I'm analyzing behaviour's persons in transportation and have the following data :
I'm wondering to verify the following hypothesis : Individual will look to confort (Type:no=0,yes=1) proportionnaly if their duration's journey is more important and if their age is more important.
Visually, Ii seems that datas follows this hypothesis, but how to verify it statistically ? which type of test to use ?
df=structure(list(Type = c("0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0",
"0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0",
"1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1",
"1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0",
"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
"1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0",
"0", "1", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0",
"0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0",
"1", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0",
"0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0",
"0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0",
"0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0",
"1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0",
"1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0",
"1", "1", "0"), Times = c(9L, 25L, 23L, 50L, 9L, 4L, 20L, 36L,
25L, 28L, 32L, 26L, 26L, 26L, 26L, 4L, 16L, 9L, 25L, 26L, 28L,
32L, 4L, 6L, 6L, 6L, 6L, 6L, 4L, 44L, 15L, 9L, 4L, 4L, 9L, 6L,
26L, 33L, 44L, 44L, 4L, 36L, 14L, 4L, 4L, 36L, 9L, 32L, 32L,
4L, 44L, 26L, 9L, 6L, 4L, 33L, 26L, 26L, 26L, 23L, 26L, 9L, 14L,
36L, 44L, 4L, 35L, 32L, 28L, 28L, 9L, 6L, 4L, 36L, 26L, 9L, 9L,
9L, 4L, 4L, 14L, 33L, 15L, 4L, 4L, 58L, 26L, 4L, 33L, 9L, 4L,
4L, 4L, 39L, 26L, 9L, 6L, 33L, 28L, 33L, 20L, 33L, 6L, 14L, 20L,
50L, 58L, 17L, 36L, 28L, 33L, 50L, 16L, 4L, 33L, 50L, 9L, 26L,
28L, 4L, 58L, 9L, 17L, 6L, 14L, 58L, 28L, 9L, 6L, 50L, 9L, 9L,
9L, 4L, 26L, 9L, 9L, 14L, 36L, 44L, 20L, 26L, 50L, 6L, 9L, 16L,
14L, 11L, 44L, 9L, 58L, 9L, 14L, 9L, 36L, 28L, 17L, 28L, 23L,
11L, 33L, 6L, 14L, 36L, 9L, 9L, 11L, 17L, 17L, 20L, 9L, 14L,
11L, 20L, 6L, 4L, 9L, 14L, 11L, 4L, 6L, 14L, 23L, 36L, 23L, 20L,
11L, 9L, 9L, 14L, 26L, 9L, 6L, 16L, 18L, 23L, 43L, 23L, 6L, 6L,
9L, 28L, 20L, 58L, 36L, 11L, 51L, 20L, 26L, 33L, 9L, 6L, 9L,
17L, 14L, 58L, 11L, 20L, 6L, 17L, 14L, 28L, 16L, 6L, 6L, 28L,
6L, 6L, 9L, 28L, 9L, 22L, 14L, 6L, 6L, 14L, 17L, 36L, 37L, 20L,
20L, 35L, 23L, 9L, 25L, 23L, 23L, 33L, 18L, 51L, 9L, 6L, 6L,
9L, 17L, 9L, 29L, 28L, 20L, 28L, 14L, 50L, 14L, 17L, 6L, 11L,
11L, 28L, 20L, 28L, 20L, 6L, 6L, 9L, 9L, 47L, 9L, 9L, 11L, 17L,
23L, 23L, 44L, 20L, 36L, 52L, 17L, 17L, 44L, 28L, 11L, 14L, 28L,
