W4_Mini1

*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: Fri, 03 Dec 2010 07:27:32 +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/03/t12913611458wqmzv4qx0jwty1.htm/, Retrieved Fri, 03 Dec 2010 08:25:57 +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/03/t12913611458wqmzv4qx0jwty1.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:

» Textbox « » Textfile « » CSV «

1 162556 1081 213118 6282929 1 29790 309 81767 4324047 1 87550 458 153198 4108272 0 84738 588 -26007 -1212617 1 54660 299 126942 1485329 1 42634 156 157214 1779876 0 40949 481 129352 1367203 1 42312 323 234817 2519076 1 37704 452 60448 912684 1 16275 109 47818 1443586 0 25830 115 245546 1220017 0 12679 110 48020 984885 1 18014 239 -1710 1457425 0 43556 247 32648 -572920 1 24524 497 95350 929144 0 6532 103 151352 1151176 0 7123 109 288170 790090 1 20813 502 114337 774497 1 37597 248 37884 990576 0 17821 373 122844 454195 1 12988 119 82340 876607 1 22330 84 79801 711969 0 13326 102 165548 702380 0 16189 295 116384 264449 0 7146 105 134028 450033 0 15824 64 63838 541063 1 26088 267 74996 588864 0 11326 129 31080 -37216 0 8568 37 32168 783310 0 14416 361 49857 467359 1 3369 28 87161 688779 1 11819 85 106113 608419 1 6620 44 80570 696348 1 4519 49 102129 597793 0 2220 22 301670 821730 0 18562 155 102313 377934 0 10327 91 88577 651939 1 5336 81 112477 697458 1 2365 79 191778 70 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 27 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Group[t] = + 0.148333867864412 + 1.19864028653261e-06Costs[t] + 0.000147266911271850Trades[t] + 8.066983191959e-07Dividends[t] + 1.52159973027087e-07`Wealth `[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) 0.148333867864412 0.053208 2.7878 0.005544 0.002772 Costs 1.19864028653261e-06 3e-06 0.3551 0.722711 0.361355 Trades 0.000147266911271850 0.000304 0.4847 0.62811 0.314055 Dividends 8.066983191959e-07 1e-06 1.0763 0.282394 0.141197 `Wealth ` 1.52159973027087e-07 0 2.1546 0.031753 0.015877 Multiple Linear Regression - Regression Statistics Multiple R 0.230458663993570 R-squared 0.053111195809701 Adjusted R-squared 0.0442202211224683 F-TEST (value) 5.97360780769817 F-TEST (DF numerator) 4 F-TEST (DF denominator) 426 p-value 0.000110163020384024 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.438709333112807 Sum Squared Residuals 81.9904644370811 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 1.63030780892835 -0.630307808928346 2 1 0.953455013936768 0.0465449860632317 3 1 1.06942219612496 -0.0694221961249564 4 0 0.131005619092946 -0.131005619092946 5 1 0.586295871008285 0.413704128991715 6 1 0.620060489704475 0.379939510295525 7 0 0.580633985866576 -0.580633985866576 8 1 0.819346963440792 0.180653036559208 9 1 0.447729317943721 0.552270682056279 10 1 0.442124538905950 0.557875461094050 11 0 0.579949740559675 -0.579949740559675 12 0 0.368328516619831 -0.368328516619831 13 1 0.425505260343158 0.574494739656842 14 0 0.176078366247202 -0.176078366247202 15 1 0.469218187867056 0.530781812132944 16 0 0.46859019119341 -0.46859019119341 17 0 0.525610203685669 -0.525610203685669 18 1 0.457292065957945 0.542707934042055 19 1 0.411208317278294 0.588791682721706 20 0 0.392833741587448 -0.392833741587448 21 1 0.381234607425193 0.618765392574807 22 1 0.360178442415794 0.639821557584206 23 0 0.419749588473482 -0.419749588473482 24 0 0.345307724176620 -0.345307724176620 25 0 0.348959548502005 -0.348959548502005 26 0 0.310552372866684 -0.310552372866684 27 1 0.369024938472096 0.630975061527904 28 0 0.200316497508181 -0.200316497508181 29 0 0.309190993560222 -0.309190993560222 30 0 0.33010971213832 -0.33010971213832 31 1 0.331612786766409 0.668387213233591 32 1 0.353196482243049 0.646803517756951 33 1 0.333700587132298 0.666299412867702 34 1 0.334314061368512 0.665685938631488 35 0 0.52262581793587 -0.52262581793587 36 0 0.333451552488076 -0.333451552488076 37 0 0.344767452703893 -0.344767452703893 38 1 0.363518629562092 0.636481370437908 39 1 0.424077704380323 0.575922295619677 40 0 0.273328613654340 -0.273328613654340 41 0 0.434297160029007 -0.434297160029007 42 0 0.308424131593135 -0.308424131593135 43 0 0.339057241037943 -0.339057241037943 44 0 0.329788663868196 -0.329788663868196 45 0 0.276596334421621 -0.276596334421621 46 1 0.289527654539316 0.710472345460684 47 1 0.420434084420978 0.579565915579022 48 1 0.388468969316149 0.61153103068385 49 0 0.336310791998725 -0.336310791998725 50 0 0.249812500796031 -0.249812500796031 51 1 0.341032458491676 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0.562938338235927 406 0.388518645843315 0.77703729168663 0.611481354156685 407 0.344861711525597 0.689723423051195 0.655138288474403 408 0.313274015370462 0.626548030740924 0.686725984629538 409 0.282651402505338 0.565302805010676 0.717348597494662 410 0.243818821188836 0.487637642377672 0.756181178811164 411 0.209492780228160 0.418985560456320 0.79050721977184 412 0.27569326367672 0.55138652735344 0.72430673632328 413 0.364951484536237 0.729902969072474 0.635048515463763 414 0.574388667918049 0.851222664163902 0.425611332081951 415 0.489517800592716 0.979035601185432 0.510482199407284 416 0.404536699913602 0.809073399827204 0.595463300086398 417 0.484693946415235 0.96938789283047 0.515306053584765 418 0.726431518984884 0.547136962030232 0.273568481015116 419 0.641881332381258 0.716237335237484 0.358118667618742 420 0.530856968045297 0.938286063909407 0.469143031954703 421 0.404292530154516 0.808585060309031 0.595707469845484 422 0.330964389744145 0.66192877948829 0.669035610255855 423 0.886884664101075 0.226230671797851 0.113115335898925 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 57 0.137019230769231 NOK 5% type I error level 138 0.331730769230769 NOK 10% type I error level 177 0.425480769230769 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/10s3eg1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/10s3eg1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/1wczp1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/1wczp1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/2wczp1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/2wczp1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/3plga1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/3plga1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/4plga1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/4plga1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/5plga1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/5plga1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/6plga1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/6plga1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/70ufv1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/70ufv1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/8s3eg1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/8s3eg1291361223.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/9s3eg1291361223.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t12913611458wqmzv4qx0jwty1/9s3eg1291361223.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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