Whale-watching is big business in Alaska, particularly around salmon release sites where whales tend to congregate. The article “Humpback Whales Feed on Hatchery-Released Juvenile Salmon” (Roy. Soc. Open Sci. 2017) reported a study to determine what factors help predict the likelihood of spotting a humpback whale when visiting one of these sites. The following data on x₁ = days after final salmon release, x₂ = duration of visit (min), and whether a whale was sighted are from a recent year at Little Port Walter.

(The full study investigated five sites across several years before, during, and after salmon release.)
a. Use software to fit a multiple logistic regression model to this data, and confirm that the estimated log-odds function is −5.68 − .096x₁ + .210x₂.
b. What does the negative sign for the coefficient–.096 signify? What does the positive sign for the coefficient .210 signify?

c. Estimate the probability of spotting a humpback whale during a 30-minute tour one week (i.e., seven days) after the final salmon release.

d. 

e. Interpret both e^–.096 and e^.210 in this context.

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X1 2 1 1 33355N. 2 4 6 6 x2 15 15 15 15 15 15 15 30 15 15 15 Whale? Y ZZZZZZZZZZK N N N N N N N N N N X1 X2 7 15 15 8 15 8 15 15 15 10 15 12 15 12 15 778 9 9 13 13 15 35 Whale? N ZZZZZZZZZZY N N N N N N N N N