A study of king penguins looked for a relationship between h

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 mu^^\\^y|x = 2.78 + 0.0122x.

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

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

When the penguin is not diving, the mean dive duration is approximately 2.78 minutes.

For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0122 minutes.     

For every increase of 1 meter in depth, the mean dive duration decreases by approximately 0.0122 minutes.

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)

(d) What is the correct interpretation of the slope?

For every increase of 1 meter in depth, the mean dive duration increases by exactly 0.0122 minutes.

For every increase of 1 meter in depth, the mean dive duration decreases by exactly 0.0122 minutes.     

For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0122 minutes.

For every increase of 1 meter in depth, the mean dive duration decreases by approximately 0.0122 minutes.

(e) Based on the slope in (c), the correlation for this data is

Zero

Positive     

Negative

Solution

The regression equation for this bird y = 2.78 + 0.0122x.
a.
Y - intercept = 2.78

b.
When the penguin is not diving, the mean dive duration is approximately 2.78 minutes

When x= 0 ; Y = 2.78 + 0.0122(0) = 2.78

c.
Slope (m) = 0.0122

d.
For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0122 minutes.

e.
Positive correlation

Value of slope near to zero, it indicates the positive correlation b/w variables