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Case: the seatbelt law

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 09:41:55 -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/t1195144665824rrcy0wno4oar.htm/, Retrieved Thu, 15 Nov 2007 17:37:45 +0100

User-defined keywords:

Q3

Dataseries X:

» Textbox « » Textfile « » CSV «

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 0 519 0 509 0 512 0 519 0 517 0 510 0 509 0 501 0 507 0 569 0 580 0 578 0 565 0 547 0 555 0 562 0 561 0 555 0 544 0 537 0 543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 533.950757575758 + 0.462121212121239`x `[t] -8.87752525252522M1[t] -9.79166666666669M2[t] -30.4381313131313M3[t] -30.9179292929293M4[t] -29.8080808080808M5[t] -34.6212121212121M6[t] -44.2676767676768M7[t] -52.9141414141414M8[t] -61.3939393939394M9[t] -62.2070707070707M10[t] -8.6868686868687M11[t] + 1.31313131313131t + 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) 533.950757575758 17.091069 31.2415 0 0 `x ` 0.462121212121239 16.111584 0.0287 0.977215 0.488607 M1 -8.87752525252522 19.023756 -0.4667 0.642466 0.321233 M2 -9.79166666666669 19.812262 -0.4942 0.622984 0.311492 M3 -30.4381313131313 19.78737 -1.5383 0.129331 0.064666 M4 -30.9179292929293 19.769774 -1.5639 0.12319 0.061595 M5 -29.8080808080808 19.889394 -1.4987 0.139285 0.069643 M6 -34.6212121212121 19.842009 -1.7448 0.086219 0.043109 M7 -44.2676767676768 19.801826 -2.2355 0.02918 0.01459 M8 -52.9141414141414 19.768888 -2.6766 0.009613 0.004807 M9 -61.3939393939394 19.743231 -3.1096 0.002883 0.001442 M10 -62.2070707070707 19.724885 -3.1537 0.002535 0.001268 M11 -8.6868686868687 19.713869 -0.4406 0.661079 0.330539 t 1.31313131313131 0.380552 3.4506 0.00104 0.00052 Multiple Linear Regression - Regression Statistics Multiple R 0.746082785022105 R-squared 0.55663952210634 Adjusted R-squared 0.458949925282314 F-TEST (value) 5.69804298720819 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 1.30832598277397e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 34.1390595870493 Sum Squared Residuals 68763.047979798 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 513 526.386363636363 -13.3863636363634 2 503 526.785353535354 -23.7853535353536 3 471 507.45202020202 -36.4520202020202 4 471 508.285353535354 -37.2853535353536 5 476 510.708333333333 -34.7083333333334 6 475 507.208333333333 -32.2083333333333 7 470 498.875 -28.875 8 461 491.541666666667 -30.5416666666667 9 455 484.375 -29.375 10 456 484.875 -28.875 11 517 539.708333333333 -22.7083333333334 12 525 549.708333333333 -24.7083333333334 13 523 542.14393939394 -19.1439393939395 14 519 542.542929292929 -23.5429292929293 15 509 523.209595959596 -14.2095959595960 16 512 524.042929292929 -12.0429292929293 17 519 526.465909090909 -7.4659090909091 18 517 522.965909090909 -5.9659090909091 19 510 514.632575757576 -4.63257575757576 20 509 507.299242424242 1.70075757575758 21 501 500.132575757576 0.86742424242424 22 507 500.632575757576 6.36742424242424 23 569 555.465909090909 13.5340909090909 24 580 565.465909090909 14.5340909090909 25 578 557.901515151515 20.0984848484848 26 565 558.300505050505 6.69949494949496 27 547 538.967171717172 8.0328282828283 28 555 539.800505050505 15.1994949494950 29 562 542.223484848485 19.7765151515152 30 561 538.723484848485 22.2765151515152 31 555 530.390151515152 24.6098484848485 32 544 523.056818181818 20.9431818181818 33 537 515.890151515152 21.1098484848485 34 543 516.390151515152 26.6098484848485 35 594 571.223484848485 22.7765151515151 36 611 581.223484848485 29.7765151515152 37 613 573.659090909091 39.3409090909091 38 611 574.058080808081 36.9419191919192 39 594 554.724747474747 39.2752525252525 40 595 555.558080808081 39.4419191919192 41 591 558.443181818182 32.5568181818182 42 589 554.943181818182 34.0568181818182 43 584 546.609848484848 37.3901515151515 44 573 539.276515151515 33.7234848484848 45 567 532.109848484848 34.8901515151515 46 569 532.609848484848 36.3901515151515 47 621 587.443181818182 33.5568181818182 48 629 597.443181818182 31.5568181818182 49 628 589.878787878788 38.1212121212121 50 612 590.277777777778 21.7222222222222 51 595 570.944444444444 24.0555555555556 52 597 571.777777777778 25.2222222222222 53 593 574.200757575758 18.7992424242424 54 590 570.700757575758 19.2992424242424 55 580 562.367424242424 17.6325757575758 56 574 555.034090909091 18.9659090909091 57 573 547.867424242424 25.1325757575758 58 573 548.367424242424 24.6325757575758 59 620 603.200757575758 16.7992424242424 60 626 613.200757575758 12.7992424242424 61 620 605.636363636364 14.3636363636363 62 588 606.035353535354 -18.0353535353535 63 566 586.70202020202 -20.7020202020202 64 557 587.535353535354 -30.5353535353535 65 561 589.958333333333 -28.9583333333333 66 549 586.458333333333 -37.4583333333333 67 532 578.125 -46.125 68 526 570.791666666667 -44.7916666666666 69 511 563.625 -52.625 70 499 564.125 -65.125 71 555 618.958333333333 -63.9583333333333 72 565 628.958333333333 -63.9583333333333 73 542 621.39393939394 -79.3939393939395

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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