Model 4

*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: Tue, 17 Nov 2009 14:51:39 -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/17/t1258494807w4idznri8vo19ob.htm/, Retrieved Tue, 17 Nov 2009 22:53:40 +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/17/t1258494807w4idznri8vo19ob.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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3759 36.71 3922 5560 4138 36.72 3759 3922 4634 36.73 4138 3759 3996 36.73 4634 4138 4308 36.87 3996 4634 4429 37.31 4308 3996 5219 37.39 4429 4308 4929 37.42 5219 4429 5755 37.51 4929 5219 5592 37.67 5755 4929 4163 37.67 5592 5755 4962 37.71 4163 5592 5208 37.78 4962 4163 4755 37.79 5208 4962 4491 37.84 4755 5208 5732 37.88 4491 4755 5731 38.34 5732 4491 5040 38.58 5731 5732 6102 38.72 5040 5731 4904 38.83 6102 5040 5369 38.9 4904 6102 5578 38.92 5369 4904 4619 38.94 5578 5369 4731 39.1 4619 5578 5011 39.14 4731 4619 5299 39.16 5011 4731 4146 39.32 5299 5011 4625 39.34 4146 5299 4736 39.44 4625 4146 4219 39.92 4736 4625 5116 40.19 4219 4736 4205 40.2 5116 4219 4121 40.27 4205 5116 5103 40.28 4121 4205 4300 40.3 5103 4121 4578 40.34 4300 5103 3809 40.4 4578 4300 5526 40.43 3809 4578 4247 40.48 5526 3809 3830 40.48 4247 5526 4394 40.63 3830 4247 4826 40.74 4394 3830 4409 40.77 4826 4394 4569 40.91 4409 4826 4106 40.92 4569 4409 4794 41.03 4106 4569 3914 41 4794 4106 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 Y1[t] = -14573.6863254658 + 0.286065503358865Y[t] + 459.077940222844X[t] + 0.172963208384406Y2[t] + 263.451877994075M1[t] + 270.461141609439M2[t] + 718.898880064055M3[t] + 200.951950880125M4[t] + 554.657601557322M5[t] + 304.09070366431M6[t] + 134.175190321277M7[t] + 803.65049328323M8[t] + 323.783975068084M9[t] + 382.612353324275M10[t] + 1149.28201806185M11[t] -51.1841435474764t + 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) -14573.6863254658 14958.587512 -0.9743 0.335501 0.167751 Y 0.286065503358865 0.148166 1.9307 0.060288 0.030144 X 459.077940222844 416.924803 1.1011 0.277122 0.138561 Y2 0.172963208384406 0.144688 1.1954 0.238629 0.119314 M1 263.451877994075 379.092278 0.695 0.490911 0.245455 M2 270.461141609439 384.662919 0.7031 0.485865 0.242933 M3 718.898880064055 378.815311 1.8978 0.064616 0.032308 M4 200.951950880125 370.652147 0.5422 0.590575 0.295287 M5 554.657601557322 382.617656 1.4496 0.154586 0.077293 M6 304.09070366431 379.21696 0.8019 0.42713 0.213565 M7 134.175190321277 390.902398 0.3432 0.733127 0.366563 M8 803.65049328323 384.186933 2.0918 0.042539 0.02127 M9 323.783975068084 363.724633 0.8902 0.378435 0.189217 M10 382.612353324275 385.360681 0.9929 0.32646 0.16323 M11 1149.28201806185 386.044247 2.9771 0.004814 0.002407 t -51.1841435474764 41.091625 -1.2456 0.219812 0.109906 Multiple Linear Regression - Regression Statistics Multiple R 0.686774285814741 R-squared 0.471658919656347 Adjusted R-squared 0.282965676676471 F-TEST (value) 2.49960683386341 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 0.00992526955596018 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 535.137166105338 Sum Squared Residuals 12027615.0349846 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3922 4528.32826030459 -606.328260304594 2 3759 4313.8492502141 -554.849250214103 3 4138 4829.38911122281 -691.389111222806 4 4634 4143.30130332614 490.698696673864 5 3996 4685.13591049369 -689.135910493687 6 4308 4509.64256170842 -201.642561708424 7 4429 4605.22540870518 -176.225408705179 8 5219 5175.25845856678 43.7415414332157 9 