*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, 02 Dec 2010 22:18:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t12913281759j9g5v9cfb9f5un.htm/, Retrieved Thu, 02 Dec 2010 23:16:25 +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/2010/Dec/02/t12913281759j9g5v9cfb9f5un.htm/}, year = {2010}, } @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 = {2010}, 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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-820,8 0 993,3 0 741,7 0 603,6 0 -145,8 0 -35,1 0 395,1 0 523,1 0 462,3 0 183,4 0 791,5 0 344,8 0 -217,0 0 406,7 0 228,6 0 -580,1 0 -1550,4 0 -1447,5 0 -40,1 0 -1033,5 0 -925,6 0 -347,8 0 -447,7 0 -102,6 0 -2062,2 0 -929,7 1 -720,7 1 -1541,8 1 -1432,3 1 -1216,2 1 -212,8 1 -378,2 1 76,9 1 -101,3 1 220,4 1 495,6 1 -1035,2 1 61,8 1 -734,8 1 -6,9 1 -1061,1 1 -854,6 1 -186,5 1 244,0 1 -992,6 1 -335,2 1 316,8 1 477,6 1 -572,1 1 1115,2 1

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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Totaal[t] = -33.5225000000001 + 40.6773461538463Dummy[t] -9.98165384615385t + 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) -33.5225000000001 239.130731 -0.1402 0.889113 0.444557 Dummy 40.6773461538463 417.711632 0.0974 0.922838 0.461419 t -9.98165384615385 14.47285 -0.6897 0.493786 0.246893 Multiple Linear Regression - Regression Statistics Multiple R 0.174547615419622 R-squared 0.0304668700486763 Adjusted R-squared -0.0107898588854227 F-TEST (value) 0.738470325588399 F-TEST (DF numerator) 2 F-TEST (DF denominator) 47 p-value 0.483306201821193 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 737.973458856313 Sum Squared Residuals 25596426.8208885 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -820.8 -43.5041538461539 -777.295846153846 2 993.3 -53.4858076923072 1046.78580769231 3 741.7 -63.4674615384629 805.167461538463 4 603.6 -73.4491153846157 677.049115384616 5 -145.8 -83.4307692307694 -62.3692307692306 6 -35.1 -93.4124230769232 58.3124230769232 7 395.1 -103.394076923077 498.494076923077 8 523.1 -113.375730769231 636.475730769231 9 462.3 -123.357384615385 585.657384615385 10 183.4 -133.339038461538 316.739038461538 11 791.5 -143.320692307692 934.820692307692 12 344.8 -153.302346153846 498.102346153846 13 -217 -163.284 -53.716 14 406.7 -173.265653846154 579.965653846154 15 228.6 -183.247307692308 411.847307692308 16 -580.1 -193.228961538461 -386.871038461539 17 -1550.4 -203.210615384615 -1347.18938461538 18 -1447.5 -213.192269230769 -1234.30773076923 19 -40.1 -223.173923076923 183.073923076923 20 -1033.5 -233.155576923077 -800.344423076923 21 -925.6 -243.137230769231 -682.46276923077 22 -347.8 -253.118884615384 -94.6811153846156 23 -447.7 -263.100538461538 -184.599461538462 24 -102.6 -273.082192307692 170.482192307692 25 -2062.2 -283.063846153846 -1779.13615384615 26 -929.7 -252.368153846154 -677.331846153846 27 -720.7 -262.349807692308 -458.350192307692 28 -1541.8 -272.331461538462 -1269.46853846154 29 -1432.3 -282.313115384616 -1149.98688461538 30 -1216.2 -292.294769230769 -923.90523076923 31 -212.8 -302.276423076923 89.4764230769232 32 -378.2 -312.258076923077 -65.9419230769229 33 76.9 -322.239730769231 399.139730769231 34 -101.3 -332.221384615385 230.921384615385 35 220.4 -342.203038461538 562.603038461538 36 495.6 -352.184692307692 847.784692307692 37 -1035.2 -362.166346153846 -673.033653846154 38 61.8 -372.148 433.948 39 -734.8 -382.129653846154 -352.670346153846 40 -6.9 -392.111307692308 385.211307692308 41 -1061.1 -402.092961538462 -659.007038461538 42 -854.6 -412.074615384615 -442.525384615385 43 -186.5 -422.056269230769 235.556269230769 44 244 -432.037923076923 676.037923076923 45 -992.6 -442.019576923077 -550.580423076923 46 -335.2 -452.001230769231 116.801230769231 47 316.8 -461.982884615384 778.782884615384 48 477.6 -471.964538461538 949.564538461538 49 -572.1 -481.946192307692 -90.153807692308 50 1115.2 -491.927846153846 1607.12784615385 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.744458490649744 0.511083018700513 0.255541509350256 7 0.609324486684428 0.781351026631144 0.390675513315572 8 0.486792401528445 0.97358480305689 0.513207598471555 9 0.375280284465933 0.750560568931867 0.624719715534067 10 0.287402097258486 0.574804194516972 0.712597902741514 11 0.265695921073347 0.531391842146694 0.734304078926653 12 0.220286659083348 0.440573318166696 0.779713340916652 13 0.227285323146826 0.454570646293653 0.772714676853174 14 0.21113505782531 0.42227011565062 0.78886494217469 15 0.202508330904942 0.405016661809883 0.797491669095058 16 0.255730448546975 0.51146089709395 0.744269551453025 17 0.553645183384746 0.892709633230508 0.446354816615254 18 0.627969609372807 0.744060781254386 0.372030390627193 19 0.628567031058956 0.742865937882087 0.371432968941044 20 0.566259610259559 0.867480779480882 0.433740389740441 21 0.483278636899921 0.966557273799841 0.516721363100079 22 0.441412680260366 0.882825360520732 0.558587319739634 23 0.396192405680290 0.792384811360581 0.60380759431971 24 0.557318527531296 0.885362944937408 0.442681472468704 25 0.625123891641997 0.749752216716005 0.374876108358003 26 0.540456599252838 0.919086801494323 0.459543400747162 27 0.460087093602879 0.920174187205758 0.539912906397121 28 0.464480070295985 0.92896014059197 0.535519929704015 29 0.467961773483598 0.935923546967197 0.532038226516402 30 0.468058953577888 0.936117907155777 0.531941046422112 31 0.475461579020336 0.950923158040671 0.524538420979664 32 0.434198946538067 0.868397893076133 0.565801053461933 33 0.461559458212324 0.923118916424648 0.538440541787676 34 0.431881057474489 0.863762114948979 0.56811894252551 35 0.485419012468224 0.970838024936448 0.514580987531776 36 0.699799997612747 0.600400004774506 0.300200002387253 37 0.618709735107964 0.762580529784072 0.381290264892036 38 0.671502663685786 0.656994672628428 0.328497336314214 39 0.564009068338002 0.871981863323996 0.435990931661998 40 0.629291555940091 0.741416888119817 0.370708444059909 41 0.516265028887584 0.967469942224833 0.483734971112416 42 0.396790316520795 0.79358063304159 0.603209683479205 43 0.29454829676077 0.58909659352154 0.70545170323923 44 0.368411354911255 0.73682270982251 0.631588645088745 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 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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