*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, 20 Nov 2009 12:02:11 -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/20/t1258743757dix0nkeb6x8bgy0.htm/, Retrieved Fri, 20 Nov 2009 20:02:50 +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/20/t1258743757dix0nkeb6x8bgy0.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 «

500857 1,1 509127 509933 517009 519164 506971 1,6 500857 509127 509933 517009 569323 1,5 506971 500857 509127 509933 579714 1,6 569323 506971 500857 509127 577992 1,7 579714 569323 506971 500857 565464 1,6 577992 579714 569323 506971 547344 1,7 565464 577992 579714 569323 554788 1,6 547344 565464 577992 579714 562325 1,6 554788 547344 565464 577992 560854 1,3 562325 554788 547344 565464 555332 1,1 560854 562325 554788 547344 543599 1,6 555332 560854 562325 554788 536662 1,9 543599 555332 560854 562325 542722 1,6 536662 543599 555332 560854 593530 1,7 542722 536662 543599 555332 610763 1,6 593530 542722 536662 543599 612613 1,4 610763 593530 542722 536662 611324 2,1 612613 610763 593530 542722 594167 1,9 611324 612613 610763 593530 595454 1,7 594167 611324 612613 610763 590865 1,8 595454 594167 611324 612613 589379 2 590865 595454 594167 611324 584428 2,5 589379 590865 595454 594167 573100 2,1 584428 589379 590865 595454 567456 2,1 573100 584428 589379 590865 569028 2,3 567456 573100 5 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 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation TWIB[t] = + 17275.6362570304 + 1316.09095825163GI[t] + 0.993868125182958TWIB1[t] -0.0712656523643038TWIB2[t] + 0.0674558849413127TWIB3[t] -0.0287714131544064TWIB4[t] -3746.49879045247M1[t] + 7599.43785050854M2[t] + 58721.4905633282M3[t] + 16139.1979301117M4[t] + 2816.99152249312M5[t] -7256.21688681164M6[t] -7886.08593225942M7[t] + 11261.2367889179M8[t] + 8262.97224709365M9[t] + 2729.07025670023M10[t] -2820.30522071984M11[t] -171.699244602508t + 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) 17275.6362570304 17561.365367 0.9837 0.329985 0.164992 GI 1316.09095825163 1186.514877 1.1092 0.272647 0.136324 TWIB1 0.993868125182958 0.147446 6.7406 0 0 TWIB2 -0.0712656523643038 0.203243 -0.3506 0.727329 0.363665 TWIB3 0.0674558849413127 0.204108 0.3305 0.742409 0.371205 TWIB4 -0.0287714131544064 0.163704 -0.1758 0.861198 0.430599 M1 -3746.49879045247 4270.554276 -0.8773 0.384527 0.192264 M2 7599.43785050854 4474.853782 1.6983 0.095676 0.047838 M3 58721.4905633282 4549.386707 12.9076 0 0 M4 16139.1979301117 10133.028737 1.5927 0.117523 0.058762 M5 2816.99152249312 10768.99041 0.2616 0.794717 0.397359 M6 -7256.21688681164 10088.815973 -0.7192 0.475345 0.237673 M7 -7886.08593225942 4241.612296 -1.8592 0.068886 0.034443 M8 11261.2367889179 4638.97371 2.4275 0.018845 0.009423 M9 8262.97224709365 5705.528505 1.4482 0.153792 0.076896 M10 2729.07025670023 5403.998736 0.505 0.615771 0.307885 M11 -2820.30522071984 4349.957979 -0.6484 0.519724 0.259862 t -171.699244602508 77.763277 -2.208 0.031861 0.015931 Multiple Linear Regression - Regression Statistics Multiple R 0.99031942858933 R-squared 0.980732570641498 Adjusted R-squared 0.974181644659608 F-TEST (value) 149.708998903765 F-TEST (DF numerator) 17 F-TEST (DF denominator) 50 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6547.42229412788 Sum Squared Residuals 2143436934.88214 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 500857 504407.745017719 -3550.74501771933 2 506971 507662.863167248 -691.863167248181 3 569323 565296.70127828 4026.29872172049 4 579714 583673.595229676 -3959.5952296759 5 577992 576845.391273155 1146.60872684491 6 565464 568047.013135975 -2583.01313597482 7 547344 553955.572470251 -6611.57247025056 8 554788 555268.389727549 -480.389727548675 9 562325 559992.570932732 2332.42906726787 10 560854 559990.572582427 863.427417573398 11 555332 553030.650048601 2301.34995139921 12 543599 551248.234096493 -7649.23409649282 13 536662 536141.259820804 520.740179196085 14 542722 540532.197996587 2189.80200341266 15 593530 597498.787075112 -3968.78707511180 16 610763 604547.401469138 6215.59853086158 17 612613 604905.111717016 7707.88828298418 18 611324 599444.946616662 11879.0533833384 