Box-Cox Normality Plot | |
# observations x | 244 |
maximum correlation | 0.918703684794893 |
optimal lambda | 1.31 |
transformation formula | for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda |
Obs. | Original | Transformed |
1 | 0.5 | -0.455480244571708 |
2 | 0.5 | -0.455480244571708 |
3 | 0.5 | -0.455480244571708 |
4 | 0.5 | -0.455480244571708 |
5 | 0.5 | -0.455480244571708 |
6 | 0.5 | -0.455480244571708 |
7 | 2.5 | 1.7719456538573 |
8 | 2.5 | 1.7719456538573 |
9 | 2.5 | 1.7719456538573 |
10 | 2.5 | 1.7719456538573 |
11 | 2.5 | 1.7719456538573 |
12 | 2.5 | 1.7719456538573 |
13 | 2.5 | 1.7719456538573 |
14 | 3.5 | 3.17629305189021 |
15 | 3.5 | 3.17629305189021 |
16 | 3.5 | 3.17629305189021 |
17 | 3.5 | 3.17629305189021 |
18 | 3.5 | 3.17629305189021 |
19 | 3.5 | 3.17629305189021 |
20 | 3.5 | 3.17629305189021 |
21 | 3.5 | 3.17629305189021 |
22 | 3.5 | 3.17629305189021 |
23 | 4.5 | 4.71230908542078 |
24 | 4.5 | 4.71230908542078 |
25 | 4.5 | 4.71230908542078 |
26 | 4.5 | 4.71230908542078 |
27 | 4.5 | 4.71230908542078 |
28 | 4.5 | 4.71230908542078 |
29 | 4.5 | 4.71230908542078 |
30 | 4.5 | 4.71230908542078 |
31 | 4.5 | 4.71230908542078 |
32 | 4.5 | 4.71230908542078 |
33 | 5.5 | 6.35867169479425 |
34 | 5.5 | 6.35867169479425 |
35 | 5.5 | 6.35867169479425 |
36 | 5.5 | 6.35867169479425 |
37 | 5.5 | 6.35867169479425 |
38 | 5.5 | 6.35867169479425 |
39 | 5.5 | 6.35867169479425 |
40 | 5.5 | 6.35867169479425 |
41 | 5.5 | 6.35867169479425 |
42 | 5.5 | 6.35867169479425 |
43 | 5.5 | 6.35867169479425 |
44 | 5.5 | 6.35867169479425 |
45 | 5.5 | 6.35867169479425 |
46 | 5.5 | 6.35867169479425 |
47 | 5.5 | 6.35867169479425 |
48 | 5.5 | 6.35867169479425 |
49 | 5.5 | 6.35867169479425 |
50 | 5.5 | 6.35867169479425 |
51 | 5.5 | 6.35867169479425 |
52 | 5.5 | 6.35867169479425 |
53 | 5.5 | 6.35867169479425 |
54 | 5.5 | 6.35867169479425 |
55 | 5.5 | 6.35867169479425 |
56 | 5.5 | 6.35867169479425 |
57 | 5.5 | 6.35867169479425 |
58 | 5.5 | 6.35867169479425 |
59 | 5.5 | 6.35867169479425 |
60 | 5.5 | 6.35867169479425 |
61 | 5.5 | 6.35867169479425 |
62 | 5.5 | 6.35867169479425 |
63 | 5.5 | 6.35867169479425 |
64 | 6.5 | 8.1009566481989 |
65 | 6.5 | 8.1009566481989 |
66 | 6.5 | 8.1009566481989 |
67 | 6.5 | 8.1009566481989 |
68 | 6.5 | 8.1009566481989 |
69 | 6.5 | 8.1009566481989 |
70 | 6.5 | 8.1009566481989 |
71 | 6.5 | 8.1009566481989 |
72 | 6.5 | 8.1009566481989 |
73 | 6.5 | 8.1009566481989 |
74 | 6.5 | 8.1009566481989 |
75 | 6.5 | 8.1009566481989 |
76 | 6.5 | 8.1009566481989 |
77 | 6.5 | 8.1009566481989 |
78 | 6.5 | 8.1009566481989 |
79 | 6.5 | 8.1009566481989 |
80 | 6.5 | 8.1009566481989 |
81 | 6.5 | 8.1009566481989 |
82 | 6.5 | 8.1009566481989 |
83 | 6.5 | 8.1009566481989 |
84 | 6.5 | 8.1009566481989 |
