::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Box-Cox Linearity Plot. This analysis is used to identify a (quasi-)optimal Box-Cox transformation of the independent data series (x) in the linear relationship
y = a + b x

Click here to edit the underlying code of this R Module.

Enter (or paste) your data delimited by hard returns.

Send output to:
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Data X:
18 38 15 20 18 36 20 43 45 65 43 38 33 10 50 10 50 15 53 60 18 38 15 20 18 36 20 43 45 65 43 38 33 10 50 10 50 15 53 15 37 15 18 11 35 20 40 50 36 50 38 10 75 10 85 13 50 58 58 48 12 63 10 63 13 28 35 63 13 45 9 20 18 35 20 38 50 70 40 21 19 10 33 16 5 32 23 30 45 33 25 12 53 36 5 63 43 25 73 45 52 9 30 22 56 15 45
Data Y:
20.2 56 12.5 21.2 15.5 39 21 38.2 55.6 81.9 39.5 56.4 40.5 14.3 81.5 13.7 81.5 20.5 56 80.7 20 56.5 12.1 19.6 15.5 38.8 19.5 38 55 80 38.5 55.8 38.8 12.5 80.4 12.7 80.9 20.5 55 19 55.5 12.3 18.4 11.5 38 18.5 38 55.3 38.7 54.5 38 12 81.7 11.5 80 18.3 55.3 80.2 80.7 55.8 15 81 12 81.4 12.5 38.2 54.2 79.3 18.2 55.5 11.4 19.5 15.5 37.5 19.5 37.5 55.5 80 37.5 15.5 23.7 9.8 40.8 17.5 4.3 36.5 26.3 30.4 50.2 30.1 25.5 13.8 58.9 40 6 72.5 38.8 19.4 81.5 77.4 54.6 6.8 32.6 19.8 58.8 12.9 49
Sample Range: (leave blank to include all observations)
From:
To:
Chart options
Width:
Height:

Click here to edit the underlying code of this R Module.

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Cite this software as:

Wessa P., (2008), Box-Cox Linearity Plot (v1.0.4) in Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_boxcoxlin.wasp/

The R code is based on :

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03.

Source code of R module
1	n <- length(x)
2	c <- array(NA,dim=c(401))
3	l <- array(NA,dim=c(401))
4	mx <- 0
5	mxli <- -999
6	for (i in 1:401)
7	{
8	l[i] <- (i-201)/100
9	if (l[i] != 0)
10	{
11	x1 <- (x^l[i] - 1) / l[i]
12	} else {
13	x1 <- log(x)
14	}
15	c[i] <- cor(x1,y)
16	if (mx < abs(c[i]))
17	{
18	mx <- abs(c[i])
19	mxli <- l[i]
20	}
21	}
22	c
23	mx
24	mxli
25	if (mxli != 0)
26	{
27	x1 <- (x^mxli - 1) / mxli
28	} else {
29	x1 <- log(x)
30	}
31	r<-lm(y~x)
32	se <- sqrt(var(r$residuals))
33	r1 <- lm(y~x1)
34	se1 <- sqrt(var(r1$residuals))
35	bitmap(file="test1.png")
36	plot(l,c,main="Box-Cox Linearity Plot",xlab="Lambda",ylab="correlation")
37	grid()
38	dev.off()
39	bitmap(file="test2.png")
40	plot(x,y,main="Linear Fit of Original Data",xlab="x",ylab="y")
41	abline(r)
42	grid()
43	mtext(paste("Residual Standard Deviation = ",se))
44	dev.off()
45	bitmap(file="test3.png")
46	plot(x1,y,main="Linear Fit of Transformed Data",xlab="x",ylab="y")
47	abline(r1)
48	grid()
49	mtext(paste("Residual Standard Deviation = ",se1))
50	dev.off()
51	load(file="createtable")
52	a<-table.start()
53	a<-table.row.start(a)
54	a<-table.element(a,"Box-Cox Linearity Plot",2,TRUE)
55	a<-table.row.end(a)
56	a<-table.row.start(a)
57	a<-table.element(a,"# observations x",header=TRUE)
58	a<-table.element(a,n)
59	a<-table.row.end(a)
60	a<-table.row.start(a)
61	a<-table.element(a,"maximum correlation",header=TRUE)
62	a<-table.element(a,mx)
63	a<-table.row.end(a)
64	a<-table.row.start(a)
65	a<-table.element(a,"optimal lambda(x)",header=TRUE)
66	a<-table.element(a,mxli)
67	a<-table.row.end(a)
68	a<-table.row.start(a)
69	a<-table.element(a,"Residual SD (orginial)",header=TRUE)
70	a<-table.element(a,se)
71	a<-table.row.end(a)
72	a<-table.row.start(a)
73	a<-table.element(a,"Residual SD (transformed)",header=TRUE)
74	a<-table.element(a,se1)
75	a<-table.row.end(a)
76	a<-table.end(a)
77	table.save(a,file="mytable.tab")

To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/

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Software Version : 1.1.22-r6
Algorithms & Software : Prof. dr. P. Wessa
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