Question

A researcher is attempting to predict the number of lions in an African habitat based on previous data. He has formed a regression equation which is: Y = 25 + 0.5X - 2ZX, where X is the number of years since the first population sample, and Z is the death rate of the lions. If it has been 10 years, and the death rate is 1 lion per year, what is the predicted number of lions in the habitat?

A. 10
B. 12
C. 16
D. 18
E. 20

Answer 1

The predicted number of lions in the habitat after 10 years with a death rate of 1 lion per year is 10.

Step-by-step explanation:

To predict the number of lions in the habitat, plug in the values into the given regression equation:

Y = 25 + 0.5X - 2ZX

Where X is the number of years since the first population sample and Z is the death rate of the lions.

For the given values, X = 10 years and Z = 1 lion per year.

Now substitute these values into the equation:

Y = 25 + 0.5(10) - 2(1)(10)

Simplify to get:

Y = 25 + 5 - 20

Y = 10

Therefore, the predicted number of lions in the habitat after 10 years with a death rate of 1 lion per year is 10.