Boxplots: valid method for visualizing collinearity?

Question

I recently heard one can detect collinearity between a factor (Species) and a continuous covariate (TL) simply by making a boxplot. If the plots don't overlap, there is evidence of collinearity. I'm not skeptical, just surprised I haven't heard this before and hoping someone can confirm this is a thing. How does this indicate no collinearity in a regression?

boxplot(TL ~ Species, data = sunfish2)

> dput(sunfish2)
structure(list(Species = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 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, 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, 8L, 
8L, 8L, 8L, 8L, 8L, 8L, 8L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 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, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
9L, 9L, 9L, 9L, 9L, 9L, 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, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 10L), levels = c("BlackCrappie", 
"Bluegill", "Flier", "Green", "LargemouthBass", "Longear", "SmallmouthBass", 
"SpottedBass", "Warmouth", "WhiteCrappie"), class = "factor"), 
    TL = c(135L, 77L, 133L, 50L, 58L, 166L, 145L, 125L, 50L, 
    52L, 120L, 67L, 112L, 56L, 67L, 54L, 47L, 115L, 125L, 69L, 
    110L, 60L, 90L, 80L, 87L, 81L, 56L, 73L, 72L, 102L, 135L, 
    70L, 37L, 65L, 162L, 127L, 130L, 82L, 112L, 81L, 53L, 174L, 
    157L, 89L, 74L, 126L, 121L, 125L, 191L, 174L, 89L, 82L, 102L, 
    91L, 113L, 151L, 128L, 131L, 134L, 118L, 91L, 96L, 118L, 
    81L, 85L, 86L, 133L, 123L, 117L, 114L, 92L, 108L, 81L, 91L, 
    82L, 152L, 105L, 136L, 157L, 151L, 144L, 117L, 126L, 131L, 
    99L, 137L, 120L, 123L, 92L, 130L, 131L, 69L, 123L, 78L, 62L, 
    149L, 116L, 70L, 76L, 140L, 96L, 57L, 142L, 89L, 139L, 67L, 
    120L, 84L, 68L, 126L, 142L, 68L, 112L, 71L, 124L, 65L, 127L, 
    91L, 132L, 137L, 138L, 84L, 81L, 136L, 104L, 75L, 120L, 92L, 
    132L, 80L, 60L, 140L, 81L, 78L, 121L, 122L, 80L, 83L, 76L, 
    81L, 158L, 92L, 85L, 110L, 114L, 84L, 93L, 97L, 106L, 75L, 
    102L, 92L, 54L, 65L, 79L, 56L, 45L, 108L, 106L, 79L, 100L, 
    80L, 81L, 82L, 61L, 67L, 78L, 97L, 102L, 81L, 79L, 113L, 
    72L, 116L, 109L, 104L, 103L, 102L, 79L, 70L, 78L, 97L, 93L, 
    97L, 58L, 105L, 78L, 109L, 64L, 117L, 95L, 107L, 89L, 121L, 
    99L, 78L, 99L, 104L, 95L, 101L, 141L, 135L, 112L, 91L, 67L, 
    64L, 118L, 77L, 71L, 68L, 70L, 85L, 81L, 73L, 75L, 128L, 
    113L, 119L, 121L, 115L, 82L, 100L, 102L, 73L, 76L, 115L, 
