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Case: the Seatbelt Law question 3 (seasonally adjusted)

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 10:53:24 -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/t11953216674h1wxpl2ln31yyz.htm/, Retrieved Sat, 17 Nov 2007 18:47:47 +0100

User-defined keywords:

Dataseries X:

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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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Werkloosheid*1000[t] = + 465.407101309638 + 14.4669259774709Inflatie[t] + 4.10330363550572M1[t] + 0.382515156201070M2[t] -7.5595962840048M3[t] -15.9230306851118M4[t] -22.2864650862189M5[t] -21.2072535655235M6[t] + 30.6039423965235M7[t] + 38.3938153976694M8[t] + 36.1197195161118M9[t] + 20.7989310368071M10[t] + 1.49946551840354M11[t] + 1.9207884793047t + 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) 465.407101309638 11.574922 40.2082 0 0 Inflatie 14.4669259774709 4.056099 3.5667 0.000857 0.000429 M1 4.10330363550572 11.915413 0.3444 0.732138 0.366069 M2 0.382515156201070 11.893193 0.0322 0.974482 0.487241 M3 -7.5595962840048 11.860036 -0.6374 0.527024 0.263512 M4 -15.9230306851118 11.824585 -1.3466 0.184706 0.092353 M5 -22.2864650862189 11.802603 -1.8883 0.065306 0.032653 M6 -21.2072535655235 11.791237 -1.7986 0.078652 0.039326 M7 30.6039423965235 11.784404 2.597 0.012587 0.006294 M8 38.3938153976694 11.777464 3.2599 0.002101 0.00105 M9 36.1197195161118 11.769472 3.0689 0.003596 0.001798 M10 20.7989310368071 11.766068 1.7677 0.083743 0.041871 M11 1.49946551840354 11.761906 0.1275 0.899112 0.449556 t 1.9207884793047 0.149986 12.8065 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.936746926230519 R-squared 0.877494803802325 Adjusted R-squared 0.842873770094286 F-TEST (value) 25.3457135682976 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18.5950118887617 Sum Squared Residuals 15905.6254885868 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 476 513.385278759115 -37.3852787591147 2 475 507.245200965873 -32.2452009658732 3 470 502.670570602719 -32.6705706027192 4 461 483.207691301193 -22.2076913011930 5 455 471.531582390655 -16.5315823906553 6 456 468.744811999667 -12.7448119996669 7 517 528.263566832007 -11.2635668320070 8 525 537.974228312458 -12.9742283124576 9 523 537.620920910205 -14.6209209102047 10 519 524.220920910205 -5.22092091020473 11 509 503.948858675612 5.0511413243883 12 512 508.710259429754 3.28974057024589 13 519 511.84096634907 7.15903365092962 14 517 517.274429337806 -0.274429337805853 15 510 512.699798974652 -2.69979897465177 16 509 501.917075259608 7.08292474039182 17 501 490.24096634907 10.7590336509296 18 507 501.921121935553 5.07887806444706 19 569 554.206413779158 14.7935862208424 20 580 568.25715305285 11.7428469471505 21 578 567.903845650597 10.0961543494035 22 565 551.610460455102 13.3895395448976 23 547 538.571861209245 8.42813879075522 24 555 536.099798974652 18.9002010253482 25 562 540.677198491715 21.3228015082849 26 561 534.537120698474 26.4628793015261 27 555 525.622412542079 29.3775874579215 28 544 530.753307402253 13.2466925977471 29 537 536.43750966468 0.562490335319803 30 543 535.097431871439 7.90256812856106 31 594 590.276108910538 3.72389108946224 32 611 597.093385195494 13.9066148045058 33 613 593.846692597747 19.1533074022529 34 611 593.466925977471 17.5330740225291 35 594 571.748171145131 22.2518288548692 36 595 567.829416312791 27.1705836872093 37 591 573.853508427601 17.1464915723989 38 589 576.393586220842 12.6064137791576 39 584 577.605726248677 6.39427375132333 40 573 566.823002533633 6.17699746636692 41 567 558.04027881859 8.9597211814105 42 569 566.827049209578 2.17295079042217 43 621 623.452418846424 -2.45241884642379 44 629 633.163080326874 -4.16308032687435 45 628 634.256465522369 -6.25646552236853 46 612 610.729617338139 1.2703826618611 47 595 594.797632896787 0.202367103212828 48 597 599.55903365093 -2.55903365092959 49 593 601.243047972499 -8.24304797249874 50 590 596.549662777005 -6.54966277700462 51 580 580.401491631874 -0.401491631873829 52 574 578.298923503313 -4.29892350331279 53 573 576.749662777005 -3.74966277700462 54 573 575.409584983763 -2.40958498376335 55 620 624.801491631874 -4.80149163187383 56 626 634.512153112324 -8.5121531123244 57 620 628.372075319083 -8.37207531908314 58 588 614.972075319083 -26.9720753190831 59 566 601.933476073226 -35.9334760732256 60 557 603.801491631874 -46.8014916318738

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')

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Software written by Ed van Stee & Patrick Wessa

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