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 3363247.36872550 + 0.862675215502543X[t] -1820347.80707848M1[t] -187455.186940559M2[t] -343912.623172632M3[t] -812292.839266948M4[t] -1681766.40358488M5[t] -1375785.78428621M6[t] -621772.351334577M7[t] -437174.629128277M8[t] -736462.116213925M9[t] -445829.754652919M10[t] + 39658.6322933237M11[t] -16183.9076883882t + 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) 3363247.36872550 646794.843193 5.1999 4e-06 2e-06 X 0.862675215502543 0.034712 24.8521 0 0 M1 -1820347.80707848 303545.710237 -5.9969 0 0 M2 -187455.186940559 301037.135597 -0.6227 0.536558 0.268279 M3 -343912.623172632 301687.329693 -1.14 0.260202 0.130101 M4 -812292.839266948 299846.518977 -2.709 0.009447 0.004723 M5 -1681766.40358488 298648.982151 -5.6312 1e-06 1e-06 M6 -1375785.78428621 298420.525039 -4.6102 3.2e-05 1.6e-05 M7 -621772.351334577 298420.956303 -2.0835 0.042786 0.021393 M8 -437174.629128277 303881.998335 -1.4386 0.157024 0.078512 M9 -736462.116213925 298027.095406 -2.4711 0.017233 0.008617 M10 -445829.754652919 297948.368363 -1.4963 0.141397 0.070699 M11 39658.6322933237 302299.838359 0.1312 0.896197 0.448099 t -16183.9076883882 3591.581556 -4.5061 4.5e-05 2.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.977947644368567 R-squared 0.95638159512603 Adjusted R-squared 0.944054654618168 F-TEST (value) 77.584668678827 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 470540.281698332 Sum Squared Residuals 10184775208234.3 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13768040.14 14235472.9875384 -467432.847538398 2 17487530.67 17353030.6112547 134500.058745351 3 16198106.13 16095503.0038045 102603.126195539 4 17535166.38 17701555.8749018 -166389.494901839 5 16571771.6 17104893.2456888 -533121.64568878 6 16198892.67 16466321.7825869 -267429.112586945 7 16554237.93 17033100.4025637 -478862.472563677 8 19554176.37 19784039.0840916 -229862.714091583 9 15903762.33 16224150.7859289 -320388.455928858 10 18003781.65 17804616.3870943 199165.26290569 11 18329610.38 18493690.7419348 -164080.361934776 12 16260733.42 16272901.7129714 -12168.2929714352 13 14851949.2 14852978.2375658 -1029.03756583872 14 18174068.44 17770662.8994049 403405.540595129 15 18406552.23 18015641.8940353 390910.335964743 16 18466459.42 17701880.156063 764579.263937019 17 16016524.6 15349160.5770064 667364.022993623 18 17428458.32 16761591.0017982 666867.318201772 19 17167191.42 16902866.2519991 264325.168000877 20 19629987.6 19085410.4306657 544577.169334302 21 17183629.01 16711986.5651599 471642.444840083 22 18344657.85 18228647.3012262 116010.548773801 23 19301440.71 18998743.6378353 302697.072164704 24 18147463.68 18332814.3990092 -185350.719009240 25 16192909.22 15294689.7923872 898219.427612768 26 18374420.6 18255336.3183380 119084.281662049 27 20515191.95 20083118.223053 432073.726946982 28 18957217.2 18952133.0472841 5084.15271586714 29 16471529.53 16759185.1538739 -287655.623873907 30 18746813.27 18923081.3221046 -176268.052104617 31 19009453.59 18673388.7484459 336064.841554093 32 19211178.55 19872806.6932722 -661628.143272149 33 20547653.75 20617201.936238 -69548.1862380049 34 19325754.03 19339094.6243122 -13340.5943121525 35 20605542.58 20998523.4875892 -392980.907589235 36 20056915.06 20171710.3073347 -114795.247334700 37 16141449.72 16647913.9524341 -506464.232434103 38 20359793.22 20926697.4446745 -566904.224674528 39 19711553.27 20014631.9575503 -303078.687550287 40 15638580.7 16724699.2413541 -1086118.54135410 41 14384486 14662690.2970804 -278204.297080378 42 13855616.12 14309822.8123737 -454206.692373723 43 14308336.46 14572577.8383604 -264241.378360400 44 15290621.44 15731057.0649904 -440435.624990354 45 14423755.53 14275210.7479184 148544.782081633 46 13779681.49 14147759.5403470 -368078.050347027 47 15686348.94 15984348.6453855 -297999.705385525 48 14733828.17 14869390.4523193 -135562.282319270 49 12522497.94 12445791.2500744 76706.6899255716 50 16189383.57 16279469.226328 -90085.6563280014 51 16059123.25 16681631.7515570 -622508.501556977 52 16007123.26 15524278.6403969 482844.619603058 53 15806842.33 15375224.7863506 431617.543649441 54 15159951.13 14928914.5911365 231036.538863513 55 15692144.17 15549430.3286309 142713.841369107 56 18908869.11 18121519.7969802 787349.313019784 57 16969881.42 17200132.0047549 -230250.584754853 58 16997477.78 16931234.9470203 66242.8329796886 59 19858875.65 19306511.7472552 552363.902744832 60 17681170.13 17233293.5883654 447876.541634646 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0493635850289076 0.0987271700578153 0.950636414971092 18 0.0307962937926038 0.0615925875852076 0.969203706207396 19 0.00934696751309037 0.0186939350261807 0.99065303248691 20 0.00357336170395309 0.00714672340790618 0.996426638296047 21 0.00159420799551703 0.00318841599103406 0.998405792004483 22 0.0109824474504471 0.0219648949008942 0.989017552549553 23 0.00510395136729925 0.0102079027345985 0.9948960486327 24 0.00246874547832629 0.00493749095665259 0.997531254521674 25 0.0053739268325206 0.0107478536650412 0.99462607316748 26 0.0728793986371764 0.145758797274353 0.927120601362824 27 0.125514089348669 0.251028178697337 0.874485910651332 28 0.271325899366375 0.542651798732749 0.728674100633625 29 0.417751233466306 0.835502466932611 0.582248766533694 30 0.362551167145486 0.725102334290973 0.637448832854514 31 0.411868556793835 0.82373711358767 0.588131443206165 32 0.655994293797886 0.688011412404229 0.344005706202114 33 0.589524122975804 0.820951754048392 0.410475877024196 34 0.615943025192155 0.76811394961569 0.384056974807845 35 0.540053122125875 0.91989375574825 0.459946877874125 36 0.481699505513217 0.963399011026433 0.518300494486783 37 0.462346441554567 0.924692883109133 0.537653558445433 38 0.389999866757065 0.77999973351413 0.610000133242935 39 0.704295909907654 0.591408180184692 0.295704090092346 40 0.822580686684407 0.354838626631186 0.177419313315593 41 0.713036193112562 0.573927613774876 0.286963806887438 42 0.576502215353404 0.846995569293192 0.423497784646596 43 0.437684607963632 0.875369215927264 0.562315392036368 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.111111111111111 NOK 5% type I error level 7 0.259259259259259 NOK 10% type I error level 9 0.333333333333333 NOK

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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