Model 5

*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 05:57:14 -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/Dec/19/t1261227490j6nistbvq2ayr4h.htm/, Retrieved Sat, 19 Dec 2009 13:58:22 +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/t1261227490j6nistbvq2ayr4h.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:

» Textbox « » Textfile « » CSV «

4132 537 4486 4625 4685 543 4132 4486 3172 594 4685 4132 4280 611 3172 4685 4207 613 4280 3172 4158 611 4207 4280 3933 594 4158 4207 3151 595 3933 4158 3616 591 3151 3933 4221 589 3616 3151 4436 584 4221 3616 4807 573 4436 4221 4849 567 4807 4436 5024 569 4849 4807 3521 621 5024 4849 4650 629 3521 5024 5393 628 4650 3521 5147 612 5393 4650 4845 595 5147 5393 3995 597 4845 5147 4493 593 3995 4845 4680 590 4493 3995 5463 580 4680 4493 4761 574 5463 4680 5307 573 4761 5463 5069 573 5307 4761 3501 620 5069 5307 4952 626 3501 5069 5152 620 4952 3501 5317 588 5152 4952 5189 566 5317 5152 4030 557 5189 5317 4420 561 4030 5189 4571 549 4420 4030 4551 532 4571 4420 4819 526 4551 4571 5133 511 4819 4551 4532 499 5133 4819 3339 555 4532 5133 4380 565 3339 4532 4632 542 4380 3339 4719 527 4632 4380 4212 510 4719 4632 3615 514 4212 4719 3420 517 3615 4212 4571 508 3420 3615 4407 493 4571 3420 4386 490 4407 4571 4386 469 4386 4407 4744 478 4386 4386 3185 528 4744 4386 3890 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -513.810663688752 + 1.63308823271502X[t] + 0.468641624549366Y1[t] + 0.467230093477431Y2[t] -78.0707028585922M1[t] -49.7223636565174M2[t] -1482.34079692405M3[t] + 161.088672144258M4[t] + 702.060124181986M5[t] -59.3880078675724M6[t] -412.849543664895M7[t] -1029.54724635694M8[t] -241.784142392865M9[t] + 358.552685645115M10[t] + 291.710793442415M11[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) -513.810663688752 633.711693 -0.8108 0.421485 0.210743 X 1.63308823271502 1.129062 1.4464 0.15456 0.07728 Y1 0.468641624549366 0.131392 3.5668 0.000831 0.000416 Y2 0.467230093477431 0.143941 3.246 0.002137 0.001068 M1 -78.0707028585922 193.120067 -0.4043 0.687817 0.343909 M2 -49.7223636565174 191.627779 -0.2595 0.796379 0.39819 M3 -1482.34079692405 197.254797 -7.5149 0 0 M4 161.088672144258 303.53858 0.5307 0.598072 0.299036 M5 702.060124181986 241.224746 2.9104 0.005458 0.002729 M6 -59.3880078675724 200.385357 -0.2964 0.768227 0.384113 M7 -412.849543664895 205.566596 -2.0083 0.050251 0.025125 M8 -1029.54724635694 209.322581 -4.9185 1.1e-05 5e-06 M9 -241.784142392865 239.460523 -1.0097 0.3177 0.15885 M10 358.552685645115 206.899391 1.733 0.08952 0.04476 M11 291.710793442415 200.357394 1.456 0.151916 0.075958 Multiple Linear Regression - Regression Statistics Multiple R 0.924165273843683 R-squared 0.85408145337857 Adjusted R-squared 0.811521877280653 F-TEST (value) 20.0679032002945 F-TEST (DF numerator) 14 F-TEST (DF denominator) 48 p-value 2.10942374678780e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 311.962855999084 Sum Squared Residuals 4671399.52910904 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4132 4548.3525244822 -416.352524482203 2 4685 4355.65527499672 329.344725003276 3 3172 3100.08370688245 71.9162931175536 4 4280 4320.59913965674 -40.5991396567388 5 4207 4677.17255672924 -470.17255672924 6 4158 4395.93835319514 -237.938353195142 7 3933 3957.64308101489 -24.6430810148915 8 3151 3214.23982645156 -63.239826451562 9 3616 3523.86605605475 92.1339439452506 10 4221 3973.4811299434 247.518870056596 11 4436 4399.2639728965 36.7360271034989 12 4807 4473.02136472618 333.97863527382 13 4849 4659.47264527676 189.52735472324 14 5024 4884.11247385547 139.887526144535 15 3521 3638.05057691131 -117.050576911305 16 4650 4671.94165650219 -21.9416565021865 17 5393 5038.12958392686 354.870416073145 18 5147 