23L, 9L, 9L, 17L, 18L, 22L, 28L, 9L, 14L, 14L, 14L, 23L, 23L,
52L, 17L, 28L, 14L, 28L, 9L, 6L, 6L, 28L, 23L, 23L, 4L, 37L,
51L, 51L, 14L, 23L, 6L, 28L, 20L, 17L, 26L, 11L, 35L, 15L, 14L,
20L, 18L, 4L, 29L, 6L, 30L, 51L, 23L, 9L, 23L, 14L, 23L, 14L,
15L, 36L, 9L, 37L, 29L, 28L, 30L, 23L, 51L, 51L, 17L, 17L, 30L,
18L, 23L, 28L, 15L, 14L, 9L, 28L, 33L, 14L, 23L, 9L, 14L, 26L,
9L, 23L, 14L, 9L, 44L, 43L, 15L, 4L, 14L, 14L, 23L, 52L, 23L,
14L, 32L, 17L, 17L, 44L, 20L, 30L, 28L, 43L, 33L, 23L, 9L, 44L,
33L, 23L, 18L, 26L, 26L, 26L, 9L, 6L, 11L, 6L, 18L, 30L, 51L,
44L, 23L, 43L, 30L, 23L, 17L, 44L, 43L, 23L, 15L, 28L, 17L, 18L,
23L, 26L, 14L, 9L, 28L, 15L, 16L, 9L, 17L, 30L, 15L, 20L, 6L,
23L, 18L, 32L, 30L, 18L, 17L, 23L, 18L, 18L, 6L, 17L, 30L, 51L,
44L, 23L, 28L, 18L, 15L, 18L, 28L, 26L, 44L, 23L, 23L, 17L, 28L,
30L, 17L, 44L, 43L, 30L, 38L, 17L, 28L, 26L, 17L, 17L, 18L, 23L,
28L, 6L, 30L, 17L, 9L, 28L, 28L, 28L, 11L, 17L, 17L, 20L, 9L,
30L, 18L, 47L, 30L, 23L, 33L, 18L, 30L, 17L, 36L, 30L, 23L, 17L,
30L, 33L, 14L, 18L, 15L, 32L, 23L, 23L, 30L, 23L, 30L, 30L, 43L,
30L, 30L, 17L, 36L, 17L, 17L, 51L, 30L, 17L, 15L, 50L, 11L, 11L,
4L, 32L, 26L, 17L), Age = c(27L, 38L, 16L, 50L, 30L, 26L, 65L,
28L, 25L, 57L, 26L, 53L, 26L, 21L, 21L, 25L, 55L, 16L, 59L, 22L,
45L, 19L, 40L, 10L, 54L, 51L, 30L, 20L, 22L, 22L, 37L, 39L, 50L,
35L, 20L, 44L, 26L, 32L, 20L, 26L, 56L, 36L, 31L, 30L, 38L, 58L,
40L, 58L, 53L, 34L, 48L, 55L, 27L, 48L, 47L, 16L, 29L, 45L, 19L,
49L, 48L, 34L, 26L, 52L, 39L, 30L, 39L, 21L, 19L, 34L, 39L, 63L,
21L, 43L, 50L, 25L, 54L, 55L, 42L, 43L, 29L, 26L, 43L, 37L, 25L,
31L, 21L, 23L, 30L, 30L, 55L, 18L, 45L, 28L, 51L, 43L, 15L, 18L,
39L, 52L, 52L, 36L, 20L, 52L, 64L, 52L, 42L, 45L, 17L, 19L, 60L,
55L, 48L, 67L, 58L, 26L, 34L, 56L, 62L, 36L, 32L, 51L, 30L, 54L,
56L, 60L, 49L, 50L, 40L, 51L, 28L, 59L, 35L, 20L, 53L, 35L, 54L,
27L, 22L, 46L, 33L, 33L, 41L, 34L, 39L, 46L, 58L, 25L, 58L, 33L,
28L, 39L, 22L, 25L, 59L, 49L, 50L, 46L, 54L, 37L, 20L, 50L, 22L,
32L, 30L, 25L, 25L, 60L, 26L, 55L, 44L, 53L, 19L, 29L, 36L, 28L,
54L, 56L, 48L, 35L, 39L, 28L, 37L, 41L, 22L, 54L, 50L, 57L, 56L,
40L, 22L, 34L, 21L, 14L, 35L, 65L, 54L, 42L, 38L, 14L, 28L, 55L,
64L, 46L, 37L, 39L, 45L, 42L, 20L, 20L, 35L, 17L, 46L, 20L, 19L,
45L, 55L, 28L, 33L, 45L, 52L, 42L, 30L, 37L, 33L, 18L, 56L, 36L,
60L, 50L, 47L, 27L, 22L, 25L, 19L, 51L, 24L, 55L, 32L, 60L, 19L,
50L, 44L, 41L, 46L, 28L, 56L, 25L, 51L, 30L, 32L, 19L, 37L, 39L,
60L, 18L, 28L, 45L, 58L, 29L, 22L, 50L, 17L, 33L, 26L, 28L, 31L,
23L, 49L, 52L, 22L, 30L, 37L, 33L, 32L, 33L, 22L, 27L, 37L, 17L,
24L, 30L, 40L, 18L, 54L, 49L, 41L, 47L, 44L, 53L, 48L, 40L, 20L,
