dummy2

*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, 07 Dec 2008 05:43:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/07/t1228653901fji8tbjjyfwzqky.htm/, Retrieved Sun, 07 Dec 2008 12:45:10 +0000

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/2008/Dec/07/t1228653901fji8tbjjyfwzqky.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

493 0 481 0 462 0 457 0 442 0 439 0 488 0 521 0 501 0 485 0 464 0 460 0 467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 0 476 0 475 0 470 0 461 0 455 0 456 0 517 0 525 0 523 0 519 0 509 0 512 0 519 0 517 0 510 0 509 0 501 0 507 0 569 0 580 0 578 0 565 0 547 0 555 0 562 0 561 0 555 0 544 0 537 0 543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 1 565 1 542 1 527 1 510 1 514 1 517 1 508 1 493 1 490 1 469 1 478 1 528 1 534 1 518 1 506 1 502 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Werkloosheid[t] = + 457.194308186739 -115.178788903924`Wel(1)_geen(0)_financiële_crisis`[t] + 5.09270574913525M1[t] -2.01522092542481M2[t] -14.3453698222073M3[t] -22.3421853856563M4[t] -33.5612231713276M5[t] -34.780260956999M6[t] + 29.7983444688769M7[t] + 42.0237511276500M8[t] + 33.1380466753120M9[t] + 18.1412311118628M10[t] -1.07780667380851M11[t] + 1.66348223011577t + 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) 457.194308186739 10.407204 43.9306 0 0 `Wel(1)_geen(0)_financiële_crisis` -115.178788903924 8.886232 -12.9615 0 0 M1 5.09270574913525 12.538933 0.4062 0.685564 0.342782 M2 -2.01522092542481 12.535661 -0.1608 0.872632 0.436316 M3 -14.3453698222073 12.53326 -1.1446 0.255319 0.127659 M4 -22.3421853856563 12.531729 -1.7828 0.077874 0.038937 M5 -33.5612231713276 12.531071 -2.6782 0.008751 0.004375 M6 -34.780260956999 12.531284 -2.7755 0.006664 0.003332 M7 29.7983444688769 12.556323 2.3732 0.019694 0.009847 M8 42.0237511276500 12.553092 3.3477 0.001178 0.000589 M9 33.1380466753120 12.55073 2.6403 0.009714 0.004857 M10 18.1412311118628 12.549238 1.4456 0.15165 0.075825 M11 -1.07780667380851 12.548617 -0.0859 0.931738 0.465869 t 1.66348223011577 0.104524 15.9148 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.88711550745224 R-squared 0.786973923562245 Adjusted R-squared 0.757196084920408 F-TEST (value) 26.4281747586803 F-TEST (DF numerator) 13 F-TEST (DF denominator) 93 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25.7879197163756 Sum Squared Residuals 61846.5627067357 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 493 463.950496165992 29.0495038340082 2 481 458.506051721546 22.4939482784543 3 462 447.839385054879 14.160614945121 4 457 441.506051721546 15.4939482784545 5 442 431.95049616599 10.0495038340102 6 439 432.394940610435 6.60505938956552 7 488 498.637028266426 -10.6370282664261 8 521 512.525917155315 8.47408284468521 9 501 505.303694933093 -4.30369493309283 10 485 491.970361599759 -6.9703615997594 11 464 474.414806044204 -10.4148060442039 12 460 477.156094948128 -17.1560949481280 13 467 483.912282927379 -16.9122829273792 14 460 478.467838482935 -18.4678384829347 15 448 467.801171816268 -19.8011718162682 16 443 461.467838482935 -18.4678384829349 17 436 451.912282927379 -15.9122829273793 18 431 452.356727371824 -21.3567273718237 19 484 518.598815027815 -34.5988150278153 20 510 532.487703916704 -22.4877039167042 21 513 525.265481694482 -12.2654816944820 22 503 511.932148361149 -8.93214836114865 23 471 494.376592805593 -23.3765928055931 24 471 497.117881709517 -26.1178817095174 25 476 503.874069688768 -27.8740696887683 26 475 498.429625244324 -23.4296252443241 27 470 487.762958577657 -17.7629585776575 