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 = 2.54 + 0.0124D."

(a) What is the slope of the regression line? (Enter your answer to four decimal places.)

(b) According to the regression line, how long does a typical dive to a depth of 207 meters last? (Round your answer to two decimal places.)

minutes

(c) The dives varied from 40 meters to 300 meters in depth. Use the regression equation to determine DD for D = 40 and D = 300. (Enter your answers to three decimal places.)

Explanation / Answer

Given Regression equation is,

DD = 2.54 + 0.0124D

Where, DD is dive duration = dependent variable

D is depth = independent variable.

a) Slope of this regression line is 0.0124

b) According to the regression line, how long does a typical dive to a depth of 207 meters last?

DD = 2.54 + [ 0.0124 * 207]

= 2.54 + 2.5668

DD = 5.11 minutes

c) To find DD for D = 40 and D= 300

For D = 40

DD = 2.54 + [0.0124 * 40]

= 2.54 + 0.496

DD = 3.036 minutes

For D = 300

DD = 2.54 + [ 0.0124 * 300]

= 2.54 + 3.72

DD = 6.260 minutes

Hence,

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