21L, 54L, 23L, 22L, 31L, 41L, 47L, 36L, 22L, 51L, 27L, 30L, 50L,
56L, 44L, 38L, 43L, 54L, 52L, 42L, 59L, 43L, 38L, 57L, 20L, 50L,
25L, 25L, 25L, 30L, 39L, 33L, 50L, 39L, 49L, 53L, 57L, 74L, 48L,
35L, 51L, 53L, 41L, 27L, 18L, 28L, 30L, 33L, 59L, 25L, 39L, 37L,
52L, 47L, 56L, 30L, 53L, 64L, 47L, 55L, 50L, 55L, 47L, 45L, 56L,
26L, 27L, 31L, 28L, 39L, 61L, 50L, 54L, 22L, 54L, 40L, 40L, 44L,
40L, 31L, 55L, 38L, 51L, 28L, 35L, 33L, 25L, 41L, 35L, 53L, 29L,
27L, 33L, 35L, 39L, 47L, 42L, 20L, 34L, 56L, 41L, 55L, 53L, 53L,
25L, 56L, 57L, 53L, 18L, 57L, 58L, 57L, 38L, 44L, 22L, 50L, 59L,
47L, 50L, 44L, 50L, 43L, 24L, 45L, 53L, 52L, 18L, 45L, 27L, 30L,
55L, 31L, 39L, 50L, 45L, 45L, 50L, 43L, 39L, 48L, 22L, 39L, 41L,
34L, 52L, 53L, 53L, 31L, 35L, 62L, 53L, 60L, 41L, 30L, 23L, 42L,
56L, 43L, 35L, 56L, 34L, 56L, 38L, 41L, 52L, 62L, 30L, 51L, 44L,
54L, 24L, 53L, 47L, 42L, 43L, 57L, 18L, 62L, 40L, 37L, 36L, 52L,
41L, 42L, 48L, 41L, 33L, 26L, 43L, 37L, 33L, 26L, 32L, 42L, 31L,
18L, 26L, 20L, 43L, 35L, 33L, 38L, 50L, 37L, 42L, 35L, 52L, 43L,
35L, 50L, 37L, 30L, 49L, 46L, 54L, 29L, 38L, 54L, 27L, 57L, 52L,
26L, 23L, 36L, 56L, 38L, 50L, 59L, 19L, 42L, 18L, 22L, 22L, 22L,
24L, 23L, 37L, 40L)), .Names = c("Type", "Times", "Age"), row.names = c(NA,
-531L), class = "data.frame")
EDIT 1: Reshaping data with 'withTrainStrat' (looking for comfort) 'noTrainStrat'(not looking for comfort)
res=structure(list(Age = structure(c(1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L,
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L,
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L,
8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L,
9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L,
9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 11L,
11L, 11L, 11L, 11L, 11L, 11L, 12L, 13L, NA), .Label = c("(10,15]",
"(15,20]", "(20,25]", "(25,30]", "(30,35]", "(35,40]", "(40,45]",
"(45,50]", "(50,55]", "(55,60]", "(60,65]", "(65,70]", "(70,75]",
"(75,80]"), class = "factor"), Time = c(6L, 16L, 4L, 6L, 9L,
11L, 14L, 15L, 17L, 20L, 23L, 26L, 28L, 30L, 32L, 33L, 36L, 44L,
47L, 4L, 6L, 9L, 11L, 14L, 15L, 17L, 18L, 20L, 23L, 25L, 26L,
28L, 30L, 32L, 33L, 36L, 44L, 50L, 51L, 4L, 6L, 9L, 11L, 14L,
15L, 16L, 17L, 18L, 20L, 22L, 23L, 26L, 28L, 29L, 30L, 32L, 33L,
36L, 37L, 39L, 43L, 44L, 50L, 51L, 58L, 4L, 6L, 9L, 11L, 14L,
15L, 17L, 18L, 20L, 23L, 26L, 28L, 30L, 32L, 33L, 36L, 37L, 47L,
58L, 4L, 6L, 9L, 11L, 14L, 15L, 17L, 18L, 20L, 23L, 25L, 26L,
28L, 30L, 33L, 35L, 36L, 44L, 4L, 6L, 9L, 14L, 15L, 17L, 20L,
22L, 23L, 25L, 26L, 28L, 29L, 30L, 33L, 36L, 38L, 43L, 44L, 50L,
51L, 58L, 4L, 6L, 9L, 11L, 14L, 15L, 16L, 17L, 20L, 23L, 25L,
