A study of king penguins looked for a relationship between how deep the penguins

Question

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.59 + 0.0051 D. (a) What is the slope of the regression line? (b) According to the regression line, how long does a typical dive to a depth of 325 meters last?

Explanation / Answer

We have,

DD = 2.59 + 0.0051*D

(a) From given regression line,

Intercept = 2.59

Slope = 0.0051

Hence, Answer : 0.0051

(b) Put D = 325 in give regression line, we get

DD = 2.59 + 0.0051 *(325)

= 2.59 + 1.6575

= 4.2475

Hence, Answer = 4.2475.

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