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 = 2.03 + 0.0063 D.

(a) What is the slope of the regression line?.
ANSWER ?= minutes per meter.

(b) According to the regression line, how long does a typical dive to a depth of 325 meters last?
ANSWER ? = minutes.

Answer 1

Solution:

In the line y = c + mx , m is the slope and c is the y intercept.

Here , the given regression line is

DD = 2.03 + 0.0063 D

Compare with y = c + mx ,

m = 0.0063

a)  What is the slope of the regression line?.

Answer : Slope = 0.0063 minutes per meter.

b)According to the regression line, how long does a typical dive to a depth of 325 meters last?

Put D = 325 in the equation

DD = 2.03 + (0.0063 * 325) = 4.0775

Answer :  4.0775 minutes.