26L, 28L, 30L, 32L, 33L, 35L, 36L, 37L, 43L, 44L, 50L, 51L, 52L,
58L, 4L, 6L, 9L, 11L, 14L, 15L, 16L, 17L, 18L, 20L, 23L, 26L,
28L, 29L, 30L, 32L, 33L, 36L, 43L, 44L, 50L, 51L, 52L, 4L, 6L,
9L, 14L, 17L, 18L, 20L, 23L, 25L, 26L, 28L, 30L, 32L, 33L, 35L,
36L, 43L, 44L, 51L, 52L, 58L, 6L, 9L, 20L, 23L, 26L, 28L, 36L,
4L, 15L, 6L), withTrainStrat = c(2L, 1L, 4L, 5L, 2L, 1L, 2L,
2L, 2L, 2L, 1L, 3L, 4L, 4L, 1L, 4L, 1L, 1L, 1L, 6L, 2L, 4L, 4L,
8L, 1L, 4L, 1L, 1L, 3L, 1L, 5L, 1L, 1L, 0L, 2L, 1L, 1L, 1L, 2L,
4L, 4L, 8L, 2L, 6L, 1L, 1L, 4L, 4L, 2L, 1L, 9L, 3L, 3L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 4L, 3L, 13L, 2L, 1L,
2L, 4L, 3L, 2L, 3L, 2L, 5L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 4L, 9L,
9L, 4L, 5L, 1L, 8L, 2L, 1L, 3L, 1L, 0L, 3L, 1L, 1L, 1L, 2L, 2L,
3L, 7L, 3L, 2L, 1L, 7L, 3L, 1L, 1L, 1L, 3L, 8L, 1L, 2L, 1L, 3L,
1L, 1L, 2L, 1L, 2L, 2L, 2L, 3L, 2L, 3L, 2L, 1L, 2L, 3L, 2L, 2L,
1L, 3L, 3L, 6L, 0L, 0L, 1L, 0L, 1L, 1L, 3L, 1L, 1L, 1L, 1L, 2L,
3L, 8L, 2L, 6L, 1L, 1L, 1L, 3L, 3L, 7L, 5L, 4L, 1L, 2L, 1L, 2L,
3L, 3L, 3L, 3L, 1L, 0L, 1L, 3L, 6L, 3L, 3L, 4L, 2L, 3L, 1L, 2L,
1L, 2L, 1L, 2L, 0L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 0L, 3L, 2L, 0L,
2L, 1L, 1L, 1L, 1L), noTrainStrat = c(0L, 0L, 0L, 0L, 1L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L,
0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 2L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
1L, 0L, 2L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 2L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 3L, 0L, 1L, 1L, 0L, 0L, 0L, 1L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 1L, 0L, 1L,
0L, 0L, 3L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 3L, 0L, 0L, 0L, 0L, 1L, 0L,
0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L,
0L, 0L, 0L, 0L, 0L)), class = "data.frame", row.names = c(NA,
-203L), .Names = c("Age", "Time", "withTrainStrat", "noTrainStrat"
))
I tried glm :
attach(res)
glm(cbind(withTrainStrat,noTrainStrat) ~ Age + Time , family=binomial)
Call: glm(formula = cbind(withTrainStrat, noTrainStrat) ~ Age + Time,
family = binomial)
Coefficients:
(Intercept) Age(15,20] Age(20,25] Age(25,30] Age(30,35] Age(35,40] Age(40,45] Age(45,50] Age(50,55] Age(55,60] Age(60,65] Age(65,70]
16.92263 -13.58371 -14.31765 -12.32297 -13.72855 -14.55698 -14.70179 -15.26747 -14.29382 -13.85213 -15.47425 -0.29318
Age(70,75] Time
-0.11887 -0.01585
Degrees of Freedom: 201 Total (i.e. Null); 188 Residual
(1 observation deleted due to missingness)
Null Deviance: 177
Residual Deviance: 150.7 AIC: 238.9
Is it the correct way to analyze my data? I think my results are not signitificant :
> 1-pchisq(150.7,188)
[1] 0.9789707