Note:
  • Make sure you use the “ln” and not the “log” button on your calculator. We always use natural logs in this class.

Marketability of Cucumbers

  1. The slope indicates that at the number of days of storage increases by 1 day the the log odds that the cucumber is marketable decreases by 0.33, on average.
  2. The exponentiated slope indicates that as the number of days of storage increases by 1 day the odds that the cucumber is marketable is 0.719 times lower, on average. In other words, the probability of marketability of the cucumber is only about 71.9% of what it was the day before.
  3. The number of days of storage where the marketability of the cucumber is at least 0.90 is 12.8 (=\(\frac{log\left(\frac{0.9}{0.1}\right)-6.43}{-0.33}\)).
  4. The number of days of storage where the marketability of the cucumber is just 0.10 is 26.1 (=\(\frac{log\left(\frac{0.1}{0.9}\right)-6.43}{-0.33}\)).

 

Bat Subspecies

  1. The equation of the best-fit logistic regression line if \(log\left(\frac{p}{1-p}\right)\)=-35.516+11.112×canine, where p is the probability that the bat is of the cinereus subspecies and canine is the height of the canine tooth in mm.
  2. The slope means that as the canine tooth height increases by 1 mm the log odds that the bat is a cinereus subspecies increases by between 7.589 and 15.524.
  3. The exponentiated slope means that as the canine tooth height increases by 1 mm the odds that the bat is a cinereus subspecies increases between 1976 and 5520616 times. Note that these values are so ridiculous because an increase of 1 mm essentially covers the whole range of observed canine tooth heights.
  4. The log odds of being a cinereus if the canine tooth height is 3 mm is -35.516+11.112×3=-2.180.
  5. The odds of being a cinereus if the canine tooth height is 3 mm is e-2.180=0.113. This means that the probability of being a cinereus is only about 11.3% as much as the probability of being a semotus when the canine tooth height is 3 mm. Alternatively, the probability of being a semotus is 8.846 times more likely than being a cinereus when canine tooth height is 3 mm.
  6. The probability of being a cinereus if the canine tooth height is 3 mm is \(\frac{0.113}{1+0.113}\)=0.102. This means that only about 10.2% of bats with a canine tooth height of 3 mm are likely to be cinereus.
  7. The log odds of being a cinereus if the canine tooth height is 4 mm is the log odds of being a cinereus when the canine tooth height is 3 mm PLUS the slope, or -2.180 + 11.112 = 8.932.
  8. The odds of being a cinereus if the canine tooth height is 4 is the odds of being a cinereus when the canine tooth height is 3 TIMES the exponentiated slope, or 0.113×66970 = 7570.391.
  9. The canine tooth height where it is “50-50” that the bat is cinereus is 3.20 mm (=\(\frac{-(-35.516)}{11.112}\)).
  10. The canine tooth height where you are “very sure” (95% likely) that the bat is a cinereus is 3.46 mm (=\(\frac{log\left(\frac{0.95}{0.05}\right)-(-35.516)}{11.112}\)).
  11. The canine tooth height where you are “very sure” (95% likely) that the bat is a semotus (i.e., not a cinereus) is 2.93 mm (=\(\frac{log\left(\frac{0.05}{0.95}\right)-(-35.516)}{11.112}\)).