Penguins diving A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay under water.31 For all but the shallowest dives, there is a linear relationship that is different for different penguins.

The study gives a scatterplot for one penguin titled “The Relation of Dive Duration (y) to Depth

(x).” Duration y is measured in minutes and depth x is in meters. The report then says, “The regression equation for this bird is: y^ = 2.69 + 0.0138x.”

(a) What is the slope of the regression line? Interpret this value.

(b) Does the y intercept of the regression line make any sense? If so, interpret it. If not, explain why not.

(c) According to the regression line, how long does a typical dive to a depth of 200 meters last?

(d) Suppose that the researchers reversed the variables, using x = dive duration and y = depth. What effect will this have on the correlation? On the equation of the least-squares regression line?