Multiple Regression Export Data

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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: Sun, 02 Nov 2008 08:01:55 -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/02/t1225638212bh7u6xp84t10nsc.htm/, Retrieved Sun, 02 Nov 2008 15:03:41 +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/02/t1225638212bh7u6xp84t10nsc.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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Dataseries X:

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69,97 6911 8488 72,13 7030,6 10900 78,27 7115,1 10456 80,31 7232,2 18508 79,06 7298,3 12880 78,98 7337,7 14034 87,35 7432,1 12419 86,16 7522,5 17256 88,71 7624,1 10407 90,16 7776,6 12245 94,09 7866,2 13394 93,57 8000,4 18333 96,73 8113,8 14076 94,67 8250,4 15359 101,05 8381,9 16592 105,16 8471,2 19188 105,27 8586,7 15428 104,88 8657,9 15564 107,11 8789,5 15451 99,41 8953,8 19825 101,37 9066,6 14813 98,86 9174,1 15309 100,64 9313,5 18573 97,16 9519,5 20255 98,1 9629,4 20138 96,79 9822,8 22204 102,71 9862,1 22981 102,95 9953,6 21986 104,07 10021,5 23139 104,31 10128,9 22081 105,02 10135,1 23989 106,08 10226,3 24503 105,28 10333,3 23818 99,36 10426,6 26013 101,53 10527,4 31911 99,32 10591,1 31889 96,91 10705,6 32091 92,65 10831,8 34476 95,7 11086,1 41941 93,2 11219,5 48062 91,93 11405,5 45848 92,24 11610,3 50496 95,32 11779,4 55803 88,72 11948,5 63784 87,99 12155,4 60869 89,2 12297,5 65960 93,78 12538,2 70186 94,99 12696,4 75412 92,9 12959,6 78046 90,61 13134,1 81311 94,26 13249,6 91629 94,17 13370,1 94094 94,81 13510,9 83424 95,77 13737,5 103268 99,4 13950,6 112481 98,76 14031,2 114416 99,37 14150,8 108963 101,02 14294,5 121533

