A biologist is studying the behaviour of bees in a hive - Edexcel - A-Level Maths Statistics - Question 1 - 2016 - Paper 1

The response variable is ( w ), the average number of wiggles, since it is dependent on the independent variable, which is the distance ( d ) from the hive.

To calculate the product moment correlation coefficient ( r ), use the formula:

$r = \frac{S_{dw}}{\sqrt{S_{d} S_{w}}}$

Using the given values:

• ( S_{d} = 394600 )
• ( S_{w} = 5601 )
• ( S_{dw} = 13833 )

Substituting into the formula:

$r = \frac{13833}{\sqrt{394600 \times 5601}} \approx 0.994$

To find the regression equation, we first calculate the slope ( b ) and intercept ( a ).

The slope is given by:

$b = \frac{S_{dw}}{S_{d}} \approx 0.0142$

And the intercept is:

$a = \frac{\sum w - b \cdot \sum d}{n} \approx 0.722$

Thus, the regression equation is:

$w = 0.722 + 0.0142d$

For ( d = 350 ) m, substitute into the regression equation:

$w = 0.722 + 0.0142 \cdot 350$

Calculating gives:

$w \approx 5.7$

The estimate of ( w ) when ( d = 350 ) is considered reliable since this distance falls within the range of the provided data (50 m to 650 m).