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
- 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.
- 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.
- The number of days of storage where the marketability of the cucumber is at least 0.90 is 12.8 (=\(\frac{log\left(\frac{0.9}{0.1}\right)-6.43}{-0.33}\)).
- 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
- 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.
- 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.
- 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.
- The log odds of being a cinereus if the canine tooth height is 3 mm is -35.516+11.112×3=-2.180.
- 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.
- 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.
- 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.
- 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.
- The canine tooth height where it is “50-50” that the bat is cinereus is 3.20 mm (=\(\frac{-(-35.516)}{11.112}\)).
- The canine tooth height where you are “very sure” (95% likely) that the bat is a cinereus is 3.46 mm (=\(\frac{log\left(\frac{0.95}{0.05}\right)-(-35.516)}{11.112}\)).
- 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 (=\(\frac{log\left(\frac{0.05}{0.95}\right)-(-35.516)}{11.112}\)).