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clarified this is a regression problem and added it as a tag
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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 over-lapoverlap, 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?

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 over-lap, 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?

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?

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Nick Cox
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Quick 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 over-lap, 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?

Quick 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 over-lap, 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?

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 over-lap, 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?

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Nate
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Boxplots: valid method for visualizing collinearity?

Quick 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 over-lap, 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?

boxplot(TL ~ Species, data = sunfish2) 

enter image description here

> 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, 
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