Draw a scatter diagram to show the relationship between the mass of a chicken and its cooking time. Use 2 cm to represent 0.5 kg on the horizontal axis and 1 cm to represent 10 minutes on the vertical axis.

Write down for this set of data

(i) the mean mass, \(\bar m\) ;

(ii) the mean cooking time, \(\bar t\) .

Label the point \({\text{M}}(\bar m,\bar t)\) on the scatter diagram.

Draw the line of best fit on the scatter diagram.

Using your line of best fit, estimate the cooking time, in minutes, for a 1.7 kg chicken.

Write down the Pearson’s product–moment correlation coefficient, r .

Using your value for r , comment on the correlation.

The cooking time of an additional 2.0 kg chicken is recorded. If the mass and cooking time of this chicken is included in the data, the correlation is weak.

(i) Explain how the cooking time of this additional chicken might differ from that of the other eight chickens.

(ii) Explain how a new line of best fit might differ from that drawn in part (d).

(A1) for correct scales and labels (mass or m on the horizontals axis, time or t on the vertical axis)

(A3) for 7 or 8 correctly placed data points

(A2) for 5 or 6 correctly placed data points

(A1) for 3 or 4 correctly placed data points, (A0) otherwise.     (A4)

Note: If axes reversed award at most (A0)(A3)(ft). If graph paper not used, award at most (A1)(A0).

(i) 1.91 (kg) (1.9125 kg)     (G1)

(ii) 83 (minutes)     (G1)

Their mean point labelled.     (A1)(ft)

Note: Follow through from part (b). Accept any clear indication of the mean point. For example: circle around point, (m, t), M , etc.

Line of best fit drawn on scatter diagram.     (A1)(ft)(A1)(ft)

Notes:Award (A1)(ft) for straight line through their mean point, (A1)(ft) for line of best fit with intercept 9(±2) . The second (A1)(ft) can be awarded even if the line does not reach the t-axis but, if extended, the t-intercept is correct.

75     (M1)(A1)(ft)(G2)

Notes: Accept 74.77 from the regression line equation. Award (M1) for indication of the use of their graph to get an estimate OR for correct substitution of 1.7 in the correct regression line equation t = 38.5m + 9.32.

0.960 (0.959614...)     (G2)

Note: Award (G0)(G1)(ft) for 0.95, 0.959

Strong and positive     (A1)(ft)(A1)(ft)

Note: Follow through from their correlation coefficient in part (f).

(i) Cooking time is much larger (or smaller) than the other eight     (A1)

(ii) The gradient of the new line of best fit will be larger (or smaller)     (A1)

Note: Some acceptable explanations may include but are not limited to:

The line of best fit may be further away from the plotted points
It may be steeper than the previous line (as the mean would change)
The t-intercept of the new line is smaller (larger)

Do not accept vague explanations, like:

The new line would vary
It would not go through all points
It would not fit the patterns
The line may be slightly tilted