Box-Cox Normality Plot | |
# observations x | 281 |
maximum correlation | 0.910761049065933 |
optimal lambda | 1.33 |
transformation formula | for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda |
Obs. | Original | Transformed |
1 | 0.5 | -0.452805833174843 |
2 | 0.5 | -0.452805833174843 |
3 | 0.5 | -0.452805833174843 |
4 | 2.5 | 1.79148459816347 |
5 | 2.5 | 1.79148459816347 |
6 | 2.5 | 1.79148459816347 |
7 | 2.5 | 1.79148459816347 |
8 | 3.5 | 3.22698213006964 |
9 | 4.5 | 4.80615178223382 |
10 | 4.5 | 4.80615178223382 |
11 | 4.5 | 4.80615178223382 |
12 | 4.5 | 4.80615178223382 |
13 | 4.5 | 4.80615178223382 |
14 | 5.5 | 6.50635046757566 |
15 | 5.5 | 6.50635046757566 |
16 | 5.5 | 6.50635046757566 |
17 | 5.5 | 6.50635046757566 |
18 | 5.5 | 6.50635046757566 |
19 | 5.5 | 6.50635046757566 |
20 | 5.5 | 6.50635046757566 |
21 | 5.5 | 6.50635046757566 |
22 | 5.5 | 6.50635046757566 |
23 | 5.5 | 6.50635046757566 |
24 | 5.5 | 6.50635046757566 |
25 | 5.5 | 6.50635046757566 |
26 | 5.5 | 6.50635046757566 |
27 | 5.5 | 6.50635046757566 |
28 | 5.5 | 6.50635046757566 |
29 | 6.5 | 8.31218764035623 |
30 | 6.5 | 8.31218764035623 |
31 | 6.5 | 8.31218764035623 |
32 | 6.5 | 8.31218764035623 |
33 | 6.5 | 8.31218764035623 |
34 | 6.5 | 8.31218764035623 |
35 | 6.5 | 8.31218764035623 |
36 | 6.5 | 8.31218764035623 |
37 | 6.5 | 8.31218764035623 |
38 | 6.5 | 8.31218764035623 |
39 | 7.5 | 10.2123932709877 |
40 | 7.5 | 10.2123932709877 |
41 | 7.5 | 10.2123932709877 |
42 | 7.5 | 10.2123932709877 |
43 | 7.5 | 10.2123932709877 |
44 | 7.5 | 10.2123932709877 |
45 | 7.5 | 10.2123932709877 |
46 | 7.5 | 10.2123932709877 |
47 | 7.5 | 10.2123932709877 |
48 | 7.5 | 10.2123932709877 |
49 | 7.5 | 10.2123932709877 |
50 | 7.5 | 10.2123932709877 |
51 | 7.5 | 10.2123932709877 |
52 | 7.5 | 10.2123932709877 |
53 | 8.5 | 12.1982921104588 |
54 | 8.5 | 12.1982921104588 |
55 | 8.5 | 12.1982921104588 |
56 | 8.5 | 12.1982921104588 |
57 | 8.5 | 12.1982921104588 |
58 | 8.5 | 12.1982921104588 |
59 | 8.5 | 12.1982921104588 |
60 | 9.5 | 14.2629618704801 |
61 | 9.5 | 14.2629618704801 |
62 | 9.5 | 14.2629618704801 |
63 | 9.5 | 14.2629618704801 |
64 | 9.5 | 14.2629618704801 |
65 | 9.5 | 14.2629618704801 |
66 | 9.5 | 14.2629618704801 |
67 | 10.5 | 16.4007268903347 |
68 | 10.5 | 16.4007268903347 |
69 | 10.5 | 16.4007268903347 |
70 | 10.5 | 16.4007268903347 |
71 | 10.5 | 16.4007268903347 |
72 | 10.5 | 16.4007268903347 |
73 | 10.5 | 16.4007268903347 |
74 | 10.5 | 16.4007268903347 |
75 | 10.5 | 16.4007268903347 |
76 | 10.5 | 16.4007268903347 |
77 | 10.5 | 16.4007268903347 |
78 | 10.5 | 16.4007268903347 |
79 | 10.5 | 16.4007268903347 |
80 | 10.5 | 16.4007268903347 |
81 | 10.5 | 16.4007268903347 |
82 | 10.5 | 16.4007268903347 |
83 | 10.5 | 16.4007268903347 |
84 | 10.5 | 16.4007268903347 |
85 | 10.5 | 16.4007268903347 |
86 | 10.5 | 16.4007268903347 |
87 | 10.5 | 16.4007268903347 |
88 | 10.5 | 16.4007268903347 |
89 | 10.5 | 16.4007268903347 |
90 | 10.5 | 16.4007268903347 |
91 | 10.5 | 16.4007268903347 |
92 | 10.5 | 16.4007268903347 |
93 | 10.5 | 16.4007268903347 |
94 | 10.5 | 16.4007268903347 |
95 | 10.5 | 16.4007268903347 |
96 | 10.5 | 16.4007268903347 |
