*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: Thu, 19 Nov 2009 02:25:14 -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/19/t12586228601x2i93giy6imt5x.htm/, Retrieved Thu, 19 Nov 2009 10:27:52 +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/2009/Nov/19/t12586228601x2i93giy6imt5x.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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3499 1 4164 3902 3186 3353 4145 1 3499 4164 3902 3186 3796 1 4145 3499 4164 3902 3711 1 3796 4145 3499 4164 3949 1 3711 3796 4145 3499 3740 1 3949 3711 3796 4145 3243 1 3740 3949 3711 3796 4407 1 3243 3740 3949 3711 4814 1 4407 3243 3740 3949 3908 1 4814 4407 3243 3740 5250 1 3908 4814 4407 3243 3937 1 5250 3908 4814 4407 4004 1 3937 5250 3908 4814 5560 1 4004 3937 5250 3908 3922 1 5560 4004 3937 5250 3759 1 3922 5560 4004 3937 4138 1 3759 3922 5560 4004 4634 1 4138 3759 3922 5560 3996 1 4634 4138 3759 3922 4308 1 3996 4634 4138 3759 4143 0 4308 3996 4634 4138 4429 0 4143 4308 3996 4634 5219 0 4429 4143 4308 3996 4929 0 5219 4429 4143 4308 5755 0 4929 5219 4429 4143 5592 0 5755 4929 5219 4429 4163 0 5592 5755 4929 5219 4962 0 4163 5592 5755 4929 5208 0 4962 4163 5592 5755 4755 0 5208 4962 4163 5592 4491 0 4755 5208 4962 4163 5732 0 4491 4755 5208 4962 5731 0 5732 4491 4755 5208 5040 0 5731 5732 4491 4755 6102 0 5040 5731 5732 4491 4904 0 6102 5040 5731 5732 5369 0 4904 6102 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 815.4400473079 -146.985860400957X[t] + 0.322066277846830Y1[t] -0.0980332042753272Y2[t] + 0.385737324810814Y3[t] + 0.120494337086232Y4[t] + 756.041550490447M1[t] + 1003.38137563738M2[t] -76.4336368920148M3[t] + 546.369797069734M4[t] + 196.75507538071M5[t] + 882.128458892924M6[t] + 58.5773967719282M7[t] + 847.254865489325M8[t] + 597.636910820808M9[t] + 482.014123979181M10[t] + 1430.83045970275M11[t] -1.58386023416724t + 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) 815.4400473079 1073.556461 0.7596 0.452079 0.22604 X -146.985860400957 193.289434 -0.7604 0.451562 0.225781 Y1 0.322066277846830 0.156003 2.0645 0.045668 0.022834 Y2 -0.0980332042753272 0.156715 -0.6256 0.535254 0.267627 Y3 0.385737324810814 0.158817 2.4288 0.019858 0.009929 Y4 0.120494337086232 0.170611 0.7063 0.48423 0.242115 M1 756.041550490447 385.700459 1.9602 0.057147 0.028574 M2 1003.38137563738 327.009559 3.0684 0.003904 0.001952 M3 -76.4336368920148 327.677084 -0.2333 0.81678 0.40839 M4 546.369797069734 392.638766 1.3915 0.171951 0.085975 M5 196.75507538071 335.584801 0.5863 0.561049 0.280524 M6 882.128458892924 378.26228 2.3321 0.024954 0.012477 M7 58.5773967719282 314.279916 0.1864 0.853108 0.426554 M8 847.254865489325 376.574529 2.2499 0.030172 0.015086 M9 597.636910820808 315.113341 1.8966 0.065308 0.032654 M10 482.014123979181 365.354846 1.3193 0.194761 0.09738 M11 1430.83045970275 367.603095 3.8923 0.000377 0.000189 t -1.58386023416724 4.618476 -0.3429 0.733485 0.366743 Multiple Linear Regression - Regression Statistics Multiple R 0.837277838225756 R-squared 0.701034178383995 Adjusted R-squared 0.570715743320609 F-TEST (value) 5.37939377527833 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 7.01224103738518e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 438.580853085848 Sum Squared Residuals 7501773.4230469 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3499 4014.44692413249 -515.44692413249 2 4145 4276.40948502811 -131.409485028112 3 3796 3655.59463305087 