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 scatter - plot 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.” (a) what is the slope of the regression line? give your answer to four decimal places. slope: choose the best explanation that describes in specific language what this slope says about this penguins dives. on average, as depth increases 1 meter, the duration of the dive increases 0.0138 minutes. on average, as depth increases 0.0138 meters, the duration of the dive increases 1 minute. on average, as depth increases 1 meter, the duration of the dive decreases by 0.0138 minutes. on average, as depth increases 0.0138 meters, the duration of the dive decreases by 1 minute.

Explanation:

Step1: Identify the regression equation

The regression equation is $DD = 2.69+0.0138D$, which is in the form $y = mx + b$ where $y = DD$ (dive - duration), $x = D$ (depth), and $m$ is the slope.

Step2: Determine the slope value

In the equation $DD = 2.69+0.0138D$, the coefficient of $D$ is the slope. So the slope $m = 0.0138$.

Step3: Interpret the slope

The slope represents the change in the dependent variable ($DD$, dive - duration) for a one - unit change in the independent variable ($D$, depth). So, on average, as depth ($D$) increases by 1 meter, the duration of the dive ($DD$) increases by 0.0138 minutes.

Answer:

a. 0.0138
On average, as depth increases 1 meter, the duration of the dive increases 0.0138 minutes.