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Q3_WS8_Rik

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

Title produced by software: Multiple Regression

Date of computation: Fri, 16 Nov 2007 08:23:36 -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/16/t1195226316nby13m7sfs6t6ju.htm/, Retrieved Fri, 16 Nov 2007 16:18:45 +0100

User-defined keywords:

Rik, workshop 8, eigen gegevens, regressie analyse, EDA

Dataseries X:

» Textbox « » Textfile « » CSV «

513 0 2 503 0 2 471 0 2 471 0 2 476 0 2 475 0 2 470 0 2 461 0 2 455 0 2 456 0 2 517 0 2 525 0 1 523 0 1 519 0 1 509 0 1 512 0 1 519 0 1 517 0 1 510 0 1 509 0 1 501 0 1 507 0 1 569 0 1 580 0 1 578 0 1 565 0 1 547 0 1 555 0 1 562 0 0 561 0 0 555 0 0 544 0 0 537 0 0 543 0 0 594 0 0 611 0 0 613 0 0 611 0 0 594 0 0 595 0 0 591 0 0 589 0 0 584 0 0 573 0 0 567 0 0 569 0 0 621 0 0 629 0 0 628 0 0 612 0 0 595 1 0 597 1 0 593 1 0 590 1 0 580 1 0 574 1 0 573 1 0 573 1 0 620 1 0 626 1 0 620 1 0 588 1 0 566 1 0 557 1 0 561 1 0 549 1 0 532 1 0 526 1 0 511 1 0 499 1 0 555 1 0 565 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werklh[t] = + 611.764523175355 -14.3070561873757LisStr[t] -52.9865133386884`9/11 `[t] -3.54164235685386M1[t] -7.7223382516665M2[t] -24.6711622204371M3[t] -23.8378288871039M4[t] -30.1689144435519M5[t] -33.668914443552M6[t] -42.0022477768852M7[t] -49.3355811102186M8[t] -56.5022477768852M9[t] -56.0022477768852M10[t] -1.16891444355192M11[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) 611.764523175355 9.463543 64.6443 0 0 LisStr -14.3070561873757 6.378918 -2.2429 0.028675 0.014338 `9/11 ` -52.9865133386884 4.005741 -13.2276 0 0 M1 -3.54164235685386 12.254717 -0.289 0.773593 0.386796 M2 -7.7223382516665 12.746818 -0.6058 0.546955 0.273477 M3 -24.6711622204371 12.75693 -1.9339 0.057921 0.028961 M4 -23.8378288871039 12.75693 -1.8686 0.066643 0.033322 M5 -30.1689144435519 12.704413 -2.3747 0.020835 0.010417 M6 -33.668914443552 12.704413 -2.6502 0.010311 0.005155 M7 -42.0022477768852 12.704413 -3.3061 0.001613 0.000807 M8 -49.3355811102186 12.704413 -3.8833 0.000263 0.000131 M9 -56.5022477768852 12.704413 -4.4475 3.9e-05 2e-05 M10 -56.0022477768852 12.704413 -4.4081 4.5e-05 2.2e-05 M11 -1.16891444355192 12.704413 -0.092 0.927003 0.463501 Multiple Linear Regression - Regression Statistics Multiple R 0.90349926934115 R-squared 0.816310929699992 Adjusted R-squared 0.775837066752533 F-TEST (value) 20.1688415746151 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.9742835076412 Sum Squared Residuals 28489.2790047774 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 513 502.249854141123 10.750145858877 2 503 498.069158246311 4.93084175368863 3 471 481.12033427754 -10.1203342775403 4 471 481.953667610874 -10.9536676108739 5 476 475.622582054426 0.377417945574162 6 475 472.122582054426 2.87741794557407 7 470 463.789248721093 6.21075127890751 8 461 456.455915387759 4.54408461224077 9 455 449.289248721092 5.71075127890764 10 456 449.789248721093 6.21075127890741 11 517 504.622582054426 12.3774179455741 12 525 558.778009836666 -33.7780098366662 13 523 555.236367479812 -32.2363674798124 14 519 551.055671585 -32.0556715849998 15 509 534.106847616229 -25.1068476162292 16 512 534.940180949562 -22.9401809495624 17 519 528.609095393114 -9.60909539311436 18 517 525.109095393114 -8.10909539311434 19 510 516.775762059781 -6.77576205978102 20 509 509.442428726448 -0.442428726447690 21 501 502.275762059781 -1.27576205978107 22 507 502.775762059781 4.22423794021898 23 569 557.609095393114 11.3909046068857 24 580 558.778009836666 21.2219901633337 25 578 555.236367479812 22.7636325201876 26 565 551.055671585 13.9443284150002 27 547 534.106847616229 12.8931523837708 28 555 534.940180949562 20.0598190504376 29 562 581.595608731803 -19.5956087318028 30 561 578.095608731803 -17.0956087318028 31 555 569.76227539847 -14.7622753984695 32 544 562.428942065136 -18.4289420651362 33 537 555.26227539847 -18.2622753984696 34 543 555.76227539847 -12.7622753984695 35 594 610.595608731803 -16.5956087318028 36 611 611.764523175355 -0.764523175354762 37 613 608.222880818501 4.77711918149906 38 611 604.042184923688 6.95781507631172 39 594 587.093360954918 6.90663904508235 40 595 587.926694288251 7.07330571174907 41 591 581.595608731803 9.40439126819715 42 589 578.095608731803 10.9043912681972 43 584 569.76227539847 14.2377246015305 44 573 562.428942065136 10.5710579348638 45 567 555.26227539847 11.7377246015305 46 569 555.76227539847 13.2377246015305 47 621 610.595608731803 10.4043912681972 48 629 611.764523175355 17.2354768246452 49 628 608.222880818501 19.7771191814991 50 612 604.042184923688 7.95781507631172 51 595 572.786304767542 22.2136952324581 52 597 573.619638100875 23.3803618991249 53 593 567.288552544427 25.7114474555730 54 590 563.788552544427 26.2114474555730 55 580 555.455219211094 24.5447807889063 56 574 548.12188587776 25.8781141222396 57 573 540.955219211094 32.0447807889063 58 573 541.455219211094 31.5447807889063 59 620 596.288552544427 23.7114474555730 60 626 597.457466987979 28.542533012021 61 620 593.915824631125 26.0841753688749 62 588 589.735128736313 -1.73512873631249 63 566 572.786304767542 -6.78630476754185 64 557 573.619638100875 -16.6196381008751 65 561 567.288552544427 -6.28855254442706 66 549 563.788552544427 -14.7885525444270 67 532 555.455219211094 -23.4552192110937 68 526 548.12188587776 -22.1218858777604 69 511 540.955219211094 -29.9552192110937 70 499 541.455219211094 -42.4552192110937 71 555 596.288552544427 -41.288552544427 72 565 597.457466987979 -32.457466987979 73 542 593.915824631125 -51.9158246311251

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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