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 = 2.16 + 0.0076 D.

a. What is the slope of the regression line? _______  minutes per meter.

b.  According to the regression line, how long does a typical dive to a depth of 250 meters last? _______ minutes.

Explanation / Answer

a.) Slope of a regression line

So it's a Y=mX+C kind of equattion where m is the slope ., let's compare the same with our actula regression equation where

DD=0.0076D+2.16 and so here

Y=DD

m=0.0076

X=D

C=2.16

and so m is the slope so slope of the regression line = m =0.0076

b.) Now we have D=250 meters

so substituting the same in the regression equation we get

DD= 2.16 + 0.0076 *250 = 4.06 minutes

So., According to the regression line, how long does a typical dive to a depth of 250 meters last for _4.06______ minutes.

Hope the above explaination has helped you in understanding the problem. Please upvote if it has really helped. Good Luck!!!

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