2 A large field of wheat is split into 8 plots of equal area. Each plot is treated with a different amount of fertiliser, \(f\) grams \(/ \mathrm { m } ^ { 2 }\). The yield of wheat, \(w\) tonnes, from each plot is recorded. The results are summarised below. $$\sum f = 28 \quad \sum w = 303 \quad \sum w ^ { 2 } = 13447 \quad \mathrm {~S} _ { f f } = 42 \quad \mathrm {~S} _ { f w } = 269.5$$

1. Calculate the product moment correlation coefficient between \(f\) and \(w\)
2. Interpret the value of your product moment correlation coefficient.
3. Find the equation of the regression line of \(w\) on \(f\) in the form \(w = a + b f\)
4. Using your equation, estimate the decrease in yield when the amount of fertiliser decreases by 0.5 grams \(/ \mathrm { m } ^ { 2 }\) The residuals of the data recorded are calculated and plotted on the graph below.
   \includegraphics[max width=\textwidth, alt={}, center]{67df73d4-6ce4-45f7-8a69-aa94292ea814-04_1232_1294_1169_301}
5. With reference to this graph, comment on the suitability of the model you found in part (c).
6. Suggest how you might be able to refine your model.