It is said that the number of times that a cricket chirps in a minute gives a very good indication of the air temperature (in °C) - NSC Mathematics - Question 2 - 2018 - Paper 2

The claim that the number of cricket chirps gives a good indication of air temperature is supported by the data observed. As the number of chirps increases, there is a corresponding increase in temperature. This linear relationship suggests a strong correlation, indicating that the chirp rate can reflect changes in temperature accurately. Moreover, studies in the field of bioacoustics have shown that various species of crickets exhibit increased chirping rates at warmer temperatures.

To determine the equation of the least squares regression line, we need to calculate the slope (m) and the y-intercept (b). The equation can be expressed as:

$y = mx + b$

where:

• m = \frac{N(\sum xy) - (\sum x)(\sum y)}{N(\sum x^2) - (\sum x)^2}
• b = \frac{(\sum y) - m(\sum x)}{N}.

Using the provided data, calculate these values to arrive at the regression line, which can be used for predictions.

Using the regression line equation derived from step 2.3, substitute x = 80 into the equation to predict the air temperature. Solve for y:

$y = m(80) + b$

This calculation will yield the estimated air temperature in °C corresponding to 80 chirps per minute.