5126.25554273005 20.7444572699457 19 4845 4976.89762679116 -131.897626791163 20 3995 4106.99772695519 -111.997726955194 21 4493 4348.77960889126 144.220391108739 22 4680 4780.45512180086 -100.455121800865 23 5463 5017.59891761351 445.401082386493 24 4761 5170.40801427723 -409.408014277234 25 5307 5127.5589659451 179.441034054899 26 5069 5083.79010652997 -14.7901065299732 27 3501 3871.49774459598 -370.497744595976 28 4952 4678.69491351954 273.305086480462 29 5152 5157.25004680949 -5.2500468094948 30 5317 5115.22228185868 201.777718141319 31 5189 4896.60469168776 292.395308312241 32 4030 4282.31603238274 -252.316032382739 33 4420 4473.65039445984 -53.6503944598448 34 4571 4695.64071893916 -124.640718939156 35 4551 4854.02094854345 -303.020948543453 36 4819 4613.69053732885 205.309462671148 37 5133 4627.37486448922 505.625135510784 38 4532 4908.49728005916 -376.497280059163 39 3339 3432.38842082142 -93.3884208214166 40 4380 4252.25402794954 127.745972050455 41 4632 4686.11488027214 -54.114880272142 42 4719 4504.6546414283 214.345358571696 43 4212 4281.94441056693 -69.944410566933 44 3615 3474.82677529176 140.173224708241 45 3420 3750.82443670495 -330.824436704947 46 4571 3966.14198805534 604.85801194466 47 4407 4323.10041399014 83.8995860098644 48 4386 4487.414967016 -101.414967016003 49 4386 4288.58220182456 97.4177981754405 50 4744 4321.81650315804 422.183496841956 51 3185 3138.62618311494 46.3738168850645 52 3890 4228.51026237199 -338.510262371992 53 4520 4345.33293226227 174.667067737732 54 3990 4188.92918078782 -198.929180787818 55 3809 3874.91018993925 -65.9101899392526 56 3236 2948.61963891875 287.380361081253 57 3551 3402.8795038892 148.120496110802 58 3264 3891.28104126124 -627.281041261236 59 3579 3842.0157469564 -263.015746956404 60 3537 3565.46511665173 -28.4651166517309 61 3038 3593.65879798216 -555.65879798216 62 2888 3388.12836140063 -500.12836140063 63 2198 1735.35336767392 462.646632326079 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.672387104846233 0.655225790307534 0.327612895153767 19 0.51506260457045 0.96987479085910 0.48493739542955 20 0.364499193899589 0.728998387799179 0.635500806100411 21 0.248356007938696 0.496712015877391 0.751643992061304 22 0.187178558567576 0.374357117135153 0.812821441432424 23 0.266627437599854 0.533254875199709 0.733372562400146 24 0.37942370872148 0.75884741744296 0.62057629127852 25 0.287211067147077 0.574422134294153 0.712788932852924 26 0.222221873200782 0.444443746401563 0.777778126799218 27 0.244418847316266 0.488837694632531 0.755581152683734 28 0.217039711494073 0.434079422988145 0.782960288505927 29 0.15255274986675 0.3051054997335 0.84744725013325 30 0.151963518531523 0.303927037063047 0.848036481468477 31 0.167798541011723 0.335597082023446 0.832201458988277 32 0.126221831189835 0.25244366237967 0.873778168810165 33 0.08842526738596 0.17685053477192 0.91157473261404 34 0.0561646709894261 0.112329341978852 0.943835329010574 35 0.0452831092037054 0.0905662184074107 0.954716890796295 36 0.0383375551111314 0.0766751102222628 0.961662444888869 37 0.125120231615131 0.250240463230262 0.874879768384869 38 0.105711012358064 0.211422024716128 0.894288987641936 39 0.0678509194205842 0.135701838841168 0.932149080579416 40 0.0884404561130894 0.176880912226179 0.91155954388691 41 0.0562219246350734 0.112443849270147 0.943778075364927 42 0.153696224061077 0.307392448122154 0.846303775938923 43 0.315937379778168 0.631874759556336 0.684062620221832 44 0.505470182413991 0.989059635172017 0.494529817586009 45 0.405439662316301 0.810879324632602 0.594560337683699 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 2 0.0714285714285714 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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