Chapter 3, Problem 3CRE

(a)

To determine

To find: The slope of the regression line

Answer to Problem 3CRE

The regression slope is b = 0.0138

Explanation of Solution

Given:

The regression equation for the bird is: $\widehat{y}=2.69+0.0138x$

Calculation:

The equation of the least squares regression line, $\widehat{y}=2.69+0.0138x$

Here the slope b of above regression line (0.0138) is the rate at which the predicted response Y changes among the line as the explanatory variable X changes.

Specifically, b is the predicted change in Y when X increases by 1 unit. Here b is positive; this shows if depth increases by 1 meter then dive duration increases by 0.0138 minutes.

Conclusion:

Hence, the slope is: b = 0.0138.

(b)

To determine

To find: The length of dive for a depth of 200 meters

Answer to Problem 3CRE

The length of dive for a depth of 200 meters is 5.45 minutes.

Explanation of Solution

Calculation:

The equation of the least squares regression line,$\widehat{y}=2.69+0.0138x$

We are supposed to find the dive the length when the depth is 200 meters. That is, we need to find the predicted value of Y for X = 200 meters.

The predicted value of Y is calculated as follows:

  $\widehat{y}=2.69+0.0138x$

= 2.69+0.0138x200

=5.45

Conclusion:

Hence, this shows that length of dive for a depth of 200 meters is 5.45 minutes.

(c)

To determine

To explain: The Y intercept makes any sense

Answer to Problem 3CRE

Zero meters depth makes no sense.

Explanation of Solution

Calculation:

The Y intercept of above regression line is 2.69

This value is the predicted response, Y when the explanatory variable $X=0$

In case of penguins diving, zero meters depth makes no sense.