SHw WS7

*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: Wed, 18 Nov 2009 10:51:18 -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/18/t1258566794ysqw2vboibqcrot.htm/, Retrieved Wed, 18 Nov 2009 18:53:26 +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/18/t1258566794ysqw2vboibqcrot.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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627 356 696 386 825 444 677 387 656 327 785 448 412 225 352 182 839 460 729 411 696 342 641 361 695 377 638 331 762 428 635 340 721 352 854 461 418 221 367 198 824 422 687 329 601 320 676 375 740 364 691 351 683 380 594 319 729 322 731 386 386 221 331 187 707 344 715 342 657 365 653 313 642 356 643 337 718 389 654 326 632 343 731 357 392 220 344 228 792 391 852 425 649 332 629 298 685 360 617 326 715 325 715 393 629 301 916 426 531 265 357 210 917 429 828 440 708 357 858 431

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 Y[t] = + 236.298697179728 + 1.27981243762731X[t] -22.5586870633913M1[t] -22.3697630863033M2[t] + 1.07905234521315M3[t] -33.072487662169M4[t] + 16.0430108408864M5[t] + 35.2112537423614M6[t] -103.367482809061M7[t] -143.340997142818M8[t] + 55.8020533431762M9[t] + 27.5423396081969M10[t] -13.3303257734214M11[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) 236.298697179728 61.469188 3.8442 0.000362 0.000181 X 1.27981243762731 0.165377 7.7388 0 0 M1 -22.5586870633913 25.328363 -0.8906 0.377654 0.188827 M2 -22.3697630863033 25.349605 -0.8825 0.382025 0.191012 M3 1.07905234521315 26.054776 0.0414 0.967141 0.48357 M4 -33.072487662169 25.305548 -1.3069 0.197596 0.098798 M5 16.0430108408864 25.681456 0.6247 0.535194 0.267597 M6 35.2112537423614 27.178 1.2956 0.201448 0.100724 M7 -103.367482809061 32.693864 -3.1617 0.002746 0.001373 M8 -143.340997142818 35.970378 -3.985 0.000234 0.000117 M9 55.8020533431762 26.809692 2.0814 0.042869 0.021434 M10 27.5423396081969 25.911984 1.0629 0.29325 0.146625 M11 -13.3303257734214 25.38486 -0.5251 0.601962 0.300981 Multiple Linear Regression - Regression Statistics Multiple R 0.96911896449989 R-squared 0.93919156735334 Adjusted R-squared 0.923666010081853 F-TEST (value) 60.4932596576194 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 40.0058078818977 Sum Squared Residuals 75221.8392213155 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 627 669.35323791166 -42.3532379116603 2 696 707.936535017567 -11.9365350175667 3 825 805.614471831467 19.3855281685327 4 677 698.513622879329 -21.5136228793285 5 656 670.840375124745 -14.8403751247454 6 785 844.865922979125 -59.8659229791249 7 412 420.889012836812 -8.88901283681249 8 352 325.883563685081 26.1164363149188 9 839 880.814471831467 -41.8144718314673 10 729 789.84394865275 -60.8439486527499 11 696 660.664225074847 35.3357749251528 12 641 698.310987163187 -57.3109871631874 13 695 696.229299101833 -1.22929910183311 14 638 637.546850948065 0.453149051935056 15 762 785.13747282943 -23.1374728294304 16 635 638.362438310845 -3.36243831084497 17 721 702.835686065428 18.1643139345719 18 854 861.50348466828 -7.50348466827982 19 418 415.769763086303 2.23023691369671 20 367 346.360562687118 20.6394373128819 21 824 832.18159920163 -8.18159920162955 22 687 684.89932876731 2.10067123268946 23 601 632.508351447046 -31.5083514470464 24 676 716.22836128997 -40.2283612899698 25 740 679.591737412678 60.4082625873219 26 691 663.143099700611 27.8569002993889 27 683 723.706475823319 -40.7064758233195 28 594 611.486377120671 -17.4863771206715 29 729 664.441312936609 64.5586870633912 30 731 765.517551846232 -34.5175518462316 31 386 415.769763086303 -29.7697630863033 32 331 332.282625873218 -1.28262587321766 33 707 732.3562290667 -25.3562290666994 34 715 701.536890456466 13.4631095435344 35 657 690.099911140275 -33.0999111402754 36 653 636.879990157077 16.1200098429234 37 642 669.35323791166 -27.3532379116596 38 643 645.225725573829 -2.22572557382880 39 718 735.224787761965 -17.2247877619653 40 654 620.445064184063 33.5549358159373 41 632 691.317374126782 -59.3173741267823 42 731 728.40299115504 2.59700884496034 43 392 414.489950648676 -22.489950648676 44 344 384.754935815937 -40.7549358159374 45 792 792.507413635183 -0.507413635182951 46 852 807.761322779532 44.2386772204678 47 649 647.866100698574 1.13389930142586 48 629 617.682803592667 11.317196407333 49 685 674.472487662169 10.5275123378311 50 617 631.147788759928 -14.1477887599284 51 715 653.316791753817 61.6832082461825 52 715 706.192497505092 8.80750249490763 53 629 637.565251746435 -8.56525174643535 54 916 816.710049351324 99.289950648676 55 531 472.081510341905 58.9184896580951 56 357 361.718311938646 -4.71831193864575 57 917 841.140286265021 75.8597137349793 58 828 826.958509343942 1.04149065605816 59 708 679.861411639257 28.1385883607431 60 858 787.897857797099 70.1021422029009 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.248598780377043 0.497197560754086 0.751401219622957 17 0.169277030968389 0.338554061936778 0.830722969031611 18 0.183254653332618 0.366509306665237 0.816745346667382 19 0.102772322397121 0.205544644794241 0.89722767760288 20 0.0562377739064841 0.112475547812968 0.943762226093516 21 0.0460761888934273 0.0921523777868546 0.953923811106573 22 0.0454091691702165 0.0908183383404331 0.954590830829783 23 0.0815568354530674 0.163113670906135 0.918443164546933 24 0.0721230471785923 0.144246094357185 0.927876952821408 25 0.191000462553835 0.382000925107670 0.808999537446165 26 0.154232035961420 0.308464071922839 0.84576796403858 27 0.180371661326591 0.360743322653183 0.819628338673409 28 0.126445934373514 0.252891868747028 0.873554065626486 29 0.247364714353621 0.494729428707242 0.752635285646379 30 0.286459376156497 0.572918752312994 0.713540623843503 31 0.255011262485648 0.510022524971295 0.744988737514352 32 0.211426967368664 0.422853934737328 0.788573032631336 33 0.177550783636913 0.355101567273826 0.822449216363087 34 0.148767883698465 0.297535767396930 0.851232116301535 35 0.152990298859182 0.305980597718365 0.847009701140818 36 0.139697401176044 0.279394802352088 0.860302598823956 37 0.116747827031168 0.233495654062336 0.883252172968832 38 0.0739186002923679 0.147837200584736 0.926081399707632 39 0.157446213025520 0.314892426051040 0.84255378697448 40 0.192322016229864 0.384644032459728 0.807677983770136 41 0.399795935084198 0.799591870168395 0.600204064915802 42 0.384775264715502 0.769550529431005 0.615224735284498 43 0.414899517079412 0.829799034158824 0.585100482920588 44 0.40708525071982 0.81417050143964 0.59291474928018 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 0.0689655172413793 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/10ifqd1258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/10ifqd1258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/1fq1y1258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/1fq1y1258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/242mv1258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/242mv1258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/32q7c1258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/32q7c1258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/4vj9r1258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/4vj9r1258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/5gjj91258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/5gjj91258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/6snc11258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/6snc11258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/7ege41258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/7ege41258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/859h51258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/859h51258566673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/9uwm91258566673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566794ysqw2vboibqcrot/9uwm91258566673.ps (open in new window)

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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