140.405366949125 4 3711 3876.13782116545 -165.137821165453 5 3949 3700.83477158281 248.165228417188 6 3740 4412.82590675054 -672.82590675054 7 3243 3422.20703345585 -179.207033455847 8 4407 4151.28610619539 255.713893804612 9 4814 4271.75049257232 542.249507427683 10 3908 3954.6194039217 -46.6194039217033 11 5250 4959.27287808975 290.727121910246 12 3937 4345.1400856631 -408.140085663099 13 4004 4244.7273718845 -240.727371884502 14 5560 5049.27099512249 510.729004877507 15 3922 4117.66931889528 -195.669318895280 16 3759 3926.43999982545 -167.439999825446 17 4138 4291.60340120661 -153.603401206612 18 4634 4669.08690655155 -35.086906551549 19 3996 3706.29736549665 289.702634503346 20 4308 4365.84208855129 -57.8420885512853 21 4143 4661.64906392728 -518.649063927276 22 4429 4274.37989923832 154.620100761676 23 5219 5373.37346717731 -154.373467177309 24 4929 4141.30158489376 787.698415106238 25 5755 4815.35313247362 939.646867526383 26 5592 5694.75933913491 -102.759339134912 27 4163 4463.21493845389 -300.214938453886 28 4962 4923.85688597395 38.1431140260491 29 5208 5006.73184744888 201.268152551116 30 4755 5120.56193076156 -365.561930761556 31 4491 4261.43253111766 229.567468882337 32 5732 5199.07604102141 532.923958978588 33 5731 5228.34184163925 502.658158360755 34 5040 4832.7353333298 207.264666670195 35 6102 6004.40755913078 97.5924408692193 36 4904 5130.91630542065 -226.916305420648 37 5369 5128.76234609467 240.237653905330 38 5578 5968.11436095055 -390.114360950549 39 4619 4574.29357113117 44.7064288688274 40 4731 4901.17828491782 -170.178284917823 41 5011 4816.71393664407 194.286063355926 42 5299 5234.96352079785 64.0364792021519 43 4146 4402.78290037860 -256.782900378595 44 4625 4911.80234437382 -286.802344373821 45 4736 5072.73332501888 -336.733325018880 46 4219 4534.26536351017 -315.265363510168 47 5116 5349.94609560216 -233.946095602156 48 4205 4357.64202402249 -152.642024022491 49 4121 4544.71022541472 -423.710225414722 50 5103 4989.44581976393 113.554180236066 51 4300 3989.22753846879 310.772461531213 52 4578 4113.38700811733 464.612991882673 53 3809 4299.11604311762 -490.116043117618 54 5526 4516.56173513851 1009.43826486149 55 4247 4330.28016955124 -83.2801695512407 56 3830 4273.99341985809 -443.993419858094 57 4394 4583.52527684228 -189.525276842281 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.461157042169415 0.92231408433883 0.538842957830585 22 0.322264588115125 0.64452917623025 0.677735411884875 23 0.282387861262816 0.564775722525631 0.717612138737184 24 0.457247229182125 0.91449445836425 0.542752770817875 25 0.898620517092309 0.202758965815383 0.101379482907691 26 0.829837687380563 0.340324625238874 0.170162312619437 27 0.761146176888672 0.477707646222656 0.238853823111328 28 0.728539768476059 0.542920463047883 0.271460231523941 29 0.646525829016407 0.706948341967187 0.353474170983593 30 0.914631158327735 0.170737683344531 0.0853688416722653 31 0.933830314305215 0.132339371389570 0.0661696856947852 32 0.891750276910248 0.216499446179504 0.108249723089752 33 0.820316898065299 0.359366203869401 0.179683101934701 34 0.809816774290042 0.380366451419916 0.190183225709958 35 0.742816551332103 0.514366897335794 0.257183448667897 36 0.711762725573635 0.57647454885273 0.288237274426365 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 0 0 OK

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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