85 | 6.5 | 8.1009566481989 |
86 | 6.5 | 8.1009566481989 |
87 | 6.5 | 8.1009566481989 |
88 | 7.5 | 9.92864145040347 |
89 | 7.5 | 9.92864145040347 |
90 | 7.5 | 9.92864145040347 |
91 | 7.5 | 9.92864145040347 |
92 | 7.5 | 9.92864145040347 |
93 | 7.5 | 9.92864145040347 |
94 | 7.5 | 9.92864145040347 |
95 | 7.5 | 9.92864145040347 |
96 | 7.5 | 9.92864145040347 |
97 | 7.5 | 9.92864145040347 |
98 | 7.5 | 9.92864145040347 |
99 | 7.5 | 9.92864145040347 |
100 | 7.5 | 9.92864145040347 |
101 | 7.5 | 9.92864145040347 |
102 | 7.5 | 9.92864145040347 |
103 | 7.5 | 9.92864145040347 |
104 | 7.5 | 9.92864145040347 |
105 | 7.5 | 9.92864145040347 |
106 | 7.5 | 9.92864145040347 |
107 | 8.5 | 11.8336518859596 |
108 | 8.5 | 11.8336518859596 |
109 | 8.5 | 11.8336518859596 |
110 | 8.5 | 11.8336518859596 |
111 | 8.5 | 11.8336518859596 |
112 | 8.5 | 11.8336518859596 |
113 | 8.5 | 11.8336518859596 |
114 | 8.5 | 11.8336518859596 |
115 | 8.5 | 11.8336518859596 |
116 | 8.5 | 11.8336518859596 |
117 | 8.5 | 11.8336518859596 |
118 | 8.5 | 11.8336518859596 |
119 | 8.5 | 11.8336518859596 |
120 | 8.5 | 11.8336518859596 |
121 | 8.5 | 11.8336518859596 |
122 | 8.5 | 11.8336518859596 |
123 | 8.5 | 11.8336518859596 |
124 | 8.5 | 11.8336518859596 |
125 | 8.5 | 11.8336518859596 |
126 | 8.5 | 11.8336518859596 |
127 | 8.5 | 11.8336518859596 |
128 | 9.5 | 13.8095627810995 |
129 | 9.5 | 13.8095627810995 |
130 | 9.5 | 13.8095627810995 |
131 | 9.5 | 13.8095627810995 |
132 | 9.5 | 13.8095627810995 |
133 | 9.5 | 13.8095627810995 |
134 | 9.5 | 13.8095627810995 |
135 | 9.5 | 13.8095627810995 |
136 | 9.5 | 13.8095627810995 |
137 | 9.5 | 13.8095627810995 |
138 | 9.5 | 13.8095627810995 |
139 | 9.5 | 13.8095627810995 |
140 | 9.5 | 13.8095627810995 |
141 | 10.5 | 15.8511186523613 |
142 | 10.5 | 15.8511186523613 |
143 | 10.5 | 15.8511186523613 |
144 | 10.5 | 15.8511186523613 |
145 | 10.5 | 15.8511186523613 |
146 | 10.5 | 15.8511186523613 |
147 | 10.5 | 15.8511186523613 |
148 | 10.5 | 15.8511186523613 |
149 | 10.5 | 15.8511186523613 |
150 | 10.5 | 15.8511186523613 |
151 | 10.5 | 15.8511186523613 |
152 | 10.5 | 15.8511186523613 |
153 | 10.5 | 15.8511186523613 |
154 | 10.5 | 15.8511186523613 |
155 | 10.5 | 15.8511186523613 |
156 | 10.5 | 15.8511186523613 |
157 | 10.5 | 15.8511186523613 |
158 | 10.5 | 15.8511186523613 |
159 | 10.5 | 15.8511186523613 |
160 | 10.5 | 15.8511186523613 |
161 | 10.5 | 15.8511186523613 |
162 | 10.5 | 15.8511186523613 |
163 | 10.5 | 15.8511186523613 |
164 | 10.5 | 15.8511186523613 |
165 | 10.5 | 15.8511186523613 |
166 | 10.5 | 15.8511186523613 |
167 | 10.5 | 15.8511186523613 |
168 | 10.5 | 15.8511186523613 |
169 | 10.5 | 15.8511186523613 |
170 | 10.5 | 15.8511186523613 |
171 | 10.5 | 15.8511186523613 |
172 | 10.5 | 15.8511186523613 |