97 | 10.5 | 16.4007268903347 |
98 | 10.5 | 16.4007268903347 |
99 | 10.5 | 16.4007268903347 |
100 | 10.5 | 16.4007268903347 |
101 | 10.5 | 16.4007268903347 |
102 | 10.5 | 16.4007268903347 |
103 | 10.5 | 16.4007268903347 |
104 | 10.5 | 16.4007268903347 |
105 | 10.5 | 16.4007268903347 |
106 | 10.5 | 16.4007268903347 |
107 | 10.5 | 16.4007268903347 |
108 | 10.5 | 16.4007268903347 |
109 | 10.5 | 16.4007268903347 |
110 | 10.5 | 16.4007268903347 |
111 | 10.5 | 16.4007268903347 |
112 | 10.5 | 16.4007268903347 |
113 | 10.5 | 16.4007268903347 |
114 | 10.5 | 16.4007268903347 |
115 | 10.5 | 16.4007268903347 |
116 | 10.5 | 16.4007268903347 |
117 | 10.5 | 16.4007268903347 |
118 | 10.5 | 16.4007268903347 |
119 | 0.5 | -0.452805833174843 |
120 | 0.5 | -0.452805833174843 |
121 | 0.5 | -0.452805833174843 |
122 | 2.5 | 1.79148459816347 |
123 | 2.5 | 1.79148459816347 |
124 | 2.5 | 1.79148459816347 |
125 | 2.5 | 1.79148459816347 |
126 | 3.5 | 3.22698213006964 |
127 | 3.5 | 3.22698213006964 |
128 | 3.5 | 3.22698213006964 |
129 | 3.5 | 3.22698213006964 |
130 | 3.5 | 3.22698213006964 |
131 | 3.5 | 3.22698213006964 |
132 | 3.5 | 3.22698213006964 |
133 | 4.5 | 4.80615178223382 |
134 | 4.5 | 4.80615178223382 |
135 | 4.5 | 4.80615178223382 |
136 | 4.5 | 4.80615178223382 |
137 | 4.5 | 4.80615178223382 |
138 | 4.5 | 4.80615178223382 |
139 | 4.5 | 4.80615178223382 |
140 | 5.5 | 6.50635046757566 |
141 | 5.5 | 6.50635046757566 |
142 | 5.5 | 6.50635046757566 |
143 | 5.5 | 6.50635046757566 |
144 | 5.5 | 6.50635046757566 |
145 | 5.5 | 6.50635046757566 |
146 | 5.5 | 6.50635046757566 |
147 | 5.5 | 6.50635046757566 |
148 | 5.5 | 6.50635046757566 |
149 | 5.5 | 6.50635046757566 |
150 | 5.5 | 6.50635046757566 |
151 | 5.5 | 6.50635046757566 |
152 | 5.5 | 6.50635046757566 |
153 | 5.5 | 6.50635046757566 |
154 | 5.5 | 6.50635046757566 |
155 | 5.5 | 6.50635046757566 |
156 | 5.5 | 6.50635046757566 |
157 | 5.5 | 6.50635046757566 |
158 | 5.5 | 6.50635046757566 |
159 | 6.5 | 8.31218764035623 |
160 | 6.5 | 8.31218764035623 |
161 | 6.5 | 8.31218764035623 |
162 | 6.5 | 8.31218764035623 |
163 | 6.5 | 8.31218764035623 |
164 | 6.5 | 8.31218764035623 |
165 | 6.5 | 8.31218764035623 |
166 | 6.5 | 8.31218764035623 |
167 | 6.5 | 8.31218764035623 |
168 | 6.5 | 8.31218764035623 |
169 | 6.5 | 8.31218764035623 |
170 | 6.5 | 8.31218764035623 |
171 | 6.5 | 8.31218764035623 |
172 | 6.5 | 8.31218764035623 |
173 | 6.5 | 8.31218764035623 |
174 | 6.5 | 8.31218764035623 |
175 | 7.5 | 10.2123932709877 |
176 | 7.5 | 10.2123932709877 |
177 | 7.5 | 10.2123932709877 |
178 | 7.5 | 10.2123932709877 |
179 | 7.5 | 10.2123932709877 |
180 | 7.5 | 10.2123932709877 |
181 | 7.5 | 10.2123932709877 |
182 | 7.5 | 10.2123932709877 |
183 | 7.5 | 10.2123932709877 |
184 | 8.5 | 12.1982921104588 |
185 | 8.5 | 12.1982921104588 |
186 | 8.5 | 12.1982921104588 |
187 | 8.5 | 12.1982921104588 |
188 | 8.5 | 12.1982921104588 |
189 | 8.5 | 12.1982921104588 |
190 | 8.5 | 12.1982921104588 |
191 | 8.5 | 12.1982921104588 |
192 | 8.5 | 12.1982921104588 |
193 | 8.5 | 12.1982921104588 |
194 | 8.5 | 12.1982921104588 |
195 | 8.5 | 12.1982921104588 |
196 | 8.5 | 12.1982921104588 |
