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?
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