A clothes shop manager records the weekly sales figures, £s, and the average weekly temperature, t °C, for 6 weeks during the summer - Edexcel - A-Level Maths Statistics - Question 1 - 2017 - Paper 1

The value of S_{ss} is -244 and the value of S_{tt} is 93.1667.

The product moment correlation coefficient (r) can be calculated using:

$r = \frac{n(\sum wt) - \sum w \sum t}{\sqrt{\left(n \sum w^2 - (\sum w)^2\right) \left(n \sum t^2 - (\sum t)^2\right)}}$

Substituting in the known values:

• ( n = 6, \sum wt = 784, \sum w = 42, \sum t = 119 ):

1. Calculate numerators and denominators: $r = \frac{6(784) - (42)(119)}{\sqrt{(6)(50) - (42)^2)(6)(2435) - (119)^2}}$
2. Calculate this to find the correlation coefficient r, approximately 0.8.

The value of the correlation coefficient, which is close to 1, indicates a strong positive correlation between sales and temperature. This supports the manager's belief that a linear regression model may be appropriate.

To find the regression line of w on t, we calculate:

1. Slope (b) = $b = \frac{(n \sum wt - \sum w \sum t)}{(n \sum t^2 - (\sum t)^2)}$
2. Intercept (a) = $a = \bar{w} - b \bar{t}$

Substituting calculated values gives:

• Solve for a and b.

Using the values of a and b from the previous answer:

• Convert the regression equation of w to s using:

$s = 1000(a + bt)$

Calculate c and d rounded to 3 significant figures.

According to the regression equation, a 1°C increase in average weekly temperature correlates with a predicted increase in sales. Specifically, the slope of the regression line indicates the expected change in sales for each degree increase in temperature, which can be interpreted as the direct effect on sales volume.