19 594167 596667.87197037 -2500.87197037077 20 595454 598049.31888168 -2595.31888168041 21 590865 597372.599515779 -6507.59951577861 22 589379 586157.382484993 3221.61751500652 23 584428 580524.950146184 3903.04985381575 24 573100 577485.795545908 -4385.79554590806 25 567456 562693.688203579 4762.31179642101 26 569028 569037.829636641 -9.82963664104096 27 620735 621462.683237327 -727.683237327405 28 628884 629931.802456431 -1047.80245643126 29 628232 620988.812480671 7243.18751932896 30 612117 612168.217214259 -51.2172142585296 31 595404 594853.771126114 550.228873886237 32 597141 598483.710419055 -1342.71041905507 33 593408 596768.038502108 -3360.03850210763 34 590072 586564.800235606 3507.19976439398 35 579799 577470.979957666 2328.02004233444 36 574205 570371.968520231 3833.03147976879 37 572775 561771.773284433 11003.2267155672 38 572942 571063.228257736 1878.77174226378 39 619567 622068.078996888 -2501.07899688827 40 625809 625837.381557325 -28.3815573246587 41 619916 615408.457050431 4507.54294956895 42 587625 602133.77923798 -14508.7792379797 43 565742 568738.776302509 -2996.77630250886 44 557274 567689.714085332 -10415.7140853318 45 560576 555786.122338448 4789.87766155205 46 548854 553550.28086485 -4696.28086485043 47 531673 535738.935004051 -4065.9350040508 48 525919 522613.644357082 3305.35564291816 49 511038 512525.768638526 -1487.76863852633 50 498662 508498.615973561 -9836.6159735607 51 555362 548447.151280625 6914.84871937448 52 564591 561825.987310169 2765.01268983071 53 541657 553188.650559148 -11531.6505591479 54 527070 524331.529781122 2738.47021887835 55 509846 510184.46123992 -338.461239919696 56 514258 511795.123945436 2462.87605456408 57 516922 514176.668710934 2745.33128906632 58 507561 510456.963832123 -2895.96383212348 59 492622 497088.484843499 -4466.48484349860 60 490243 485346.357480286 4896.64251971393 61 469357 480604.765034939 -11247.7650349387 62 477580 471110.264968227 6469.73503177348 63 528379 532122.598131767 -3743.5981317675 64 533590 537534.83197726 -3944.83197726046 65 517945 527018.576919579 -9073.57691957914 66 506174 503648.514014004 2525.48598599633 67 501866 489968.546890836 11897.4531091636 68 516141 503769.742940948 12371.2570590519 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.244755101856145 0.48951020371229 0.755244898143855 22 0.131062324440033 0.262124648880067 0.868937675559966 23 0.131429522329580 0.262859044659161 0.86857047767042 24 0.0959278348596336 0.191855669719267 0.904072165140366 25 0.0644993318449881 0.128998663689976 0.935500668155012 26 0.0704632139261235 0.140926427852247 0.929536786073876 27 0.0721121292654934 0.144224258530987 0.927887870734507 28 0.0633604626136546 0.126720925227309 0.936639537386345 29 0.0469818879513698 0.0939637759027396 0.95301811204863 30 0.0496422749715974 0.0992845499431948 0.950357725028403 31 0.0289026372518688 0.0578052745037376 0.971097362748131 32 0.0156041633738551 0.0312083267477102 0.984395836626145 33 0.0107307255446393 0.0214614510892786 0.98926927445536 34 0.00597005126666958 0.0119401025333392 0.99402994873333 35 0.00342244969225003 0.00684489938450006 0.99657755030775 36 0.00310376382352101 0.00620752764704201 0.996896236176479 37 0.0128347198687290 0.0256694397374581 0.987165280131271 38 0.0153706438994184 0.0307412877988369 0.984629356100582 39 0.0102845303507961 0.0205690607015921 0.989715469649204 40 0.00655635205502375 0.0131127041100475 0.993443647944976 41 0.17445130612217 0.34890261224434 0.82554869387783 42 0.379965149056181 0.759930298112363 0.620034850943819 43 0.297880621384943 0.595761242769885 0.702119378615057 44 0.366985552014130 0.733971104028261 0.63301444798587 45 0.309924112901617 0.619848225803234 0.690075887098383 46 0.199407648793982 0.398815297587965 0.800592351206018 47 0.117564038001995 0.23512807600399 0.882435961998005 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0740740740740741 NOK 5% type I error level 9 0.333333333333333 NOK 10% type I error level 12 0.444444444444444 NOK

Charts produced by software:

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Parameters (Session):

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