    150L, 145L, 110L, 120L, 115L, 135L, 82L, 113L, 116L, 116L, 
    79L, 116L, 86L, 74L, 117L, 64L, 76L, 69L, 100L, 90L, 114L, 
    66L, 68L, 71L, 75L, 140L, 81L, 68L, 78L, 122L, 71L, 72L, 
    76L, 81L, 81L, 80L, 100L, 64L, 104L, 62L, 67L, 140L, 114L, 
    121L, 160L, 113L, 98L, 112L, 123L, 93L, 96L, 151L, 86L, 95L, 
    115L, 73L, 80L, 83L, 168L, 110L, 85L, 200L, 85L, 116L, 116L, 
    95L, 100L, 80L, 78L, 66L, 91L, 75L, 67L, 55L, 186L, 187L, 
    212L, 302L, 217L, 172L, 218L, 189L, 155L, 140L, 316L, 221L, 
    242L, 195L, 235L, 162L, 132L, 130L, 90L, 122L, 30L, 31L, 
    35L, 30L, 83L, 45L, 207L, 52L, 218L, 185L, 271L, 314L, 211L, 
    138L, 255L, 293L, 213L, 183L, 250L, 232L, 247L, 192L, 174L, 
    215L, 291L, 276L, 210L, 56L, 53L, 87L, 67L, 68L, 57L, 61L, 
    51L, 45L, 80L, 70L, 66L, 81L, 62L, 60L, 65L, 65L, 45L, 66L, 
    67L, 71L, 60L, 46L, 51L, 60L, 75L, 63L, 60L, 60L, 53L, 62L, 
    70L, 75L, 73L, 65L, 61L, 57L, 63L, 60L, 54L, 71L, 42L, 43L, 
    45L, 61L, 56L, 50L, 48L, 41L, 45L, 43L, 49L, 46L, 42L, 52L, 
    45L, 40L, 39L, 45L, 46L, 53L, 41L, 42L, 39L, 128L, 92L, 67L, 
    67L, 100L, 86L, 60L, 150L, 65L, 90L, 71L, 75L, 96L, 73L, 
    106L, 88L, 66L, 77L, 79L, 65L, 80L, 78L, 62L, 73L, 85L, 85L, 
    85L, 59L, 70L, 85L, 89L, 87L, 80L, 90L, 94L, 84L, 81L, 65L, 
    91L, 82L, 84L, 136L, 61L, 83L, 75L, 55L, 78L, 57L, 67L, 63L, 
    67L, 57L, 56L, 56L, 117L, 49L, 70L, 65L, 62L, 65L, 58L, 63L, 
    60L, 60L, 80L, 80L, 61L, 65L, 76L, 60L, 58L, 65L, 67L, 76L, 
    71L, 75L, 56L, 60L, 74L, 70L, 60L, 66L, 61L, 60L, 60L, 62L, 
    57L, 55L, 67L, 63L, 53L, 57L, 56L, 59L, 80L, 123L, 150L, 
    98L, 160L, 140L, 306L, 76L, 71L, 73L, 77L, 68L, 67L, 82L, 
    104L, 108L, 155L, 128L, 91L, 87L, 80L, 96L, 216L, 227L, 231L, 
    253L, 287L, 180L, 200L, 215L, 166L, 233L, 197L, 243L, 232L, 
    229L, 222L, 212L, 43L, 105L, 82L, 93L, 46L, 45L, 105L, 102L, 
    93L, 165L, 165L, 75L, NA, 92L, 56L, 29L, 27L, 50L, 119L, 
    28L, 32L, 40L, 41L, 40L, 42L, 37L, 37L, 29L, 40L, 81L, 67L, 
    75L, 67L, 71L, 98L, 70L, 87L, 65L, 55L, 125L, 63L, 65L, 150L, 
    54L, 80L, 110L, 96L, 67L, 65L, 55L, 78L, 110L, 90L, 64L, 
    51L, 181L, 172L, 155L, 81L, 85L, 54L, 136L, 135L, 135L, 125L, 
    122L, 120L, 80L, 75L, 54L, 76L, 72L, 69L, 82L, 172L, 80L, 
    96L, 80L, 130L, 135L, 111L, 140L, 77L, 81L, 72L, 169L, 101L, 
    83L, 93L, 73L, 65L, 74L, 59L, 66L, 55L, 64L, 49L, 56L, 47L, 
    45L, 37L, 46L, 56L, 55L, 46L, 39L, 195L, 219L, 146L, 185L, 
    167L, 211L, 128L, 117L, 91L, 126L, 81L, 80L, 93L, 40L, 78L, 
    82L, 110L, 115L, 120L, 156L, 48L, 96L, 74L, 87L, 74L, 80L, 
