Forse questa domanda ha una risposta in medicina, ma ci sono dei motivi statistici per cui l' indice BMI è calcolato come ? Perché non ad esempio solo ? La mia prima idea è che abbia qualcosa a che fare con la regressione quadratica. peso / altezza
Esempio di dati reali (200 individui con peso, altezza, età e sesso):
structure(list(Age = c(18L, 21L, 17L, 20L, 19L, 53L, 27L, 22L,
19L, 27L, 19L, 20L, 19L, 20L, 42L, 17L, 23L, 20L, 20L, 19L, 20L,
19L, 19L, 18L, 19L, 15L, 19L, 15L, 19L, 21L, 60L, 19L, 17L, 23L,
60L, 33L, 24L, 19L, 19L, 22L, 20L, 21L, 19L, 19L, 20L, 18L, 19L,
20L, 22L, 20L, 20L, 27L, 19L, 22L, 19L, 20L, 20L, 21L, 16L, 19L,
41L, 54L, 18L, 23L, 19L, 19L, 22L, 18L, 20L, 19L, 25L, 18L, 20L,
15L, 61L, 19L, 34L, 15L, 19L, 16L, 19L, 18L, 15L, 20L, 20L, 20L,
20L, 19L, 16L, 37L, 37L, 18L, 20L, 16L, 20L, 36L, 18L, 19L, 19L,
20L, 18L, 17L, 22L, 17L, 22L, 16L, 24L, 17L, 33L, 17L, 17L, 15L,
18L, 18L, 16L, 20L, 29L, 24L, 18L, 17L, 18L, 36L, 16L, 17L, 20L,
16L, 43L, 19L, 18L, 20L, 19L, 18L, 21L, 19L, 20L, 23L, 19L, 19L,
20L, 24L, 19L, 20L, 38L, 18L, 17L, 19L, 19L, 20L, 20L, 21L, 20L,
20L, 42L, 17L, 20L, 25L, 20L, 21L, 21L, 22L, 19L, 25L, 19L, 40L,
25L, 52L, 25L, 21L, 20L, 41L, 34L, 24L, 30L, 21L, 27L, 47L, 21L,
16L, 31L, 21L, 37L, 20L, 22L, 19L, 20L, 25L, 23L, 20L, 20L, 21L,
36L, 19L, 21L, 16L, 20L, 18L, 21L, 21L, 18L, 19L), Height = c(180L,
175L, 178L, 160L, 172L, 172L, 180L, 165L, 160L, 187L, 165L, 176L,
164L, 155L, 166L, 167L, 171L, 158L, 170L, 182L, 182L, 175L, 197L,
170L, 165L, 176L, 167L, 170L, 168L, 163L, 155L, 152L, 158L, 165L,
180L, 187L, 177L, 170L, 178L, 170L, 170L, NA, 188L, 180L, 161L,
178L, 178L, 165L, 187L, 178L, 168L, 168L, 180L, 192L, 188L, 173L,
193L, 184L, 167L, 177L, 177L, 160L, 167L, 190L, 187L, 163L, 173L,
165L, 190L, 178L, 167L, 160L, 169L, 174L, 165L, 176L, 183L, 166L,
178L, 158L, 180L, 167L, 170L, 170L, 180L, 184L, 170L, 180L, 169L,
165L, 156L, 166L, 178L, 162L, 178L, 181L, 168L, 185L, 175L, 167L,
193L, 160L, 171L, 182L, 165L, 174L, 169L, 185L, 173L, 170L, 182L,
165L, 160L, 158L, 186L, 173L, 168L, 172L, 164L, 185L, 175L, 162L,
182L, 170L, 187L, 169L, 178L, 189L, 166L, 161L, 180L, 185L, 179L,
170L, 184L, 180L, 166L, 167L, 178L, 175L, 190L, 178L, 157L, 179L,
180L, 168L, 164L, 187L, 174L, 176L, 170L, 170L, 168L, 158L, 175L,
174L, 170L, 173L, 158L, 185L, 170L, 178L, 166L, 176L, 167L, 168L,
169L, 168L, 178L, 183L, 166L, 165L, 160L, 176L, 186L, 162L, 172L,
164L, 171L, 175L, 164L, 165L, 160L, 180L, 170L, 180L, 175L, 167L,
165L, 168L, 176L, 166L, 164L, 165L, 180L, 173L, 168L, 177L, 167L,
173L), Weight = c(60L, 63L, 70L, 46L, 60L, 68L, 80L, 68L, 55L,
89L, 55L, 63L, 60L, 44L, 62L, 57L, 59L, 50L, 60L, 65L, 63L, 72L,
96L, 50L, 55L, 53L, 54L, 49L, 72L, 49L, 75L, 47L, 57L, 70L, 105L,
85L, 80L, 55L, 67L, 60L, 70L, NA, 76L, 85L, 53L, 69L, 74L, 50L,
91L, 68L, 55L, 55L, 57L, 80L, 98L, 58L, 85L, 120L, 62L, 63L,
88L, 80L, 57L, 90L, 83L, 51L, 52L, 65L, 92L, 58L, 76L, 53L, 64L,
63L, 72L, 68L, 110L, 52L, 68L, 50L, 78L, 57L, 75L, 55L, 75L,
68L, 60L, 65L, 48L, 56L, 65L, 65L, 88L, 55L, 68L, 74L, 65L, 62L,
58L, 55L, 84L, 60L, 52L, 92L, 60L, 65L, 50L, 73L, 51L, 60L, 76L,
48L, 50L, 53L, 63L, 68L, 56L, 68L, 60L, 70L, 65L, 52L, 75L, 65L,
68L, 63L, 54L, 76L, 60L, 59L, 80L, 74L, 96L, 68L, 72L, 62L, 58L,
50L, 75L, 70L, 85L, 67L, 65L, 55L, 78L, 58L, 53L, 56L, 72L, 62L,
60L, 56L, 82L, 70L, 53L, 67L, 58L, 58L, 49L, 90L, 58L, 77L, 55L,
70L, 64L, 98L, 60L, 60L, 65L, 74L, 99L, 49L, 47L, 75L, 77L, 74L,
68L, 50L, 66L, 75L, 54L, 60L, 65L, 80L, 90L, 95L, 79L, 57L, 70L,
60L, 85L, 44L, 58L, 50L, 88L, 60L, 54L, 68L, 56L, 69L), Gender = c(1L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L,
2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L)), .Names = c("Age", "Height", "Weight",
"Gender"), row.names = 304:503, class = "data.frame")
library(MASS); rlm(log(Weight) ~ log(Height) + cut(Age, 3) + as.factor(Gender), data=y)
rlm(Weight ~ Height + cut(Age, 3) + as.factor(Gender), data=y)
y