*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: Sun, 13 Dec 2009 06:47:53 -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/13/t1260712151h28kaas9jmmihcs.htm/, Retrieved Sun, 13 Dec 2009 14:49:30 +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/13/t1260712151h28kaas9jmmihcs.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 «

431 436 443 448 460 467 484 431 436 443 448 460 510 484 431 436 443 448 513 510 484 431 436 443 503 513 510 484 431 436 471 503 513 510 484 431 471 471 503 513 510 484 476 471 471 503 513 510 475 476 471 471 503 513 470 475 476 471 471 503 461 470 475 476 471 471 455 461 470 475 476 471 456 455 461 470 475 476 517 456 455 461 470 475 525 517 456 455 461 470 523 525 517 456 455 461 519 523 525 517 456 455 509 519 523 525 517 456 512 509 519 523 525 517 519 512 509 519 523 525 517 519 512 509 519 523 510 517 519 512 509 519 509 510 517 519 512 509 501 509 510 517 519 512 507 501 509 510 517 519 569 507 501 509 510 517 580 569 507 501 509 510 578 580 569 507 501 509 565 578 580 569 507 501 547 565 578 580 569 507 555 547 565 578 580 569 562 555 547 565 578 580 561 562 555 547 565 578 555 561 562 555 547 565 544 555 561 562 555 547 537 544 555 561 562 555 543 537 544 555 561 562 594 543 537 544 555 561 611 594 543 537 544 555 613 611 594 543 537 544 611 613 611 594 543 537 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 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 Y[t] = -45.7369064542018 + 1.13418044850272`Y(t-1)`[t] -0.16358852083517`Y(t-2)`[t] -0.0100567924246914`Y(t-3)`[t] + 0.116041570443329`Y(t-4)`[t] + 0.0199336238572533`Y(t-5) `[t] + 6.59174048804482M1[t] + 59.2644444889681M2[t] + 11.8349664900739M3[t] + 6.5260619174202M4[t] -2.29913043626265M5[t] -13.1189551740509M6[t] + 5.31204725573158M7[t] + 2.18713491252564M8[t] -0.462164422370506M9[t] -1.93905835432363M10[t] -1.94342270003405M11[t] -0.332543357065598t + 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) -45.7369064542018 27.93241 -1.6374 0.107951 0.053976 `Y(t-1)` 1.13418044850272 0.143357 7.9116 0 0 `Y(t-2)` -0.16358852083517 0.219819 -0.7442 0.460311 0.230156 `Y(t-3)` -0.0100567924246914 0.240403 -0.0418 0.966802 0.483401 `Y(t-4)` 0.116041570443329 0.245562 0.4726 0.638628 0.319314 `Y(t-5) ` 0.0199336238572533 0.167659 0.1189 0.905846 0.452923 M1 6.59174048804482 3.52776 1.8685 0.067672 0.033836 M2 59.2644444889681 3.924635 15.1006 0 0 M3 11.8349664900739 9.576717 1.2358 0.222422 0.111211 M4 6.5260619174202 9.758682 0.6687 0.506797 0.253399 M5 -2.29913043626265 9.761515 -0.2355 0.814779 0.407389 M6 -13.1189551740509 8.982316 -1.4605 0.150527 0.075263 M7 5.31204725573158 4.34379 1.2229 0.227214 0.113607 M8 2.18713491252564 4.80296 0.4554 0.650853 0.325426 M9 -0.462164422370506 5.124348 -0.0902 0.928504 0.464252 M10 -1.93905835432363 5.117028 -0.3789 0.706368 0.353184 M11 -1.94342270003405 3.589363 -0.5414 0.590658 0.295329 t -0.332543357065598 0.162008 -2.0526 0.045468 0.022734 Multiple Linear Regression - Regression Statistics Multiple R 0.995598893828259 R-squared 0.991217157392052 Adjusted R-squared 0.988170048732152 F-TEST (value) 325.297607675240 F-TEST (DF numerator) 17 F-TEST (DF denominator) 49 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.52017753496632 Sum Squared Residuals 1493.14564085979 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 431 440.737933232989 -9.73793323298886 2 484 487.070561029982 -3.07056102998181 3 510 499.489032257311 10.5109677426890 4 513 513.804409234132 -0.80440923413228 5 503 502.543160109451 0.456839890548531 6 471 485.347280478233 -14.3472804782331 7 471 472.831242925902 -1.83124292590170 8 476 475.575586748221 0.424413251778947 9 475 477.485848823501 -2.48584882350152 10 470 469.811621989045 0.188378010954846 11 461 463.279240639035 -2.27924063903517 12 455 456.090703194296 -1.09070319429636 13 456 457.051024832742 -1.05102483274220 14 517 510.997266705862 6.00273329413807 