Question

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit ofsome data collected by a biologist gives the model y= 25.2 + 3.3x, 9 < x < 25, where x is the number of chirps per minute and y is the estimatedtemperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase in 5 chirps per minute?

Answer 1

The given model is:

Now, an increase of 5 chirps will let us to 10+5=15 chirps per minute, and the temperature will be:

`\begin{gathered} y=25.2+3.3\cdot15 \\ y=25.2+49.5 \\ y=74.7\text{ F} \end{gathered}`

The estimated increase in temperature is then:

`\begin{gathered} \text{Increase}=\text{ final temperature - initial temperature} \\ \text{Increase}=74.7F-58.2F \\ \text{Increase}=16.5F \end{gathered}`

The estimated increase in temperature that corresponds to an increase in 5 chirps per minute is 16.5 °F