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Case: the Seatbelt Law question 3

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

Title produced by software: Multiple Regression

Date of computation: Sat, 17 Nov 2007 10:42:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/17/t119532103874ikykd3g1ct9e8.htm/, Retrieved Sat, 17 Nov 2007 18:37:27 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

476 2.9 475 2.6 470 2.7 461 1.8 455 1.3 456 0.9 517 1.3 525 1.3 523 1.3 519 1.3 509 1.1 512 1.4 519 1.2 517 1.7 510 1.8 509 1.5 501 1 507 1.6 569 1.5 580 1.8 578 1.8 565 1.6 547 1.9 555 1.7 562 1.6 561 1.3 555 1.1 544 1.9 537 2.6 543 2.3 594 2.4 611 2.2 613 2 611 2.9 594 2.6 595 2.3 591 2.3 589 2.6 584 3.1 573 2.8 567 2.5 569 2.9 621 3.1 629 3.1 628 3.2 612 2.5 595 2.6 597 2.9 593 2.6 590 2.4 580 1.7 574 2 573 2.2 573 1.9 620 1.6 626 1.6 620 1.2 588 1.2 566 1.5 557 1.6

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 y[t] = + 498.337442925548 + 30.0901376736558x[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) 498.337442925548 18.395266 27.0905 0 0 x 30.0901376736558 8.816647 3.4129 0.001178 0.000589 Multiple Linear Regression - Regression Statistics Multiple R 0.408947204637615 R-squared 0.167237816180920 Adjusted R-squared 0.152879847494384 F-TEST (value) 11.6477351241019 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00117789228039977 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 43.1762204039982 Sum Squared Residuals 108122.788485729 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 476 585.598842179148 -109.598842179148 2 475 576.571800877053 -101.571800877053 3 470 579.580814644418 -109.580814644418 4 461 552.499690738128 -91.4996907381282 5 455 537.4546219013 -82.4546219013003 6 456 525.418566831838 -69.418566831838 7 517 537.4546219013 -20.4546219013003 8 525 537.4546219013 -12.4546219013003 9 523 537.4546219013 -14.4546219013003 10 519 537.4546219013 -18.4546219013003 11 509 531.436594366569 -22.4365943665691 12 512 540.463635668666 -28.4636356686658 13 519 534.445608133935 -15.4456081339347 14 517 549.490676970763 -32.4906769707626 15 510 552.499690738128 -42.4996907381282 16 509 543.472649436031 -34.4726494360314 17 501 528.427580599204 -27.4275805992035 18 507 546.481663203397 -39.481663203397 19 569 543.472649436031 25.5273505639686 20 580 552.499690738128 27.5003092618718 21 578 552.499690738128 25.5003092618718 22 565 546.481663203397 18.518336796603 23 547 555.508704505494 -8.50870450549375 24 555 549.490676970763 5.50932302923741 25 562 546.481663203397 15.518336796603 26 561 537.4546219013 23.5453780986997 27 555 531.436594366569 23.5634056334309 28 544 555.508704505494 -11.5087045054938 29 537 576.571800877053 -39.5718008770528 30 543 567.544759574956 -24.5447595749561 31 594 570.553773342322 23.4462266576783 32 611 564.53574580759 46.4642541924095 33 613 558.517718272859 54.4822817271407 34 611 585.59884217915 25.4011578208504 35 594 576.571800877053 17.4281991229472 36 595 567.544759574956 27.4552404250439 37 591 567.544759574956 23.4552404250439 38 589 576.571800877053 12.4281991229472 39 584 591.616869713881 -7.61686971388073 40 573 582.589828411784 -9.58982841178397 41 567 573.562787109687 -6.56278710968724 42 569 585.59884217915 -16.5988421791496 43 621 591.616869713881 29.3831302861193 44 629 591.616869713881 37.3831302861193 45 628 594.625883481246 33.3741165187537 46 612 573.562787109687 38.4372128903128 47 595 576.571800877053 18.4281991229472 48 597 585.59884217915 11.4011578208504 49 593 576.571800877053 16.4281991229472 50 590 570.553773342322 19.4462266576783 51 580 549.490676970763 30.5093230292374 52 574 558.517718272859 15.4822817271407 53 573 564.53574580759 8.4642541924095 54 573 555.508704505494 17.4912954945062 55 620 546.481663203397 73.518336796603 56 626 546.481663203397 79.518336796603 57 620 534.445608133935 85.5543918660653 58 588 534.445608133935 53.5543918660653 59 566 543.472649436031 22.5273505639686 60 557 546.481663203397 10.518336796603

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')

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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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