Question

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled " The relation of dive duration (Y) to depth (X)." Duration Y is measured in seconds and depth X is in meters. The report then says, " The regression equation for this bird is: Y = 34.8 + 0.67 X.

a) What is the slope of the regression line?.

ANSWER seconds per meter.

(b) According to the regression line, how long does a typical
dive to a depth of 90 meters last? (use at least three decimals of
accuracy)

ANSWER seconds.

Answer #1

**Solution:**

Given: The relation of dive duration (Y) to depth (X)." Duration Y is measured in seconds and depth X is in meters and

the regression equation for this bird is: Y = 34.8 + 0.67 X.

**Part a)** What is the slope of the regression
line?.

We have: Y = 34.8 + 0.67 X.

From given regression equation , we have:

Slope = 0.67

**Thus required answer is: the slope of the regression
line is 0.67 seconds per meter.**

**Part b)** According to the regression line, how
long does a typical dive to a depth of 90 meters last?

Put X = 90 in given regression equation and solve for Y.

Thus

Y = 34.8 + 0.67 * X.

Y = 34.8 + 0.67 * 90

Y = 34.8 + 60.300

**seconds.**

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 14 minutes ago

asked 24 minutes ago

asked 25 minutes ago

asked 27 minutes ago

asked 37 minutes ago

asked 37 minutes ago

asked 37 minutes ago

asked 42 minutes ago