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. What is the slope of the regression line?

Question

Mathematics

Quinn Simmons

5 January, 04:45

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. What is the slope of the regression line?

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Fletcher Nolan · Answer 1

The slope of the regression line is 0.0138

Step-by-step explanation:

The problem tells us that there is a linear relationship between the dive duration and the depth.

Linear equations have the form y = mx + b where m is the slope, y is the dependent variable and x is the independent variable.

In this problem we have that the depth is the independent variable, the dive duration is the dependent variable and the regression equation is DD = 2.69 + 0.0138D where DD is the dive duration and D is the depth. From the previous paragraph, we can observe that the slope is the coefficient of the dependent variable. Therefore, for this equation the slope is 0.0138.