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Author's title

Author

*Unverified author*

R Software Module

rwasp_boxcoxnorm.wasp

Title produced by software

Box-Cox Normality Plot

Date of computation

Tue, 24 Oct 2017 07:50:58 +0200

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Oct/24/t1508824418vbu0b1b5ruviock.htm/, Retrieved Fri, 10 May 2024 04:24:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308041, Retrieved Fri, 10 May 2024 04:24:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Box-Cox Normality Plot] [] [2017-10-24 05:50:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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14,123,21,1986
59,20,22,1986
17,443,22,1987
2,276,22,1991
96,295,24,1972
15,344,24,1994
14,90,24,1995
202,242,27,1968
46,226,28,1987
46,262,30,1949
57,279,32,1978
125,165,35,1973
30,242,36,1982
62,905,37,1980
16,355,37,1994
17,375,40,1996
37,135,42,1992
148,171,44,1972
110,284,47,1987
16,242,47,1989
30,371,50,1984
61,115,51,1961
27,355,56,1988
45,355,61,1987
15,835,61,1982
25,223,62,1852
203,172,66,1943
646,62,67,1970
59,191,68,1922
27,411,69,1987
31,274,69,1996
532,130,69,1947
52,100,75,1975
87,80,76,1963
27,235,78,1982
291,392,80,1948
9,410,81,1991
24,464,82,1976
49,650,85,1981
24,558,87,1986
323,317,87,1961
69,495,89,1994
21,535,89,1983
212,123,97,1969
14,717,97,1992
38,481,98,1991
22,54,98,1964
77,379,100,1967
290,168,109,1982
386,82,112,1970
50,355,119,1986
144,95,121,1984
48,240,121,1991
33,448,122,1978
29,255,124,1985
58,448,126,1990
71,392,126,1980
135,475,134,1967
183,85,137,1979
573,108,138,1941
268,394,138,1973
57,336,140,1930
52,565,143,1978
21,255,144,1974
479,165,147,1960
77,99,150,1865
89,203,151,1953
83,318,154,1970
59,476,162,1990
67,473,164,1979
225,186,170,1978
56,170,179,1985
36,824,180,1981
101,805,183,1973
288,132,183,1969
183,50,188,1925
25,424,188,1992
120,130,189,1945
263,90,193,1964
101,805,214,1977
43,96,220,1948
73,448,224,1982
221,130,227,1980
83,595,237,1970
37,474,239,1984
185,410,245,1977
61,395,245,1981
57,437,249,1985
186,270,254,1948
199,265,261,1963
165,899,264,1992
95,133,292,1967
82,262,294,1963
214,506,299,1962
152,1140,302,1981
33,211,313,1844
81,799,313,1983
137,760,317,1982
59,442,338,1982
98,296,339,1898
163,272,351,1976
462,45,355,1967
99,614,370,1971
52,436,382,1971
47,481,383,1990
394,95,388,1966
227,357,388,1964
65,280,390,1985
242,142,397,1961
154,710,406,1979
45,490,412,1988
81,870,412,1986
79,1147,418,1974
120,743,427,1981
91,759,440,1967
218,36,445,1975
97,224,488,1971
322,82,495,1970
283,160,497,1953
40,1170,499,1989
552,90,502,1948
222,742,508,1964
29,575,544,1992
390,163,545,1947
95,175,547,1988
305,120,556,1967
98,590,574,1981
146,2120,578,1958
271,205,582,1949
515,128,597,1952
172,1539,602,1977
127,346,617,1939
58,1046,636,1979
524,97,646,1932
222,686,654,1964
385,914,662,1981
413,85,670,1964
366,206,684,1962
75,1154,698,1980
238,45,700,1972
142,1146,707,1974
437,95,730,1925
269,138,733,1983
643,115,737,1941
230,640,787,1974
313,122,825,1933
512,110,834,1969
211,923,838,1971
171,1000,871,1966
34,1234,922,1972
81,1492,930,1978
144,810,957,1982
190,90,988,1983
339,177,1039,1970
771,74,1083,1928
522,113,1113,1966
284,145,1113,1960
202,590,1152,1974
118,1154,1243,1969
160,1450,1408,1973
141,1431,1437,1972
972,47,1530,1963
542,45,1580,1968
866,47,1583,1987
267,81,1812,1918
186,1010,1860,1975
558,334,2022,1954
523,190,2331,1919
325,180,2411,1933
129,1893,2479,1973
165,1400,2514,1969
531,301,2540,1890
231,1339,2676,1974
536,90,2762,1974
487,310,2800,1971
799,226,3791,1945
660,148,4138,1886
737,159,6697,1892
346,178,7943,1932
1098,47,8999,1911

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308041&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

0 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308041&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	Big Analytics Cloud Computing Center

Parameters (Session):

par1 = Simple Box-Cox transform ; par2 = -4 ; par3 = 4 ; par4 = 0 ; par5 = No ;

Parameters (R input):

par1 = Simple Box-Cox transform ; par2 = -4 ; par3 = 4 ; par4 = 0 ; par5 = No ;

R code (references can be found in the software module):

par5 <- 'No'
par4 <- '0'
par3 <- '4'
par2 <- '-4'
par1 <- 'Simple Box-Cox transform'
library(car)
par2 <- abs(as.numeric(par2)*100)
par3 <- as.numeric(par3)*100
if(par4=='') par4 <- 0
par4 <- as.numeric(par4)
numlam <- par2 + par3 + 1
x <- x + par4
n <- length(x)
c <- array(NA,dim=c(numlam))
l <- array(NA,dim=c(numlam))
mx <- -1
mxli <- -999
for (i in 1:numlam)
{
l[i] <- (i-par2-1)/100
if (l[i] != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
if (par1 == 'Simple Box-Cox transform') x1 <- x^l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),sort(x1))
if (mx < c[i])
{
mx <- c[i]
mxli <- l[i]
x1.best <- x1
}
}
print(c)
print(mx)
print(mxli)
print(x1.best)
if (mxli != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
if (par1 == 'Simple Box-Cox transform') x1 <- x^mxli
} else {
x1 <- log(x)
}
mypT <- powerTransform(x)
summary(mypT)
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')
mtext(paste('Optimal Lambda =',mxli))
grid()
dev.off()
bitmap(file='test2.png')
hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test3.png')
hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test4.png')
qqPlot(x)
grid()
mtext('Original Data')
dev.off()
bitmap(file='test5.png')
qqPlot(x1)
grid()
mtext('Transformed Data')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Normality 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',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'transformation formula',header=TRUE)
if (par1 == 'Full Box-Cox transform') {
a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')
} else {
a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')
}
a<-table.row.end(a)
if(mx<0) {
a<-table.row.start(a)
a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
if(par5=='Yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Obs.',header=T)
a<-table.element(a,'Original',header=T)
a<-table.element(a,'Transformed',header=T)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i)
a<-table.element(a,x[i])
a<-table.element(a,x1.best[i])
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,'Maximum Likelihood Estimation of Lambda',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('summary(mypT)'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')

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