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) y-intercept = 2.59

b) Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

Step-by-step explanation:

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

The given regression equation is

y = 2.59 + 0.0126x

The standard form of the regression equation is given by

y = a + bx

Where a is the y-intercept of the regression line and b is the slope of the regression line.

Comparing the given equation with the standard form,

y-intercept = 2.59

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

The y-intercept is the value we get when x = 0

y = 2.59 + 0.0126 (0)

y = 2.59 + 0

y = 2.59 minutes

Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.