    99L, 97L, 104L, 93L, 166L, 90L, 134L, 127L, 77L, 78L, 304L, 
    311L, 156L, 147L, 92L, 285L, 247L, 256L, 161L, 151L, 132L, 
    142L, 102L, 89L, 72L, 32L, 36L, 37L, 38L, 38L, 38L, 33L), 
    SL = c(106L, 65L, 106L, 40L, 45L, 130L, 115L, 100L, 40L, 
    44L, 95L, 51L, 90L, 44L, 55L, 45L, 39L, 95L, 100L, 55L, 113L, 
    49L, 70L, 70L, 72L, 68L, 46L, 60L, 61L, 89L, 110L, 52L, 32L, 
    56L, 130L, 100L, 103L, 65L, 90L, 62L, 47L, 141L, 126L, 72L, 
    56L, 112L, 96L, 112L, 153L, 141L, 70L, 65L, 78L, 73L, 87L, 
    121L, 101L, 104L, 114L, 96L, 73L, 75L, 96L, 74L, 67L, 68L, 
    117L, 98L, 92L, 91L, 73L, 85L, 63L, 72L, 64L, 122L, 83L, 
    112L, 129L, 122L, 118L, 91L, 99L, 106L, 81L, 110L, 94L, 98L, 
    73L, 103L, 101L, 54L, 96L, 59L, 48L, 124L, 84L, 51L, 58L, 
    109L, 86L, 47L, 112L, 71L, 113L, 49L, 93L, 66L, 52L, 110L, 
    116L, 53L, 92L, 55L, 110L, 51L, 99L, 72L, 116L, 112L, 111L, 
    65L, 62L, 108L, 84L, 58L, 97L, 70L, 108L, 64L, 46L, 115L, 
    63L, 62L, 96L, 99L, 63L, 62L, 58L, 62L, 126L, 71L, 66L, 87L, 
    90L, 62L, 72L, 74L, 87L, 57L, 78L, 71L, 41L, 49L, 60L, 41L, 
    34L, 85L, 83L, 62L, 81L, 65L, 63L, 62L, 47L, 51L, 61L, 78L, 
    80L, 66L, 61L, 88L, 55L, 96L, 87L, 85L, 82L, 78L, 60L, 54L, 
    61L, 75L, 72L, 76L, 44L, 81L, 62L, 88L, 49L, 92L, 72L, 85L, 
    70L, 96L, 76L, 62L, 78L, 82L, 78L, 85L, 120L, 110L, 91L, 
    76L, 55L, 52L, 95L, 62L, 54L, 55L, 54L, 60L, 65L, 60L, 61L, 
    115L, 95L, 100L, 96L, 85L, 67L, 91L, 81L, 58L, 61L, 85L, 
    120L, 116L, 90L, 100L, 85L, 115L, 67L, 90L, 85L, 85L, 65L, 
    85L, 70L, 61L, 85L, 50L, 62L, 56L, 80L, 75L, 95L, 57L, 66L, 
    67L, 60L, 115L, 65L, 66L, 64L, 97L, 58L, 56L, 61L, 66L, 66L, 
    65L, 81L, 50L, 89L, 50L, 55L, 115L, 95L, 97L, 130L, 93L, 
    76L, 62L, 102L, 80L, 78L, 125L, 68L, 75L, 93L, 60L, 66L, 
    66L, 135L, 95L, 70L, 168L, 72L, 99L, 88L, 80L, 81L, 65L, 
    65L, 55L, 76L, 62L, 57L, 47L, 160L, 157L, 176L, 248L, 179L, 
    142L, 172L, 155L, 128L, 117L, 274L, 180L, 198L, 161L, 182L, 
    136L, 112L, 110L, 70L, 110L, 22L, 25L, 27L, 26L, 67L, 37L, 
    175L, 44L, 177L, 154L, 226L, 261L, 174L, 118L, 210L, 240L, 
    177L, 157L, 206L, 199L, 203L, 158L, 147L, 182L, 233L, 224L, 
    173L, 47L, 46L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
    NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 64L, 95L, 120L, 81L, 
    132L, 150L, 247L, 57L, 53L, 54L, 57L, 50L, 50L, 59L, 78L, 
    81L, 112L, 97L, 68L, 66L, 59L, 71L, 171L, 176L, 191L, 201L, 
    251L, 161L, 153L, 168L, 124L, 188L, 151L, 196L, 184L, 180L, 