28 461 481.429625244324 -20.4296252443241 29 455 471.874069688769 -16.8740696887686 30 456 472.318514133213 -16.318514133213 31 517 538.560601789205 -21.5606017892046 32 525 552.449490678094 -27.4494906780935 33 523 545.227268455871 -22.2272684558713 34 519 531.893935122538 -12.8939351225379 35 509 514.338379566982 -5.33837956698239 36 512 517.079668470907 -5.07966847090663 37 519 523.835856450158 -4.83585645015764 38 517 518.391412005713 -1.39141200571341 39 510 507.724745339047 2.27525466095327 40 509 501.391412005713 7.60858799428657 41 501 491.835856450158 9.16414354984212 42 507 492.280300894602 14.7196991053977 43 569 558.522388550594 10.4776114494061 44 580 572.411277439483 7.5887225605172 45 578 565.189055217261 12.8109447827394 46 565 551.855721883927 13.1442781160728 47 547 534.300166328372 12.6998336716283 48 555 537.041455232296 17.9585447677041 49 562 543.797643211547 18.2023567884531 50 561 538.353198767103 22.6468012328973 51 555 527.686532100436 27.313467899564 52 544 521.353198767103 22.6468012328973 53 537 511.797643211547 25.2023567884528 54 543 512.242087655992 30.7579123440084 55 594 578.484175311983 15.5158246880168 56 611 592.373064200872 18.6269357991279 57 613 585.15084197865 27.8491580213502 58 611 571.817508645316 39.1824913546835 59 594 554.261953089761 39.7380469102390 60 595 557.003241993685 37.9967580063148 61 591 563.759429972936 27.2405700270638 62 589 558.314985528492 30.6850144715080 63 584 547.648318861825 36.3516811381747 64 573 541.314985528492 31.685014471508 65 567 531.759429972936 35.2405700270635 66 569 532.203874417381 36.7961255826191 67 621 598.445962073372 22.5540379266276 68 629 612.334850962261 16.6651490377387 69 628 605.112628740039 22.8873712599609 70 612 591.779295406706 20.2207045932942 71 595 574.22373985115 20.7762601488498 72 597 576.965028755074 20.0349712449255 73 593 583.721216734325 9.27878326567454 74 590 578.276772289881 11.7232277101187 75 580 567.610105623215 12.3898943767854 76 574 561.276772289881 12.7232277101187 77 573 551.721216734326 21.2787832656742 78 573 552.16566117877 20.8343388212299 79 620 618.407748834762 1.59225116523827 80 626 632.296637723651 -6.29663772365065 81 620 625.074415501428 -5.07441550142837 82 588 611.741082168095 -23.7410821680951 83 566 594.18552661254 -28.1855266125395 84 557 596.926815516464 -39.9268155164638 85 561 603.683003495715 -42.6830034957148 86 549 598.23855905127 -49.2385590512705 87 532 587.571892384604 -55.5718923846039 88 526 581.238559051271 -55.2385590512706 89 511 571.683003495715 -60.683003495715 90 499 572.12744794016 -73.1274479401594 91 555 523.190746692227 31.8092533077733 92 565 537.079635581116 27.9203644188843 93 542 529.857413358893 12.1425866411066 94 527 516.52408002556 10.4759199744399 95 510 498.968524470005 11.0314755299955 96 514 501.709813373929 12.2901866260712 97 517 508.46600135318 8.53399864682025 98 508 503.021556908736 4.97844309126448 99 493 492.354890242069 0.645109757931141 100 490 486.021556908736 3.97844309126445 101 469 476.46600135318 -7.46600135318 102 478 476.910445797624 1.08955420237556 103 528 543.152533453616 -15.1525334536160 104 534 557.041422342505 -23.0414223425049 105 518 549.819200120283 -31.8192001202827 106 506 536.485866786949 -30.4858667869493 107 502 518.930311231394 -16.9303112313938

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) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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Software written by Ed van Stee & Patrick Wessa

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