197 | 8.5 | 12.1982921104588 |
198 | 8.5 | 12.1982921104588 |
199 | 9.5 | 14.2629618704801 |
200 | 9.5 | 14.2629618704801 |
201 | 9.5 | 14.2629618704801 |
202 | 9.5 | 14.2629618704801 |
203 | 9.5 | 14.2629618704801 |
204 | 9.5 | 14.2629618704801 |
205 | 9.5 | 14.2629618704801 |
206 | 9.5 | 14.2629618704801 |
207 | 10.5 | 16.4007268903347 |
208 | 10.5 | 16.4007268903347 |
209 | 10.5 | 16.4007268903347 |
210 | 10.5 | 16.4007268903347 |
211 | 10.5 | 16.4007268903347 |
212 | 10.5 | 16.4007268903347 |
213 | 10.5 | 16.4007268903347 |
214 | 10.5 | 16.4007268903347 |
215 | 10.5 | 16.4007268903347 |
216 | 10.5 | 16.4007268903347 |
217 | 10.5 | 16.4007268903347 |
218 | 10.5 | 16.4007268903347 |
219 | 10.5 | 16.4007268903347 |
220 | 10.5 | 16.4007268903347 |
221 | 10.5 | 16.4007268903347 |
222 | 10.5 | 16.4007268903347 |
223 | 10.5 | 16.4007268903347 |
224 | 10.5 | 16.4007268903347 |
225 | 10.5 | 16.4007268903347 |
226 | 10.5 | 16.4007268903347 |
227 | 10.5 | 16.4007268903347 |
228 | 10.5 | 16.4007268903347 |
229 | 10.5 | 16.4007268903347 |
230 | 10.5 | 16.4007268903347 |
231 | 10.5 | 16.4007268903347 |
232 | 10.5 | 16.4007268903347 |
233 | 10.5 | 16.4007268903347 |
234 | 10.5 | 16.4007268903347 |
235 | 10.5 | 16.4007268903347 |
236 | 10.5 | 16.4007268903347 |
237 | 10.5 | 16.4007268903347 |
238 | 10.5 | 16.4007268903347 |
239 | 10.5 | 16.4007268903347 |
240 | 10.5 | 16.4007268903347 |
241 | 10.5 | 16.4007268903347 |
242 | 10.5 | 16.4007268903347 |
243 | 10.5 | 16.4007268903347 |
244 | 10.5 | 16.4007268903347 |
245 | 10.5 | 16.4007268903347 |
246 | 10.5 | 16.4007268903347 |
247 | 10.5 | 16.4007268903347 |
248 | 10.5 | 16.4007268903347 |
249 | 10.5 | 16.4007268903347 |
250 | 10.5 | 16.4007268903347 |
251 | 10.5 | 16.4007268903347 |
252 | 10.5 | 16.4007268903347 |
253 | 10.5 | 16.4007268903347 |
254 | 10.5 | 16.4007268903347 |
255 | 10.5 | 16.4007268903347 |
256 | 10.5 | 16.4007268903347 |
257 | 10.5 | 16.4007268903347 |
258 | 10.5 | 16.4007268903347 |
259 | 10.5 | 16.4007268903347 |
260 | 10.5 | 16.4007268903347 |
261 | 10.5 | 16.4007268903347 |
262 | 10.5 | 16.4007268903347 |
263 | 10.5 | 16.4007268903347 |
264 | 10.5 | 16.4007268903347 |
265 | 10.5 | 16.4007268903347 |
266 | 10.5 | 16.4007268903347 |
267 | 10.5 | 16.4007268903347 |
268 | 10.5 | 16.4007268903347 |
269 | 10.5 | 16.4007268903347 |
270 | 10.5 | 16.4007268903347 |
271 | 10.5 | 16.4007268903347 |
272 | 10.5 | 16.4007268903347 |
273 | 10.5 | 16.4007268903347 |
274 | 10.5 | 16.4007268903347 |
275 | 10.5 | 16.4007268903347 |
276 | 10.5 | 16.4007268903347 |
277 | 10.5 | 16.4007268903347 |
278 | 10.5 | 16.4007268903347 |
279 | 10.5 | 16.4007268903347 |
280 | 10.5 | 16.4007268903347 |
281 | 10.5 | 16.4007268903347 |
Maximum Likelihood Estimation of Lambda |
> summary(mypT) bcPower Transformation to Normality Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd x 1.7401 2 1.4142 2.066 Likelihood ratio test that transformation parameter is equal to 0 (log transformation) LRT df pval LR test, lambda = (0) 253.175 1 < 2.22e-16 Likelihood ratio test that no transformation is needed LRT df pval LR test, lambda = (1) 26.16003 1 3.1426e-07 |