Question

# A study of king penguins looked for a relationship between how deep the penguins dive to...

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 (Y) to depth (X)." Duration Y is measured in seconds and depth X is in meters. The report then says, " The regression equation for this bird is: Y = 34.8 + 0.67 X.

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 90 meters last? (use at least three decimals of accuracy)

Solution:

Given: The relation of dive duration (Y) to depth (X)." Duration Y is measured in seconds and depth X is in meters and

the regression equation for this bird is: Y = 34.8 + 0.67 X.

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

We have: Y = 34.8 + 0.67 X.

From given regression equation , we have:

Slope = 0.67

Thus required answer is: the slope of the regression line is 0.67   seconds per meter.

Part b) According to the regression line, how long does a typical dive to a depth of 90 meters last?

Put X = 90 in given regression equation and solve for Y.

Thus

Y = 34.8 + 0.67 * X.

Y = 34.8 + 0.67 * 90

Y = 34.8 + 60.300

seconds.