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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 03:55:11 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/15/t1195124065g72zbsg9x19qf8p.htm/, Retrieved Thu, 15 Nov 2007 11:54:35 +0100

User-defined keywords:

Dataseries X:

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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 1 519 1 509 1 512 1 519 1 517 1 510 1 509 1 501 1 507 1 569 1 580 1 578 1 565 1 547 1 555 1 562 1 561 1 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1 620 1 588 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werk[t] = + 513.214322916667 + 58.9089843749999actbel[t] -13.6611436631941M1[t] -16.5647166418651M2[t] -36.5415783110118M3[t] -36.3517733134921M4[t] -34.4953016493056M5[t] -38.638829985119M6[t] -47.6156916542659M7[t] -55.5925533234127M8[t] -63.4027483258928M9[t] -63.5462766617063M10[t] -9.35647166418653M11[t] + 0.643528335813491t + 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) 513.214322916667 14.157463 36.2504 0 0 actbel 58.9089843749999 11.91453 4.9443 7e-06 3e-06 M1 -13.6611436631941 16.02044 -0.8527 0.397256 0.198628 M2 -16.5647166418651 16.708256 -0.9914 0.325535 0.162767 M3 -36.5415783110118 16.682756 -2.1904 0.032461 0.01623 M4 -36.3517733134921 16.659907 -2.182 0.033105 0.016552 M5 -34.4953016493056 16.63972 -2.0731 0.042542 0.021271 M6 -38.638829985119 16.622205 -2.3245 0.023559 0.011779 M7 -47.6156916542659 16.60737 -2.8671 0.005735 0.002867 M8 -55.5925533234127 16.595223 -3.3499 0.001414 0.000707 M9 -63.4027483258928 16.585769 -3.8227 0.00032 0.00016 M10 -63.5462766617063 16.579012 -3.8329 0.00031 0.000155 M11 -9.35647166418653 16.574957 -0.5645 0.574558 0.287279 t 0.643528335813491 0.211694 3.0399 0.003525 0.001763 Multiple Linear Regression - Regression Statistics Multiple R 0.828565341301244 R-squared 0.686520524805647 Adjusted R-squared 0.61744877603401 F-TEST (value) 9.93923763354248 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 1.40640277201953e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 28.7063265493221 Sum Squared Residuals 48619.1378534227 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 513 500.196707589284 12.8032924107156 2 503 497.936662946429 5.0633370535714 3 471 478.603329613096 -7.60332961309554 4 471 479.436662946429 -8.43666294642857 5 476 481.936662946429 -5.9366629464289 6 475 478.436662946429 -3.43666294642865 7 470 470.103329613095 -0.103329613095266 8 461 462.769996279762 -1.76999627976213 9 455 455.603329613095 -0.603329613095288 10 456 456.103329613095 -0.103329613095402 11 517 510.936662946429 6.06333705357132 12 525 520.936662946429 4.06333705357131 13 523 566.828031994048 -43.8280319940479 14 519 564.56798735119 -45.5679873511904 15 509 545.234654017857 -36.2346540178571 16 512 546.06798735119 -34.0679873511905 17 519 548.56798735119 -29.5679873511904 18 517 545.06798735119 -28.0679873511905 19 510 536.734654017857 -26.7346540178572 20 509 529.401320684524 -20.4013206845238 21 501 522.234654017857 -21.2346540178571 22 507 522.734654017857 -15.7346540178571 23 569 577.56798735119 -8.56798735119046 24 580 587.56798735119 -7.56798735119044 25 578 574.55037202381 3.44962797619026 26 565 572.290327380952 -7.2903273809524 27 547 552.956994047619 -5.95699404761901 28 555 553.790327380952 1.20967261904762 29 562 556.290327380952 5.70967261904767 30 561 552.790327380952 8.20967261904763 31 555 544.456994047619 10.5430059523810 32 544 537.123660714286 6.87633928571433 33 537 529.956994047619 7.04300595238096 34 543 530.456994047619 12.543005952381 35 594 585.290327380952 8.70967261904764 36 611 595.290327380952 15.7096726190477 37 613 582.272712053572 30.7272879464284 38 611 580.012667410714 30.9873325892857 39 594 560.679334077381 33.3206659226191 40 595 561.512667410714 33.4873325892857 41 591 564.012667410714 26.9873325892858 42 589 560.512667410714 28.4873325892857 43 584 552.179334077381 31.8206659226190 44 573 544.846000744048 28.1539992559524 45 567 537.679334077381 29.3206659226190 46 569 538.179334077381 30.8206659226191 47 621 593.012667410714 27.9873325892857 48 629 603.012667410714 25.9873325892858 49 628 589.995052083334 38.0049479166665 50 612 587.735007440476 24.2649925595238 51 595 568.401674107143 26.5983258928572 52 597 569.235007440476 27.7649925595238 53 593 571.735007440476 21.2649925595239 54 590 568.235007440476 21.7649925595238 55 580 559.901674107143 20.0983258928572 56 574 552.56834077381 21.4316592261905 57 573 545.401674107143 27.5983258928571 58 573 545.901674107143 27.0983258928572 59 620 600.735007440476 19.2649925595238 60 626 610.735007440476 15.2649925595239 61 620 597.717392113095 22.2826078869046 62 588 595.457347470238 -7.4573474702381 63 566 576.124014136905 -10.1240141369047 64 557 576.957347470238 -19.9573474702381 65 561 579.457347470238 -18.4573474702380 66 549 575.957347470238 -26.9573474702381 67 532 567.624014136905 -35.6240141369047 68 526 560.290680803571 -34.2906808035714 69 511 553.124014136905 -42.1240141369047 70 499 553.624014136905 -54.6240141369047 71 555 608.457347470238 -53.457347470238 72 565 618.457347470238 -53.457347470238 73 542 605.439732142857 -63.4397321428573

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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