*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, 19 Dec 2009 12:33:33 -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/19/t1261251346rtd5jjvffxa23sz.htm/, Retrieved Sat, 19 Dec 2009 20:35:59 +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/19/t1261251346rtd5jjvffxa23sz.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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19915 23322 19843 22558 19761 19185 20858 17869 21968 21515 23061 17686 22661 18044 22269 20398 21857 22894 21568 22016 21274 25325 20987 27683 19683 17333 19381 20190 19071 22589 20772 14588 22485 14296 24181 12237 23479 7607 22782 9303 22067 9226 21489 9351 20903 21266 20330 21377 19736 22034 19483 22483 19242 15122 20334 18982 21423 19653 22523 16653 21986 23528 21462 24612 20908 24733 20575 21839 20237 22421 19904 26543 19610 27067 19251 31403 18941 25762 20450 29359 21946 34174 23409 20163 22741 25226 22069 25077 21539 29764 21189 21372 20960 34136 20704 29126 19697 17279 19598 16163 19456 8058 20316 17888 21083 7642 22158 7458 21469 4639 20892 10276 20578 3129 20233 20023 19947 3744 20049 7848

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation X[t] = + 21491.5753445414 -0.0266653954672666Y[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) 21491.5753445414 441.856887 48.6392 0 0 Y -0.0266653954672666 0.021435 -1.244 0.218491 0.109245 Multiple Linear Regression - Regression Statistics Multiple R 0.161213140416401 R-squared 0.0259896766429184 Adjusted R-squared 0.00919639520572746 F-TEST (value) 1.54762347907542 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.21849091602018 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1237.04961438608 Sum Squared Residuals 88756921.4102592 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 19915 20869.6849914538 -954.684991453828 2 19843 20890.0573535908 -1047.05735359080 3 19761 20979.9997325019 -1218.99973250189 4 20858 21015.0913929368 -157.091392936815 5 21968 20917.8693610632 1050.13063893684 6 23061 21019.9711603073 2041.02883969267 7 22661 21010.4249487300 1650.57505126996 8 22269 20947.6546078001 1321.34539219990 9 21857 20881.0977807138 975.9022192862 10 21568 20904.5099979341 663.49000206594 11 21274 20816.2742043329 457.725795667125 12 20987 20753.3972018211 233.602798178939 13 19683 21029.3840449073 -1346.38404490727 14 19381 20953.2010100573 -1572.20101005729 15 19071 20889.2307263313 -1818.23072633132 16 20772 21102.5805554649 -330.580555464917 17 22485 21110.3668509414 1374.63314905864 18 24181 21165.2709002085 3015.72909979154 19 23479 21288.7316812219 2190.26831877809 20 22782 21243.5071705094 1538.49282949058 21 22067 21245.5604059604 821.4395940396 22 21489 21242.227231527 246.772768473008 23 20903 20924.5090445345 -21.5090445345104 24 20330 20921.5491856376 -591.549185637644 25 19736 20904.0300208157 -1168.03002081565 26 19483 20892.0572582508 -1409.05725825085 27 19242 21088.3412342854 -1846.34123428540 28 20334 20985.4128077817 -651.412807781747 29 21423 20967.5203274232 455.479672576789 30 22523 21047.516513825 1475.48348617499 31 21986 20864.1919199876 1121.80808001245 32 21462 20835.2866313010 626.713368698964 33 20908 20832.0601184495 75.939881550503 34 20575 20909.2297729318 -334.229772931767 35 20237 20893.7105127698 -656.710512769817 36 19904 20783.7957526537 -879.795752653745 37 19610 20769.8230854289 -1159.82308542890 38 19251 20654.2019306828 -1403.20193068283 39 18941 20804.6214265137 -1863.62142651368 40 20450 20708.7059990179 -258.705999017922 41 21946 20580.3121198430 1365.68788015697 42 23409 20953.9209757349 2455.07902426509 43 22741 20818.9140784841 1922.08592151587 44 22069 20822.8872224088 1246.11277759124 45 21539 20697.9065138537 841.093486146321 46 21189 20921.6825126150 267.31748738502 