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*The author of this computation has been verified*
R Software Module: /rwasp_boxcoxlin.wasp (opens new window with default values)
Title produced by software: Box-Cox Linearity Plot
Date of computation: Tue, 10 Nov 2009 10:09:26 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e.htm/, Retrieved Tue, 10 Nov 2009 18:10:13 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
344744 338653 327532 326225 318672 317756 337302 349420 336923 330758 321002 320820 327032 324047 316735 315710 313427 310527 330962 339015 341332 339092 323308 325849 330675 332225 331735 328047 326165 327081 346764 344190 343333 345777 344094 348609 354846 356427 353467 355996 352487 355178 374556 375021 375787 372720 364431 370490 376974 377632 378205 370861 369167 371551 382842 381903 384502 392058 384359 388884 386586 387495 385705 378670 377367 376911 389827 387820 387267 380575 372402 376740
 
Dataseries Y:
» Textbox « » Textfile « » CSV «
492865 480961 461935 456608 441977 439148 488180 520564 501492 485025 464196 460170 467037 460070 447988 442867 436087 431328 484015 509673 512927 502831 470984 471067 476049 474605 470439 461251 454724 455626 516847 525192 522975 518585 509239 512238 519164 517009 509933 509127 500857 506971 569323 579714 577992 565464 547344 554788 562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132


Box-Cox Linearity Plot
# observations x72
maximum correlation0.971177455976807
optimal lambda(x)2
Residual SD (orginial)13598.4850542249
Residual SD (transformed)13414.7654871982
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e/1g5b71257872960.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e/1g5b71257872960.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e/2ovuh1257872960.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e/2ovuh1257872960.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e/322y21257872960.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/10/t1257873007jng35ybfqw9r26e/322y21257872960.ps (open in new window)


 
Parameters (Session):
par1 = red ; par2 = blue ; par3 = TRUE ; par4 = iptot ; par5 = ipkl ;
 
Parameters (R input):
par1 = red ; par2 = blue ; par3 = TRUE ; par4 = iptot ; par5 = ipkl ;
 
R code (references can be found in the software module):
n <- length(x)
c <- array(NA,dim=c(401))
l <- array(NA,dim=c(401))
mx <- 0
mxli <- -999
for (i in 1:401)
{
l[i] <- (i-201)/100
if (l[i] != 0)
{
x1 <- (x^l[i] - 1) / l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(x1,y)
if (mx < abs(c[i]))
{
mx <- abs(c[i])
mxli <- l[i]
}
}
c
mx
mxli
if (mxli != 0)
{
x1 <- (x^mxli - 1) / mxli
} else {
x1 <- log(x)
}
r<-lm(y~x)
se <- sqrt(var(r$residuals))
r1 <- lm(y~x1)
se1 <- sqrt(var(r1$residuals))
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Linearity Plot',xlab='Lambda',ylab='correlation')
grid()
dev.off()
bitmap(file='test2.png')
plot(x,y,main='Linear Fit of Original Data',xlab='x',ylab='y')
abline(r)
grid()
mtext(paste('Residual Standard Deviation = ',se))
dev.off()
bitmap(file='test3.png')
plot(x1,y,main='Linear Fit of Transformed Data',xlab='x',ylab='y')
abline(r1)
grid()
mtext(paste('Residual Standard Deviation = ',se1))
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Linearity Plot',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'# observations x',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'maximum correlation',header=TRUE)
a<-table.element(a,mx)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'optimal lambda(x)',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Residual SD (orginial)',header=TRUE)
a<-table.element(a,se)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Residual SD (transformed)',header=TRUE)
a<-table.element(a,se1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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Software written by Ed van Stee & Patrick Wessa


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