R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(112.39,97.59,142.30,120.79,121.24,104.61,119.86,117.81,91.86,117.37,112.84,101.95,120.52,102.84,137.41,118.97,125.01,118.57,130.61,116.30,99.15,110.26,107.59,107.01,113.77,93.33,147.32,124.48,106.79,134.39,111.41,132.43,98.26,109.81,115.28,108.97,99.19,105.46,138.97,124.52,117.37,123.86,116.39,124.70,97.46,103.24,112.39,107.19,100.53,95.73,143.54,101.99,120.66,121.46,102.97,121.32,85.02,106.21,110.39,87.10)
> x <- c(105.81,107.16,107.83,108.85,109.52,110.19,111.20,111.54,111.88,112.55,112.55,112.55,114.24,116.26,116.60,118.62,119.63,120.64,121.65,122.33,122.66,123.00,123.34,124.68,125.02,125.02,125.36,125.70,125.70,126.03,126.37,126.37,126.71,126.71,127.04,127.04,127.38,127.72,128.05,129.40,131.09,131.42,131.76,132.10,132.43,132.77,132.77,133.11,133.45,133.78,134.12,134.46,134.79,134.79,135.13,135.13,136.82,137.15,142.54,143.89)
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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
  [1] -0.1440653 -0.1441457 -0.1442262 -0.1443067 -0.1443872 -0.1444677
  [7] -0.1445483 -0.1446289 -0.1447095 -0.1447901 -0.1448708 -0.1449515
 [13] -0.1450322 -0.1451129 -0.1451937 -0.1452745 -0.1453553 -0.1454361
 [19] -0.1455170 -0.1455979 -0.1456788 -0.1457598 -0.1458407 -0.1459217
 [25] -0.1460027 -0.1460838 -0.1461648 -0.1462459 -0.1463270 -0.1464082
 [31] -0.1464893 -0.1465705 -0.1466517 -0.1467329 -0.1468142 -0.1468955
 [37] -0.1469768 -0.1470581 -0.1471395 -0.1472208 -0.1473022 -0.1473837
 [43] -0.1474651 -0.1475466 -0.1476281 -0.1477096 -0.1477911 -0.1478727
 [49] -0.1479543 -0.1480359 -0.1481175 -0.1481992 -0.1482809 -0.1483626
 [55] -0.1484443 -0.1485260 -0.1486078 -0.1486896 -0.1487714 -0.1488532
 [61] -0.1489351 -0.1490170 -0.1490989 -0.1491808 -0.1492628 -0.1493448
 [67] -0.1494267 -0.1495088 -0.1495908 -0.1496729 -0.1497550 -0.1498371
 [73] -0.1499192 -0.1500013 -0.1500835 -0.1501657 -0.1502479 -0.1503302
 [79] -0.1504124 -0.1504947 -0.1505770 -0.1506593 -0.1507417 -0.1508240
 [85] -0.1509064 -0.1509888 -0.1510712 -0.1511537 -0.1512362 -0.1513187
 [91] -0.1514012 -0.1514837 -0.1515663 -0.1516488 -0.1517314 -0.1518140
 [97] -0.1518967 -0.1519793 -0.1520620 -0.1521447 -0.1522274 -0.1523102
[103] -0.1523929 -0.1524757 -0.1525585 -0.1526413 -0.1527241 -0.1528070
[109] -0.1528899 -0.1529728 -0.1530557 -0.1531386 -0.1532216 -0.1533046
[115] -0.1533876 -0.1534706 -0.1535536 -0.1536367 -0.1537197 -0.1538028
[121] -0.1538859 -0.1539691 -0.1540522 -0.1541354 -0.1542186 -0.1543018
[127] -0.1543850 -0.1544682 -0.1545515 -0.1546348 -0.1547181 -0.1548014
[133] -0.1548847 -0.1549681 -0.1550514 -0.1551348 -0.1552182 -0.1553017
[139] -0.1553851 -0.1554686 -0.1555520 -0.1556355 -0.1557191 -0.1558026
[145] -0.1558861 -0.1559697 -0.1560533 -0.1561369 -0.1562205 -0.1563041
[151] -0.1563878 -0.1564715 -0.1565552 -0.1566389 -0.1567226 -0.1568063
[157] -0.1568901 -0.1569738 -0.1570576 -0.1571414 -0.1572253 -0.1573091
[163] -0.1573930 -0.1574768 -0.1575607 -0.1576446 -0.1577285 -0.1578125
[169] -0.1578964 -0.1579804 -0.1580644 -0.1581484 -0.1582324 -0.1583164
[175] -0.1584005 -0.1584845 -0.1585686 -0.1586527 -0.1587368 -0.1588209
[181] -0.1589051 -0.1589892 -0.1590734 -0.1591576 -0.1592418 -0.1593260
[187] -0.1594102 -0.1594945 -0.1595787 -0.1596630 -0.1597473 -0.1598316
[193] -0.1599159 -0.1600003 -0.1600846 -0.1601690 -0.1602533 -0.1603377
[199] -0.1604221 -0.1605066 -0.1605910 -0.1606754 -0.1607599 -0.1608444
[205] -0.1609288 -0.1610133 -0.1610979 -0.1611824 -0.1612669 -0.1613515
