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Regression_Werkloosh_WS8

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 03:31:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/15/t1195122408nim8jhzagn8hzct.htm/, Retrieved Thu, 15 Nov 2007 11:26:49 +0100

User-defined keywords:

Rik, workshop 8, werkloosheid, eigen gegevens, Q3

Dataseries X:

» Textbox « » Textfile « » CSV «

513 0 0 503 -1 0 471 -1 0 471 -1 0 476 1 1 475 1 1 470 1 1 461 1 1 455 1 1 456 1 1 517 1 0 525 0 0 523 0 0 519 0 0 509 0 0 512 0 0 519 0 0 517 -1 0 510 -1 0 509 -1 0 501 0 0 507 -1 0 569 -1 0 580 -1 0 578 0 0 565 -1 0 547 0 1 555 1 1 562 1 1 561 1 1 555 1 1 544 1 1 537 0 0 543 1 1 594 0 0 611 1 1 613 0 0 611 1 0 594 0 0 595 0 0 591 1 0 589 1 0 584 0 1 573 -1 0 567 -1 0 569 -1 0 621 -1 0 629 -1 0 628 -1 0 612 0 0 595 0 0 597 0 0 593 1 0 590 1 0 580 0 0 574 0 0 573 -1 0 573 0 0 620 0 1 626 0 0 620 -1 0 588 1 1 566 1 1 557 0 0 561 1 0 549 0 1 532 0 0 526 0 1 511 0 1 499 0 1 555 -1 1 565 -1 0 542 -1 0

Text written by user:

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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Werklh[t] = + 540.875154681228 + 11.306032310809FinSit[t] -28.8350292566046`Econ `[t] -12.4156572395385M1[t] -13.1894645087279M2[t] -29.0748809254479M3[t] -34.4053070943695M4[t] -37.8790837700971M5[t] -34.1624894165475M6[t] -40.0850666057654M7[t] -46.8919825134514M8[t] -58.3380699639048M9[t] -56.2744917657598M10[t] -3.83624049774504M11[t] + 1.35792129282085t + 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) 540.875154681228 15.466311 34.9712 0 0 FinSit 11.306032310809 6.553664 1.7251 0.089826 0.044913 `Econ ` -28.8350292566046 10.298866 -2.7998 0.006933 0.003467 M1 -12.4156572395385 18.052022 -0.6878 0.494338 0.247169 M2 -13.1894645087279 18.843313 -0.7 0.486754 0.243377 M3 -29.0748809254479 18.809138 -1.5458 0.127596 0.063798 M4 -34.4053070943695 18.815841 -1.8285 0.072614 0.036307 M5 -37.8790837700971 19.874872 -1.9059 0.061626 0.030813 M6 -34.1624894165475 19.227445 -1.7768 0.080853 0.040426 M7 -40.0850666057654 18.942719 -2.1161 0.038638 0.019319 M8 -46.8919825134514 18.889068 -2.4825 0.015962 0.007981 M9 -58.3380699639048 18.713625 -3.1174 0.002838 0.001419 M10 -56.2744917657598 18.878677 -2.9808 0.004196 0.002098 M11 -3.83624049774504 18.729643 -0.2048 0.838428 0.419214 t 1.35792129282085 0.182208 7.4526 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.780914085975383 R-squared 0.609826809674768 Adjusted R-squared 0.515647074079023 F-TEST (value) 6.4751382642692 F-TEST (DF numerator) 14 F-TEST (DF denominator) 58 p-value 1.33610602137679e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 32.3008377859311 Sum Squared Residuals 60513.9590570358 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 513 529.81741873451 -16.8174187345102 2 503 519.095500447333 -16.0955004473330 3 471 504.568005323434 -33.5680053234337 4 471 500.595500447333 -29.595500447333 5 476 492.25668042944 -16.2566804294397 6 475 497.33119607581 -22.3311960758101 7 470 492.766540179413 -22.7665401794131 8 461 487.317545564548 -26.3175455645479 9 455 477.229379406915 -22.2293794069153 10 456 480.650878897881 -24.6508788978813 11 517 563.282080715321 -46.2820807153214 12 525 557.170210195078 -32.1702101950783 13 523 546.112474248361 -23.1124742483607 14 519 546.696588271992 -27.6965882719922 15 509 532.169093148093 -23.1690931480929 16 512 528.196588271992 -16.1965882719922 17 519 526.080732889085 -7.08073288908542 18 517 519.849216224647 -2.84921622464684 19 510 515.28456032825 -5.28456032824986 20 509 509.835565713385 -0.83556571338469 21 501 511.053431866561 -10.0534318665611 22 507 503.168899046718 3.83110095328199 23 569 556.965071607554 12.0349283924464 24 580 562.15923339812 17.8407666018805 25 578 562.407529762211 15.5924702377891 26 565 551.685611475033 13.3143885249666 27 547 519.629119405339 27.3708805946615 28 555 526.962646840047 28.0373531599532 29 562 524.84679145714 37.15320854286 30 561 529.92130710351 31.0786928964896 31 555 525.356651207113 29.6433487928865 32 544 519.907656592248 24.0923434077517 33 537 527.348487380411 9.65151261958872 34 543 513.240989925582 29.7590100744184 35 594 584.566159432213 9.43384056778722 36 611 572.231324276983 38.7686757230169 37 613 578.702585276061 34.2974147239389 38 611 590.592731610502 20.4072683894985 39 594 564.759204175793 29.2407958242067 40 595 560.786699299692 34.2133007003075 41 591 569.976876227595 21.0231237724052 42 589 575.051391873965 13.9486081260348 43 584 530.345674410155 53.6543255898454 44 573 542.425676741085 30.5743232589150 45 567 532.337510583452 34.6624894165476 46 569 535.759010074418 33.2409899255816 47 621 589.555182635254 31.4448173647461 48 629 594.74934442582 34.2506555741802 49 628 583.691608479102 44.3083915208978 50 612 595.581754813543 16.4182451864573 51 595 581.054259689643 13.9457403103565 52 597 577.081754813543 19.9182451864573 53 593 586.271931741445 6.72806825855504 54 590 591.346447387815 -1.3464473878154 55 580 575.47575918061 4.52424081939061 56 574 570.026764565744 3.97323543425576 57 573 548.632566097303 24.3674339026974 58 573 563.360097899078 9.63990210092241 59 620 588.321241203309 31.6787587966915 60 626 622.350432250479 3.64956774952099 61 620 599.986663992952 20.0133360070476 62 588 594.347813381597 -6.34781338159729 63 566 579.820318257698 -13.8203182576981 64 557 593.376810327393 -36.3768103273929 65 561 602.566987255295 -41.5669872552951 66 549 567.500441334252 -18.500441334252 67 532 591.77081469446 -59.7708146944596 68 526 557.48679082299 -31.4867908229898 69 511 547.398624665357 -36.3986246653572 70 499 550.820124156323 -51.8201241563232 71 555 593.31026440635 -38.3102644063497 72 565 627.33945545352 -62.3394554535202 73 542 616.281719506803 -74.2817195068026

Charts produced by software:

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Parameters:

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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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