Batesian mimicry occurs when a non-toxic or harmless organism looks highly simil

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" is the distance in km 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 these data to answer the following:
1) Based on these data, what proportion of attacks would you expect to occur at 30m distance from the coral snakes' range? 3 decimals places including the leading zero

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

Explanation / Answer

We will perform a linear regression analysis here.

Lets say the linear regression line is

y^ = a + bx

where y^ = "Proportion of Attacks on Mimics" ; x = Distance From Boundary

Here we need values of x, y,xy,x2

So here n = 17

a =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [8.63 * 150638 - 772 * 796.22] / [17 * 150638 - 7722]

a = 685324.1 / 1964862 = 0.3488

b =  [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [17 * 796.22 - 772 * 8.63] /  [17 * 150638 - 7722]

b = 6873.38 / 1964862 = 0.003498

so y^ = 0.3488 +  0.003498x

so for a distance at 30 m distace from the coral snakes' range

y^ = 0.3488 +  0.003498x = 0.3488 + 0.003498 * 30 = 0.454

Dist. From Boundary(x) Proportion of Attacks on Mimics (y) x^2 xy -97 0 9409 0 -72 0.33 5184 -23.76 -47 0.01 2209 -0.47 -33 0 1089 0 -23 0 529 0 -23 0.5 529 -11.5 -15 0.67 225 -10.05 48 0 2304 0 49 0.4 2401 19.6 80 1 6400 80 97 0.66 9409 64.02 105 1 11025 105 113 0.66 12769 74.58 138 1 19044 138 148 1 21904 148 152 0.4 23104 60.8 152 1 23104 152 Sum 772 8.63 150638 796.22

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