[211] -0.1614360 -0.1615206 -0.1616052 -0.1616898 -0.1617744 -0.1618591
[217] -0.1619437 -0.1620284 -0.1621131 -0.1621977 -0.1622824 -0.1623671
[223] -0.1624519 -0.1625366 -0.1626213 -0.1627061 -0.1627909 -0.1628757
[229] -0.1629604 -0.1630453 -0.1631301 -0.1632149 -0.1632997 -0.1633846
[235] -0.1634695 -0.1635543 -0.1636392 -0.1637241 -0.1638090 -0.1638940
[241] -0.1639789 -0.1640638 -0.1641488 -0.1642338 -0.1643187 -0.1644037
[247] -0.1644887 -0.1645737 -0.1646588 -0.1647438 -0.1648288 -0.1649139
[253] -0.1649990 -0.1650840 -0.1651691 -0.1652542 -0.1653393 -0.1654244
[259] -0.1655095 -0.1655947 -0.1656798 -0.1657650 -0.1658501 -0.1659353
[265] -0.1660205 -0.1661057 -0.1661909 -0.1662761 -0.1663613 -0.1664465
[271] -0.1665318 -0.1666170 -0.1667023 -0.1667875 -0.1668728 -0.1669581
[277] -0.1670434 -0.1671287 -0.1672140 -0.1672993 -0.1673846 -0.1674700
[283] -0.1675553 -0.1676407 -0.1677260 -0.1678114 -0.1678968 -0.1679821
[289] -0.1680675 -0.1681529 -0.1682383 -0.1683238 -0.1684092 -0.1684946
[295] -0.1685800 -0.1686655 -0.1687509 -0.1688364 -0.1689218 -0.1690073
[301] -0.1690928 -0.1691783 -0.1692638 -0.1693493 -0.1694348 -0.1695203
[307] -0.1696058 -0.1696913 -0.1697769 -0.1698624 -0.1699479 -0.1700335
[313] -0.1701190 -0.1702046 -0.1702902 -0.1703757 -0.1704613 -0.1705469
[319] -0.1706325 -0.1707181 -0.1708037 -0.1708893 -0.1709749 -0.1710605
[325] -0.1711462 -0.1712318 -0.1713174 -0.1714031 -0.1714887 -0.1715744
[331] -0.1716600 -0.1717457 -0.1718313 -0.1719170 -0.1720027 -0.1720883
[337] -0.1721740 -0.1722597 -0.1723454 -0.1724311 -0.1725168 -0.1726025
[343] -0.1726882 -0.1727739 -0.1728596 -0.1729453 -0.1730310 -0.1731168
[349] -0.1732025 -0.1732882 -0.1733739 -0.1734597 -0.1735454 -0.1736312
[355] -0.1737169 -0.1738026 -0.1738884 -0.1739742 -0.1740599 -0.1741457
[361] -0.1742314 -0.1743172 -0.1744030 -0.1744887 -0.1745745 -0.1746603
[367] -0.1747460 -0.1748318 -0.1749176 -0.1750034 -0.1750892 -0.1751749
[373] -0.1752607 -0.1753465 -0.1754323 -0.1755181 -0.1756039 -0.1756897
[379] -0.1757755 -0.1758613 -0.1759471 -0.1760328 -0.1761186 -0.1762044
[385] -0.1762902 -0.1763760 -0.1764618 -0.1765476 -0.1766334 -0.1767192
[391] -0.1768050 -0.1768908 -0.1769766 -0.1770624 -0.1771482 -0.1772341
[397] -0.1773199 -0.1774057 -0.1774915 -0.1775773 -0.1776631
> mx
[1] 0.1776631
> mxli
[1] 2
> 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))
> postscript(file="/var/www/html/rcomp/tmp/11thm1258117824.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(l,c,main='Box-Cox Linearity Plot',xlab='Lambda',ylab='correlation')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2gyza1258117824.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(x,y,main='Linear Fit of Original Data',xlab='x',ylab='y')
> abline(r)
> grid()
> mtext(paste('Residual Standard Deviation = ',se))
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3qg6z1258117824.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(x1,y,main='Linear Fit of Transformed Data',xlab='x',ylab='y')
> abline(r1)
> grid()
> mtext(paste('Residual Standard Deviation = ',se1))
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/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="/var/www/html/rcomp/tmp/4iar81258117824.tab") 
> 
> system("convert tmp/11thm1258117824.ps tmp/11thm1258117824.png")
> system("convert tmp/2gyza1258117824.ps tmp/2gyza1258117824.png")
> system("convert tmp/3qg6z1258117824.ps tmp/3qg6z1258117824.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.789   0.506   0.927