An agricultural experimenter, investigating the effect of the amount of nitrogen x applied in 45 kg per hectare on the yield of oats y measured in 35 litres per hecrare, collected the following data:
x 1 1 2 2 3 3 4 4
y 22 19 38 41 57 54 68 65
a) Predict the expected yield of oats with 95% confidence if 285 kg of nitrogen per hectare are applied.
b) Estimate the average increase in yield for an increase of 115 kg of nitrogen per hectare with 99% confidence.