173 | 10.5 | 15.8511186523613 |
174 | 10.5 | 15.8511186523613 |
175 | 10.5 | 15.8511186523613 |
176 | 10.5 | 15.8511186523613 |
177 | 10.5 | 15.8511186523613 |
178 | 10.5 | 15.8511186523613 |
179 | 10.5 | 15.8511186523613 |
180 | 10.5 | 15.8511186523613 |
181 | 10.5 | 15.8511186523613 |
182 | 10.5 | 15.8511186523613 |
183 | 10.5 | 15.8511186523613 |
184 | 10.5 | 15.8511186523613 |
185 | 10.5 | 15.8511186523613 |
186 | 10.5 | 15.8511186523613 |
187 | 10.5 | 15.8511186523613 |
188 | 10.5 | 15.8511186523613 |
189 | 10.5 | 15.8511186523613 |
190 | 10.5 | 15.8511186523613 |
191 | 10.5 | 15.8511186523613 |
192 | 10.5 | 15.8511186523613 |
193 | 10.5 | 15.8511186523613 |
194 | 10.5 | 15.8511186523613 |
195 | 10.5 | 15.8511186523613 |
196 | 10.5 | 15.8511186523613 |
197 | 10.5 | 15.8511186523613 |
198 | 10.5 | 15.8511186523613 |
199 | 10.5 | 15.8511186523613 |
200 | 10.5 | 15.8511186523613 |
201 | 10.5 | 15.8511186523613 |
202 | 10.5 | 15.8511186523613 |
203 | 10.5 | 15.8511186523613 |
204 | 10.5 | 15.8511186523613 |
205 | 10.5 | 15.8511186523613 |
206 | 10.5 | 15.8511186523613 |
207 | 10.5 | 15.8511186523613 |
208 | 10.5 | 15.8511186523613 |
209 | 10.5 | 15.8511186523613 |
210 | 10.5 | 15.8511186523613 |
211 | 10.5 | 15.8511186523613 |
212 | 10.5 | 15.8511186523613 |
213 | 10.5 | 15.8511186523613 |
214 | 10.5 | 15.8511186523613 |
215 | 10.5 | 15.8511186523613 |
216 | 10.5 | 15.8511186523613 |
217 | 10.5 | 15.8511186523613 |
218 | 10.5 | 15.8511186523613 |
219 | 10.5 | 15.8511186523613 |
220 | 10.5 | 15.8511186523613 |
221 | 10.5 | 15.8511186523613 |
222 | 10.5 | 15.8511186523613 |
223 | 10.5 | 15.8511186523613 |
224 | 10.5 | 15.8511186523613 |
225 | 10.5 | 15.8511186523613 |
226 | 10.5 | 15.8511186523613 |
227 | 10.5 | 15.8511186523613 |
228 | 10.5 | 15.8511186523613 |
229 | 10.5 | 15.8511186523613 |
230 | 10.5 | 15.8511186523613 |
231 | 10.5 | 15.8511186523613 |
232 | 10.5 | 15.8511186523613 |
233 | 10.5 | 15.8511186523613 |
234 | 10.5 | 15.8511186523613 |
235 | 10.5 | 15.8511186523613 |
236 | 10.5 | 15.8511186523613 |
237 | 10.5 | 15.8511186523613 |
238 | 10.5 | 15.8511186523613 |
239 | 10.5 | 15.8511186523613 |
240 | 10.5 | 15.8511186523613 |
241 | 10.5 | 15.8511186523613 |
242 | 10.5 | 15.8511186523613 |
243 | 10.5 | 15.8511186523613 |
244 | 10.5 | 15.8511186523613 |
Maximum Likelihood Estimation of Lambda |
> summary(mypT) bcPower Transformation to Normality Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd x 1.6192 1.62 1.2967 1.9417 Likelihood ratio test that transformation parameter is equal to 0 (log transformation) LRT df pval LR test, lambda = (0) 214.867 1 < 2.22e-16 Likelihood ratio test that no transformation is needed LRT df pval LR test, lambda = (1) 18.0754 1 2.1233e-05 |