A student is investigating the relationship between the price (y pence) of 100g of chocolate and the percentage (%) of cocoa solids in the chocolate - Edexcel - A-Level Maths Statistics - Question 3 - 2007 - Paper 2

The values for calculation are:

• $S_y = 620$
• $S_{x^2} = 15,225$
• $S_x = 315$
• Using the formula:

S_{xx} = S_{x^2} - rac{S_x^2}{n}

Substituting values:

S_{xx} = 15,225 - rac{315^2}{8} = 15,225 - 12,378.75 = 2,846.25

Thus, $S_{xx} = 2,846.25$ and $S_{xy} = 4337.5$.

To find the regression coefficients, use the formulas:

b = rac{S_{xy}}{S_{xx}} = rac{4337.5}{2846.25} ext{(approximately 1.5)}

Then, calculate $a$ by substituting for $x = 0$:

a = ar{y} - b ar{x} ext{, where } ar{y} = rac{620}{8} = 77.5 ext{ and } ar{x} = rac{315}{8} = 39.375

Thus, $a = 77.5 - 1.5 imes 39.375 = 37.4$.

Hence, $a ext{ (intercept) is approximately } 37.4 ext{ and } b ext{ (slope) is approximately } 1.5$.

To draw the regression line, use the equation obtained: y = 37.4 + 1.5x. Start from the computed y-intercept (where x = 0), it will be at (0, 37.4) and find another point by substituting x-values from the data table (e.g., for x = 70).

Calculate the corresponding y-value:

y = 37.4 + 1.5(70) = 127.4.

Then plot these points on the scatter diagram and draw the line through them.

Brand D is considered overpriced as its price, 110 pence, significantly deviates from the trend indicated by the regression line.

A fair price can be estimated by substituting its cocoa percentage (40%) into the regression equation:

y = 37.4 + 1.5(40) = 97.4.

Thus, a fair price for Brand D would be approximately 97.4 pence.