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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation exp[t] = -299135.534440977 -323.772985709723reer[t] + 49.8364278678448GDP[t] -5204.27341734299Q1[t] -3671.18155453822Q2[t] -1741.20861263880Q3[t] -4652.50574960861t + 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) -299135.534440977 27795.997285 -10.7618 0 0 reer -323.772985709723 110.153034 -2.9393 0.004932 0.002466 GDP 49.8364278678448 3.418252 14.5795 0 0 Q1 -5204.27341734299 2137.578523 -2.4347 0.018444 0.009222 Q2 -3671.18155453822 2144.48321 -1.7119 0.092987 0.046494 Q3 -1741.20861263880 2175.304135 -0.8004 0.427167 0.213583 t -4652.50574960861 450.730815 -10.3221 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.985778046455531 R-squared 0.971758356873684 Adjusted R-squared 0.968435810623529 F-TEST (value) 292.473989437587 F-TEST (DF numerator) 6 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5738.82063417228 Sum Squared Residuals 1679637175.83128 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8488 12772.8435766348 -4284.84357663484 2 10900 14914.5168136948 -4014.51681369479 3 10456 14415.196028561 -3959.19602856101 4 18508 16679.2477040677 1828.75229593232 5 12880 10521.3726513178 2358.6273486822 6 14034 9391.41586136381 4642.58413863619 7 12419 8663.46195398883 3755.53804601117 8 17256 10642.6677492667 6613.33225073329 9 10407 5023.64854012839 5383.35145987161 10 12245 9034.81907389176 3210.18092610824 11 13394 9505.20236930221 3888.79763069778 12 18333 13450.3158047662 4882.68419523378 13 14076 8221.86492318553 5854.13507681447 14 15359 12577.0794336913 2781.92056630873 15 16592 14342.3652417756 2249.63475822438 16 19188 14550.7541421375 4637.24585786255 17 15428 10414.4673654938 5013.53263450616 18 15564 10969.6786073073 4594.32139269270 19 15451 14083.6059488738 1367.39405112620 20 19825 21853.4859005557 -2028.48590055570 21 14813 16983.6607451060 -2170.66074510597 22 15309 20034.3330482268 -4725.33304822683 23 18573 23682.6823707319 -5109.68237073188 24 20255 32164.4193648079 -11909.4193648079 25 20138 27480.3170139653 -7342.31701396529 26 22204 34423.4108880823 -12219.4108880823 27 22981 31742.7136201779 -8761.71362017793 28 21986 33313.7441165456 -11327.7441165456 29 23139 26478.2326578257 -3339.23265782574 30 22081 28633.5456074581 -6552.54560745807 31 23989 25990.1198326756 -2001.11983267564 32 24503 27280.7055524009 -2777.70555240091 33 23818 23015.4425558765 802.557444123528 34 26013 26462.5034645441 -449.503464544140 35 31911 28060.8952069236 3850.10479307645 36 31889 29039.7168235540 2849.28317644603 37 32091 25669.501543031 6421.49845696898 38 34476 30218.7177722725 4257.28222772747 39 41941 39182.0809649417 2758.91903505834 40 48062 43728.3957698166 4333.60423018339 41 45848 43552.3838781355 2295.61612186452 42 50496 50539.1007930962 -43.1007930961945 43 55803 55246.6871418536 556.312858146387 44 63784 62899.6316630205 884.368336979486 45 60869 63590.363701494 -2721.36370149408 46 65960 67160.9409020022 -1200.94090200224 47 70186 74951.1560075328 -4765.15600753277 48 75412 79532.2164465472 -4120.21644654719 49 78046 83469.0706345457 -5423.07063454567 50 81311 89787.553547956 -8476.55354795597 51 91629 91639.3567611424 -10.3567611423654 52 94094 94762.4887509617 -668.488750961747 53 83424 91715.4639169484 -8291.46391694841 54 103268 99578.1625187169 3689.83748128312 55 112481 106300.476551519 6180.5234484809 56 114416 107613.210211552 6802.78978844818 57 108963 103519.366296311 5443.63370368853 58 121533 107027.221667696 14505.7783323041 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0612569233610267 0.122513846722053 0.938743076638973 11 0.0187478445305154 0.0374956890610308 0.981252155469485 12 0.00676652780894286 0.0135330556178857 0.993233472191057 13 0.00303036405901744 0.00606072811803488 0.996969635940983 14 0.00106027376422332 0.00212054752844663 0.998939726235777 15 0.000431557732470557 0.000863115464941114 0.99956844226753 16 0.000248262417518366 0.000496524835036732 0.999751737582482 17 0.000130221230904468 0.000260442461808935 0.999869778769096 18 7.74702673577128e-05 0.000154940534715426 0.999922529732642 19 5.11728012352729e-05 0.000102345602470546 0.999948827198765 20 4.51361900966728e-05 9.02723801933455e-05 0.999954863809903 21 3.00712011716101e-05 6.01424023432203e-05 0.999969928798828 22 1.66528708253705e-05 3.33057416507410e-05 0.999983347129175 23 3.21132341882645e-05 6.4226468376529e-05 0.999967886765812 24 1.82625626217758e-05 3.65251252435515e-05 0.999981737437378 25 0.000187318981036709 0.000374637962073418 0.999812681018963 26 0.00035945771998303 0.00071891543996606 0.999640542280017 27 0.000636454467153213 0.00127290893430643 0.999363545532847 28 0.000497056674609449 0.000994113349218899 0.99950294332539 29 0.0045617138848455 0.009123427769691 0.995438286115155 30 0.00318290499121981 0.00636580998243961 0.99681709500878 31 0.00344230147193037 0.00688460294386074 0.99655769852807 32 0.00189768204465398 0.00379536408930795 0.998102317955346 33 0.00143832573854777 0.00287665147709554 0.998561674261452 34 0.000955802459255557 0.00191160491851111 0.999044197540744 35 0.00375068245974910 0.00750136491949819 0.99624931754025 36 0.00230857785068164 0.00461715570136328 0.997691422149318 37 0.00246692038911291 0.00493384077822582 0.997533079610887 38 0.00187856643636907 0.00375713287273813 0.99812143356363 39 0.015847894439766 0.031695788879532 0.984152105560234 40 0.0606930153130872 0.121386030626174 0.939306984686913 41 0.139360931943786 0.278721863887573 0.860639068056214 42 0.208534901732556 0.417069803465113 0.791465098267444 43 0.249632239574987 0.499264479149973 0.750367760425013 44 0.313068824854176 0.626137649708352 0.686931175145824 45 0.58144575220595 0.8371084955881 0.41855424779405 46 0.776941435085546 0.446117129828908 0.223058564914454 47 0.656628186174287 0.686743627651425 0.343371813825713 48 0.774157555081334 0.451684889837332 0.225842444918666 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.666666666666667 NOK 5% type I error level 29 0.743589743589744 NOK 10% type I error level 29 0.743589743589744 NOK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Include Quarterly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Include Quarterly 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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