15 525 531.172962689005 -6.17296268900465 16 523 523.740349746562 -0.740349746561775 17 519 510.38852046152 8.61147953847986 18 509 502.044622695829 6.95537730417143 19 512 511.620028570547 0.379971429452562 20 519 513.168612443806 5.83138755619411 21 517 517.231801723617 -0.231801723616744 22 510 510.73856331461 -0.738563314610015 23 509 502.86796043977 6.13203956023007 24 501 505.381984429606 -4.3819844296063 25 507 502.709176266486 4.29082373351409 26 569 562.321026319648 6.67897368035186 27 580 583.721539047799 -3.72153904779922 28 578 579.404980817877 -1.40498081787724 29 565 566.092669782408 -1.09266978240755 30 547 547.726687292647 -0.726687292647053 31 555 550.069004602048 4.93099539795206 32 562 558.747510887895 3.25248911210467 33 561 561.028837768938 -0.0288377689378994 34 555 554.511760668049 0.48823933195149 35 544 548.032488582235 -4.0324885822346 36 537 539.13073089307 -2.13073089307021 37 543 539.333973164823 3.66602683517713 38 594 599.018777815697 -5.01877781569742 39 611 606.792766737318 4.20723326268211 40 613 610.99747025947 2.00252974053013 41 611 601.370908233529 9.6290917664711 42 594 593.489758564533 0.51024143546718 43 595 595.603534983781 -0.603534983781001 44 591 596.65233291752 -5.65233291751942 45 589 588.948929488759 0.0510705112407572 46 584 583.5028546484 0.497145351600041 47 573 577.63961887935 -4.63961887934948 48 567 567.168336819897 -0.168336819897217 49 569 568.160391314855 0.839608685145208 50 621 623.240993597469 -2.24099359746939 51 629 632.813393882366 -3.8133938823658 52 628 626.8031535873 1.19684641269974 53 612 614.792057453027 -2.79205745302691 54 595 591.649965274335 3.35003472566515 55 597 595.059710852417 1.94028914758324 56 593 596.855957002558 -3.85595700255832 57 590 587.304582195185 2.69541780481541 58 580 580.435199379896 -0.43519937989636 59 574 569.180691459611 4.8193085403892 60 573 565.22824466313 7.77175533687009 61 573 571.007501188105 1.99249881189465 62 620 622.351374531341 -2.35137453134130 63 626 627.010305386201 -1.01030538620139 64 620 620.249636354659 -0.249636354658566 65 588 602.812683960065 -14.8126839600650 66 566 561.741685694424 4.25831430557641 67 557 561.816478065305 -4.81647806530515 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.966224334729517 0.0675513305409657 0.0337756652704828 22 0.939879806985654 0.120240386028692 0.0601201930143459 23 0.943843125842461 0.112313748315078 0.0561568741575388 24 0.919003704778047 0.161992590443906 0.0809962952219529 25 0.888841879717768 0.222316240564464 0.111158120282232 26 0.876721094108685 0.246557811782630 0.123278905891315 27 0.880449167411242 0.239101665177515 0.119550832588758 28 0.851660164997745 0.296679670004510 0.148339835002255 29 0.834069574122196 0.331860851755608 0.165930425877804 30 0.768975783417118 0.462048433165764 0.231024216582882 31 0.706015817183324 0.587968365633352 0.293984182816676 32 0.658131395539457 0.683737208921087 0.341868604460543 33 0.592314700066349 0.815370599867303 0.407685299933651 34 0.512789095080783 0.974421809838434 0.487210904919217 35 0.471518752492833 0.943037504985665 0.528481247507167 36 0.468152364697586 0.936304729395173 0.531847635302414 37 0.368381792258546 0.736763584517093 0.631618207741454 38 0.442617923302953 0.885235846605906 0.557382076697047 39 0.339109503266060 0.678219006532119 0.66089049673394 40 0.256112950175944 0.512225900351889 0.743887049824056 41 0.666557871403663 0.666884257192675 0.333442128596337 42 0.555530960427188 0.888938079145624 0.444469039572812 43 0.44259772349594 0.88519544699188 0.55740227650406 44 0.382537594467793 0.765075188935585 0.617462405532208 45 0.256977795480819 0.513955590961637 0.743022204519181 46 0.160451016160196 0.320902032320391 0.839548983839804 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 1 0.0384615384615385 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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