A biologist is comparing the intervals (m seconds) between the mating calls of a certain species of tree frog and the surrounding temperature (t °C) - Edexcel - A-Level Maths Statistics - Question 3 - 2013 - Paper 1

The formula to compute the slope (b) of the regression line is:

$b = \frac{S_{m}}{S_{t}}$

Using the values:

• $S_{m} = -90.5$
• $S_{t} = 354$

We find:

$b = \frac{-90.5}{354} = -0.255649 \approx -0.256$

Now, we need to compute the y-intercept (a) using:

$a = \bar{m} - b \bar{t}$

Where:

• $\bar{m} = \frac{\sum m}{n} = \frac{354}{8} = 44.25$
• $\bar{t} = 17.5$

Thus:

$a = 44.25 - (-0.256)(17.5) \approx 47.03$

The equation of the regression line is:

$m = 47.03 - 0.256t$

To estimate the time interval (m) when the surrounding temperature t is 10 °C, we can substitute t into the regression equation:

$m = 47.03 - 0.256(10)$

Calculating gives:

$m = 47.03 - 2.56 = 44.47 \text{ seconds}$

Thus, the estimated time interval between mating calls is approximately 44.47 seconds.

The reliability of this estimate is questionable because the surrounding temperature of 10 °C falls outside the range of the provided data (8 °C to 30 °C). Consequently, the regression model may not accurately predict the mating call intervals for temperatures not represented in the original dataset.