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 = 2.69+0.0138d.” (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 and then plot the regression line from d = 40 to d = 300. give your answers to two decimal places. dd(40)= minutes dd(300)= minutes

Explanation:

Step1: Identify the regression equation

The regression equation is $DD = 2.69+0.0138D$.

Step2: Calculate $DD(40)$

Substitute $D = 40$ into the equation:
$DD(40)=2.69 + 0.0138\times40$
$=2.69+0.552$
$=3.242\approx3.24$

Step3: Calculate $DD(300)$

Substitute $D = 300$ into the equation:
$DD(300)=2.69+0.0138\times300$
$=2.69 + 4.14$
$=6.83$

Answer:

$DD(40)=3.24$ minutes
$DD(300)=6.83$ minutes