Question

A biologist observed a curved relationship between the average heart rates and life expectancies of several

mammal species in a large sample. The biologist took the natural logarithm for the values of both variables,
and they noticed a linear relationship in the transformed data.
Here's the least-squares regression equation for the transformed data, where life expectancy (LE) is in
years and heart rate (HR) is in beats per minute.
In(LE
6.33 – 0.78 In(HR)
According to this model, what is the predicted life expectancy of a mammal species whose average heart
rate is 200 beats per minute?
You may round your answer to the nearest whole year.
years
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Answer 1

Using the provided least-squares regression equation, the predicted life expectancy for a mammal species with an average heart rate of 200 beats per minute is approximately 9 years.

Step-by-step explanation:

To find the predicted life expectancy (LE) of a mammal species whose average heart rate (HR) is 200 beats per minute, we use the biologist's least-squares regression equation:

In(LE) = 6.33 - 0.78 In(HR)

First, find the natural logarithm of 200:

In(200) ≈ 5.30

Next, plug this value into the regression equation:

In(LE) = 6.33 - 0.78 * 5.30In(LE) = 6.33 - 4.134In(LE) ≈ 2.196

To get LE, exponentiate both sides:

LE = e^2.196 ≈ 9

The predicted life expectancy for a mammal species with a heart rate of 200 beats per minute is approximately 9 years.