A study of king penguins looked for a relationship between how deep the penguins

Question

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. For all but the shallowest dives, there is a linear relationship between depth of dive and length of time under water. The study report gives a scatterplot for a random sample of penguins. The dive duration is measured in minutes and depth (x value) is in meters. The depths are all positive numbers. The dives varied from 40 meters to 300 meters in depth. The report then says, "The regression equation for this bird is

y|x = 2.59 + 0.0126x.

(a) What is the y-intercept of the regression line? (Use 2 decimal places)

(b) What is the correct interpretation of the y-intercept?

a.When the penguin is not diving, the mean dive duration is approximately 2.59 minutes.

b. For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0126 minutes.    

c. For every increase of 1 meter in depth, the mean dive duration decreases by approximately 0.0126 minutes.

d. The intercept has no real meaning in the context of this problem: data was not observed for depths near 0 meters.

(c) What is the slope of the regression line? (Use 4 decimal places)

Explanation / Answer

The regression equation for this bird is

y|x = 2.59 + 0.0126x.

(a) the y-intercept of the regression line = 2.59

(b)  interpretation of the y-intercept is ,

d. The intercept has no real meaning in the context of this problem: data was not observed for depths near 0 meters.

(c) the slope of the regression line = 0.0126

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