    161L, 164L, 32L, 72L, 70L, 69L, 34L, 35L, 80L, 81L, 72L, 
    132L, 133L, 60L, 106L, 77L, 45L, 24L, 21L, 41L, 100L, 23L, 
    27L, 33L, 33L, 33L, 34L, 31L, 30L, 24L, 33L, 66L, 52L, 60L, 
    56L, 57L, 80L, 57L, 70L, 54L, 44L, 105L, 52L, 50L, 125L, 
    43L, 70L, 89L, 80L, 55L, 53L, 42L, 64L, 90L, 75L, 52L, 40L, 
    155L, 145L, 125L, 67L, 68L, 40L, 112L, 110L, 115L, 96L, 100L, 
    95L, 66L, 60L, 45L, 58L, 59L, 58L, 70L, 140L, 61L, 81L, 66L, 
    112L, 122L, 94L, 116L, 66L, 65L, 60L, 143L, 84L, 66L, 80L, 
    60L, 55L, 59L, 46L, 53L, 45L, 50L, 41L, 45L, 38L, 36L, 30L, 
    38L, 48L, 46L, 37L, 31L, 174L, 184L, 122L, 156L, 137L, 182L, 
    107L, 98L, 76L, 107L, 65L, 62L, 72L, 70L, 60L, 64L, 90L, 
    95L, 95L, 120L, 38L, 72L, 54L, 64L, 56L, 61L, 77L, 69L, 84L, 
    71L, 124L, 68L, 102L, 96L, 60L, 61L, 242L, 251L, 122L, 112L, 
    69L, 221L, 226L, 208L, 130L, 119L, 104L, 123L, 79L, 68L, 
    54L, 25L, 29L, 30L, 31L, 31L, 30L, 27L), Hgape = c(9.08, 
    5.95, 10.21, 2.94, 3.94, 12.55, 10.34, 8.25, 4.3, 4.11, 7.79, 
    4.13, 8.48, 4.35, 5.56, 3.56, 3.37, 8.41, 12.21, 5.22, 7.34, 
    4.6, 5.36, 6.62, 5.77, 5.74, 3.52, 4.73, 4.11, 7.96, 8.64, 
    3.25, 2.05, 5.01, 11.43, 7.82, 8.31, 4.85, 6.61, 4.8, 3.75, 
    14.27, 12.38, 6.08, 5.02, 8.93, 8.88, 9.18, 15.56, 13.56, 
    6.4, 5.65, 7.65, 6.13, 8.31, 11.53, 10.27, 10.96, 9.9, 9.2, 
    7.1, 7.3, 8.6, 7, 6.6, 6.5, 10.4, 8.6, 8.1, 8, 6.3, 7.7, 
    6.2, 6.1, 5.9, 12.3, 7.61, 9.2, 12.01, 11.83, 10.17, 9.57, 
    9.13, 9.89, 7.57, 10.72, 9.62, 10.11, 7.35, 10.93, 10.11, 
    4.85, 8.44, 5.26, 4.48, 11.28, 6.94, 4.99, 5.41, 11.29, 6.02, 
    3.47, 10.7, 5.73, 8.88, 5.11, 7.96, 4.62, 4.54, 9.39, 9.93, 
    5.06, 7.12, 4.65, 9.26, 4.14, 9.88, 5.57, 8.91, 10.08, 10.33, 
    5.89, 5.45, 10.59, 6.47, 5.21, 8.72, 5.8, 9.96, 6.02, 3.57, 
    10.02, 5.71, 5.6, 9.13, 7.37, 5.22, 5.77, 5.44, 5.32, 13.63, 
    6.09, 5.03, 7.84, 7.56, 5.12, 5.98, 5.87, 6.23, 4.16, 6.17, 
    5.87, 3.46, 3.91, 4.49, 3.87, 2.97, 7.26, 6.54, 4.93, 5.87, 
    4.92, 4.81, 4.97, 3.88, 4.16, 4.87, 5.91, 6.84, 5.03, 4.56, 
    7.98, 4.14, 8.06, 6.89, 6.93, 6.23, 5.18, 4.77, 4.27, 5.13, 
    5.18, 5.61, 6.24, 3.85, 6.07, 5.1, 7.14, 4.12, 8.92, 5.86, 
    8.86, 6.36, 12.86, 7.33, 5.58, 8.12, 7.97, 8.39, 9.44, 16.3, 
    12.99, 10.37, 8.91, 4.95, 5.22, 9.57, 6.06, 5.16, 5.16, 5.72, 
    4.93, 5.84, 5.13, 5.54, 10.16, 7.85, 8.72, 9.61, 8.6, 5.09, 
    8.61, 8.5, 5.14, 5.32, 8.88, 15.91, 14.42, 9.23, 10.15, 8.06, 
    11.97, 7.52, 9.14, 8.94, 10.02, 6.28, 8.22, 7.43, 5.51, 9.03, 
