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 study is: y = 2.56 + 0.0135x."

(a) What is the intercept of the regression line? (Use 2 decimal places)
(b) What is the slope of the regression line? (Use 4 decimal places)
(c) What is the correct interpretation of the slope?

For every increase of 1 meter in depth, the mean dive duration increases by exactly 0.0135 minutes.

For every increase of 1 meter in depth, the mean dive duration decreases by exactly 0.0135 minutes.

For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0135 minutes.

For every increase of 1 meter in depth, the mean dive duration decreases by approximately 0.0135 minutes.

Answer 1

given y=2.69+0.0138x the slope is the coefficient of x slope=0.0138 this means that the dive duration is expected to increase by about 0.0138 per minute

Step-by-step explanation:

Answer 2

Hi!

A) The intercept of the regression line is 2.56.

B)The slope of the regression line is 0.0135.

C)For every increase of 1-meter depth, the mean dive duration increases by exactly 0.0135 minutes.

Step-by-step explanation:

The definition of the regression line of a function is the value of Y(x) when x=0.

The slope of a function is the value that configures the ratio of change vertically on the regression.

In this case is represented by 0.0135 multiplied by the x.

If we are talking about depth, and the values of x are all positives values.

Y(50)=2.56+0.0135(50)=3.235

So, when the penguins go deeper, they remain more time diving.