Question

Batesian mimicry occurs when a non-toxic or harmless organism looks highly similar to an organism that is toxic or venomous. An example is the viceroy butterfly which is harmless, but looks extremely similar to the monarch butterfly, which is toxic and bad-tasting when eaten. As a result of the similarity, the harmless organism may be avoided by predators. Bright colors are often advertisements for toxicity, to alert predators to avoid the animal.

Another familiar example are coral and king snakes. Coral snakes have highly toxic venom, but king snakes are harmless. A common means for distinguishing the two is, "red touches yellow, you're a dead fellow. Red touches black, you're okay, Jack." But is the similarity as useful in the extreme reaches of the snakes' range? If king snakes live in areas where predators have little or no exposure to coral snakes, they are actually in danger, as their bright colors make them more apparent to predators. Researchers investigated the predation rates on king snakes at varying distances from the boundary of coral snakes' range, to determine whether there was an effect.

Dist. From Boundary	Proportion of Attacks on Mimics
-97	0
-47	0.01
-33	0
-23	0
-72	0.33
-23	0.5
152	0.4
-15	0.67
97	0.66
113	0.66
105	1
80	1
138	1
148	1
152	1
49	0.4
48	0

"Dist. From Boundary" is the distance in kilometers from the edge of the coral snakes' range; negative numbers mean within the range, positive numbers are outside.

"Proportion of Attacks on Mimics" is the proportion of attacks on artificial mimic snakes vs. artificial non-mimics by predators.

Use the data set to perform a linear regression relating distance from the boundary to the proportion of attacks on mimics. Use your regression formula to predict the proportion of attacks on mimics at -13 kilometers from the boundary. Report your answer to two decimal places.

Answer 1