    5.24, 5.7, 5.19, 8.59, 7.58, 10.59, 5.05, 5.65, 5.56, 4.47, 
    14.66, 6.65, 5.89, 6.22, 11.05, 5.14, 5.44, 6.39, 6.46, 6.81, 
    7.1, 7.98, 5.08, 9.59, 5.38, 5.41, 13.35, 10.85, 10.59, 13.05, 
    7.44, 7.47, 8.65, 9.9, 7.17, 6.57, 13.19, 5.52, 6.99, 8.02, 
    6.2, 6.5, 7.6, 16.4, 11.5, 8, 25.55, 7.51, 11.34, 9.78, 8.52, 
    9.58, 6.64, 6.69, 7, 9.6, 7.4, 6.5, 4.8, 21.82, 19.56, 22.93, 
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This sounds like someone has confused "significantly different location" with "collinear:" the concepts are completely different and boxplots can't show you a thing about collinearity. Overlap of boxplots tells you little about significant differences, either, but overlap is related to common misconceptions about overlaps of confidence intervals. — whuber, Commented Jan 2, 2023 at 22:12
@whuber, I thought this would help me: "In regression analysis, we want to isolate the influence of each independent variable to our dependent variable. This way, we can interpret the fitted coefficient of each independent variable as the mean change in the dependent variable for each 1 unit change in an independent variable while keeping the other independent variables constant. Now if we have collinearity, the key point above is no longer valid, as if we change the value of one independent variable, the other independent variables that are correlated will also change." — Nate, Commented Jan 2, 2023 at 22:16
So, if TL depends on Species (boxplots don't overlap) then TL isn't constant over all species and we may have collinearity, no? This looked like a fitting example too: stats.stackexchange.com/questions/48688/… — Nate, Commented Jan 2, 2023 at 22:18
That quote expresses an interesting misunderstanding of collinearity! It's definitely not the case that changing one explanatory variable necessarily causes any of the other explanatory variables to change. — whuber, Commented Jan 2, 2023 at 22:18
That site is problematic from the outset. "As the name suggests, an independent variable should be independent. It shouldn’t have any correlation with other independent variables" is laughably wrong. The next sentence, "If collinearity exists between independent variables, the key point of regression analysis is violated," is just blatantly incorrect. The mistakes pile on from there, one wrong statement after another. Whatever concept of "regression" might motivate the writer, it certainly is not what is understood in statistics! — whuber, Commented Jan 2, 2023 at 22:22