47 20960 20581.3254048708 378.674595129211 48 20704 20714.9190361618 -10.9190361617949 49 19697 21030.8239762625 -1333.82397626250 50 19598 21060.5825576040 -1462.58255760397 51 19456 21276.7055878662 -1820.70558786617 52 20316 21014.5847504229 -698.584750422937 53 21083 21287.7983923806 -204.798392380551 54 22158 21292.7048251465 865.295174853472 55 21469 21367.8745749688 101.125425031248 56 20892 21217.5617407198 -325.561740719770 57 20578 21408.1393221243 -830.139322124325 58 20233 20957.6541311003 -724.654131100323 59 19947 21391.7401039120 -1444.74010391196 60 20049 21282.3053209143 -1233.30532091429 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.465004130885894 0.930008261771788 0.534995869114106 6 0.640097527520649 0.719804944958702 0.359902472479351 7 0.587875678536216 0.824248642927568 0.412124321463784 8 0.569559453783822 0.860881092432356 0.430440546216178 9 0.568697641559567 0.862604716880867 0.431302358440433 10 0.478784433581825 0.95756886716365 0.521215566418175 11 0.408010762770738 0.816021525541475 0.591989237229262 12 0.324215084085596 0.648430168171192 0.675784915914404 13 0.444349254387703 0.888698508775405 0.555650745612297 14 0.532119081690237 0.935761836619526 0.467880918309763 15 0.62896471696703 0.742070566065942 0.371035283032971 16 0.551468276693438 0.897063446613124 0.448531723306562 17 0.543231632626437 0.913536734747126 0.456768367373563 18 0.762599557406790 0.474800885186421 0.237400442593210 19 0.792372176434897 0.415255647130207 0.207627823565103 20 0.792699170985273 0.414601658029455 0.207300829014727 21 0.778401092385753 0.443197815228495 0.221598907614247 22 0.764048121149040 0.471903757701921 0.235951878850960 23 0.700036039826105 0.59992792034779 0.299963960173895 24 0.644886052367568 0.710227895264864 0.355113947632432 25 0.632555113451758 0.734889773096485 0.367444886548242 26 0.645200655707829 0.709598688584342 0.354799344292171 27 0.776453279832386 0.447093440335228 0.223546720167614 28 0.732866323197386 0.534267353605228 0.267133676802614 29 0.679860488619761 0.640279022760478 0.320139511380239 30 0.720728641590521 0.558542716818958 0.279271358409479 31 0.738305018670635 0.52338996265873 0.261694981329365 32 0.706616487713277 0.586767024573446 0.293383512286723 33 0.641174463374064 0.717651073251871 0.358825536625936 34 0.569147343224628 0.861705313550744 0.430852656775372 35 0.506742365489109 0.986515269021783 0.493257634510891 36 0.458451867096018 0.916903734192035 0.541548132903982 37 0.442279645014834 0.884559290029668 0.557720354985166 38 0.49107188317934 0.98214376635868 0.50892811682066 39 0.65288126714433 0.694237465711341 0.347118732855671 40 0.626159915138167 0.747680169723667 0.373840084861833 41 0.668699918948736 0.662600162102527 0.331300081051264 42 0.891153016364817 0.217693967270367 0.108846983635183 43 0.955463737263043 0.0890725254739146 0.0445362627369573 44 0.967813008569357 0.0643739828612852 0.0321869914306426 45 0.965371572143927 0.0692568557121468 0.0346284278560734 46 0.952399040798979 0.0952019184020428 0.0476009592010214 47 0.940239094220308 0.119521811559383 0.0597609057796916 48 0.929709334630099 0.140581330739802 0.0702906653699009 49 0.904623400705599 0.190753198588802 0.095376599294401 50 0.889301085563031 0.221397828873938 0.110698914436969 51 0.929679758988248 0.140640482023505 0.0703202410117524 52 0.874665510266537 0.250668979466925 0.125334489733463 53 0.790442490802506 0.419115018394988 0.209557509197494 54 0.905243512881482 0.189512974237036 0.0947564871185178 55 0.941127637653329 0.117744724693343 0.0588723623466715 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 4 0.0784313725490196 OK

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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