4929 5058.45585182232 -129.455851822320 10 5755 5042.76454948772 712.235450512281 11 5592 5492.33007650352 99.6699234964825 12 4163 4510.60036672018 -347.600366720179 13 4962 4578.21124602734 383.788753972658 14 5208 4547.23707597503 660.762924024967 15 4755 4934.47222426914 -179.47222426914 16 4491 4660.35922541686 -169.359225416862 17 5732 5128.10823253225 603.89176746775 18 5731 4953.51197552931 777.488024470685 19 5040 5100.31183162873 -60.311831628734 20 6102 5306.87751445018 795.122485549823 21 4904 5124.66969486927 -220.669694869266 22 5369 4994.07325493992 374.926745060076 23 5578 5524.83140911207 53.1685908879253 24 4619 4466.00636486694 152.993635133062 25 4731 4610.86384102229 120.136158977713 26 5011 4677.62926420104 333.370735798963 27 5299 4866.9315025187 432.068497481305 28 4146 4493.82076871535 -347.820768715352 29 4625 4674.57676147297 -49.5767614729691 30 4736 4528.13664291905 207.863357080955 31 4219 4706.78770253227 -487.787702532273 32 5116 4979.64198905432 136.358010945684 33 4205 4611.84527874596 -406.84527874596 34 4121 4747.42713431711 -626.427134317115 35 5103 5227.85470561021 -124.854705610210 36 4300 4295.12774217705 4.87225782294966 37 4578 4176.06632462137 401.933675378628 38 3809 4684.92202409398 -875.922024093982 39 5526 4606.24302996867 919.756970031334 40 4247 4214.80047113264 32.1995288673625 41 3830 4526.30466966653 -696.304669666533 42 4394 4326.50684120529 67.4931587947101 43 4826 4097.44145714962 728.558542850376 44 4409 4900.49411475478 -491.494114754778 45 4569 4169.46024644293 399.539753557066 46 4106 4452.09023422857 -346.090234228566 47 4794 4821.9838087742 -27.9838087741978 48 3914 3724.26552623583 189.734473764168 49 3793 4092.5303280244 -299.530328024404 50 4405 3968.36238551585 436.637614484154 51 4022 4502.96413202069 -480.964132020692 52 4100 4105.71823140901 -5.71823140901141 53 4788 3956.87442583456 831.12557416544 54 3163 4014.20197863793 -851.201978637926 55 3585 3589.23359998419 -4.23359998418977 56 3903 4386.72792317394 -483.727923173945 57 4178 3820.56892811952 357.431071880479 58 3863 3977.64482702668 -114.644827026676 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.774948798953122 0.450102402093756 0.225051201046878 20 0.830050058651671 0.339899882696657 0.169949941348329 21 0.89247157207679 0.215056855846419 0.107528427923210 22 0.923314629343871 0.153370741312257 0.0766853706561287 23 0.891604309902073 0.216791380195855 0.108395690097928 24 0.825555777847983 0.348888444304034 0.174444222152017 25 0.755378193266417 0.489243613467166 0.244621806733583 26 0.680939749926435 0.63812050014713 0.319060250073565 27 0.601849104399755 0.79630179120049 0.398150895600245 28 0.737608598272066 0.524782803455867 0.262391401727934 29 0.725173411044574 0.549653177910852 0.274826588955426 30 0.629111031518388 0.741777936963224 0.370888968481612 31 0.56219818743132 0.875603625137361 0.437801812568680 32 0.459150169569431 0.918300339138862 0.540849830430569 33 0.358204090785821 0.716408181571641 0.641795909214179 34 0.430082432065884 0.860164864131768 0.569917567934116 35 0.313977851568805 0.62795570313761 0.686022148431195 36 0.232850948491587 0.465701896983174 0.767149051508413 37 0.165901157180902 0.331802314361804 0.834098842819098 38 0.212300087060764 0.424600174121529 0.787699912939236 39 0.220266087741130 0.440532175482261 0.77973391225887 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 = 3 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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