User1865345 · Accepted Answer · 2023-01-03 04:33:27Z

The Utility of Boxplots

Boxplots really don't provide a lot of useful information for deriving collinearity in a regression. Probably the largest issue with using this method is that it doesn't address at all how a factor variable is linearly related to the other variables in the equation. Consider a comparison of this boxplot with it's data points overlayed above the boxplots:

We have a sense of where data is distributed for the category, and we have a sense of how it is dispersed in relation to y, but we have no idea how it interacts with other predictors because they are not included in the boxplot. A descriptive plot that may be somewhat better at approximating this would be a scatterplot that highlights where data is distributed in relation to a categorical variable, as it would at least tell a story of where the data is located in relation to a category and if it has some interaction with another predictor:

Using Generalized Variance Inflation Factor

A much more straightforward solution to this problem would be using generalized variance inflation factor (GVIF), which is a type of variance inflation factor that is better equipped to approximate categorical variables than the normal VIF measure. The typical VIF formula is:

$$ \operatorname{VIF}(\hat{\beta_j}) = \frac{1}{1-R^2_j} $$

where $R^2$ is simply the r square of a regression fit with a predictor as the response and all other predictors fit as IVs. The formula for GVIF is:

$$ \operatorname{GVIF} = \frac{\det(R_{11})\det(R_{22})}{\det(R)} $$

where $R_{11}$ is the correlation matrix for $X1$, $R_{22}$ is the correlation matrix for $X2$, and $R$ is the correlation matrix for all variables in the whole design matrix excluding the constant. Here we will use a categorical predictor for $R_{11}$ and all other numeric predictors as $R_{22}$. Unlike VIF alone, we can now obtain one GVIF value for each separate category type. The worked example below will show how this is done.

Practical Example with R

We can fit a regression with a categorical variable, using Species from the iris data in the R program. I will show how to manually calculate GVIF as well as quickly obtain it with the check_collinearity function.

#### Categorical Fit ####
fit.cat <- lm(
  Petal.Length ~ Species + Petal.Width + Sepal.Width,
  iris
)

We can then manually calculate GVIF and compare it to the check_collinearity function from the performance package by using the following steps. First, we will transform our categorical data into $R_{11}$ and our numeric data into $R_{22}$. Then we calculate GVIF by plugging in everything from the GVIF formula earlier. Finally, we will check it against the R function to see if they match. The first two steps are shown below.

#### Transform Data to R11 and R22 ####
Species <- iris$Species
R11 <- cbind(model.matrix(~ Species + 0))
R22 <- cbind(iris$Petal.Width, iris$Sepal.Width)
R11 <- R11[, -1]

#### Calculate GVIF ####
tmp_gvif <- det(cor(R11)) * det(cor(R22)) / det(cor(cbind(R11, R22)))
tmp_gvif

The tmp_gvif value should now be $26.09894$. If we compare it to the R function check_collinearity:

#### Check Against R Function ####
library(performance)
vif.cat.data <- check_collinearity(fit.cat) 
vif.cat.data

We see the values are the same:

# Check for Multicollinearity

Low Correlation

        Term   VIF     VIF 95% CI Increased SE Tolerance Tolerance 95% CI
 Petal.Width 18.06 [13.47, 24.33]         4.25      0.06     [0.04, 0.07]

High Correlation

        Term   VIF     VIF 95% CI Increased SE Tolerance Tolerance 95% CI
 Sepal.Width  2.14   [1.74, 2.77]         1.46      0.47     [0.36, 0.58]
     Species 26.10 [19.40, 35.23]         5.11      0.04     [0.03, 0.05]

We can use plot(vif.cat.data) to visualize these values, wherein you can clearly see the problematic values.

Stack Exchange Network

Boxplots: valid method for visualizing collinearity?

1 Answer 1

The Utility of Boxplots

Using Generalized Variance Inflation Factor

Practical Example with R

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Boxplots: valid method for visualizing collinearity?

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The Utility of Boxplots

Using Generalized Variance Inflation Factor

Practical Example with R

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