Write down

(i)     the mean temperature;

(ii)    the standard deviation of the temperatures.

Write down the correlation coefficient, \(r\), for the variables \(n\) and \(T\).

Comment on your value for \(r\).

The equation of the line of regression for \(n\) on \(T\) is \(n = dT - 100\).

(i)     Write down the value of \(d\).

(ii)    Estimate how many bottles of water will be sold when the temperature is \({19.6^ \circ }\).

On a day when the temperature was \({36^ \circ }\) Peter calculates that \(314\) bottles would be sold. Give one reason why his answer might be unreliable.

(i)     19.2     (G1)

(ii)    1.45     (G1)

[2 marks]

\(r = 0.942\)     (G1)

[1 mark]

Strong, positive correlation.     (A1)(ft)(A1)(ft)

[2 marks]

(i)     \(d = 11.5\)     (G1)

(ii)    \(n = 11.5 \times 19.6 - 100\)

\( = 125\) (accept \(126\))     (A1)(ft)

Note: Answer must be a whole number.

[2 marks]

It is unreliable to extrapolate outside the values given (outlier).     (R1)

[1 mark]

(i)     Generally well done but many lost an AP here

(ii)    Only correct if the candidate knew how to use their GDC and even then several gave the wrong standard deviation.

Again, only correct if the candidate could use their GDC. Many answers given were greater than 1 and the candidates did not see anything wrong with this.

Many received a ft mark for this part. The word “positive” was often omitted.

(i)     Most candidates substituted the first set of points into the equation instead of finding the regression line on their GDC.

(ii)    Most managed to score a ft point here. But some did not give their answer as a whole number.

Not many candidates mentioned the idea of an outlier. Most came up with some creative reason, albeit wrong, as to why the answer might be unreliable. Some of them made interesting reading.