1 An experiment is performed to determine the response of maize to nitrogen fertilizer. Data for the amount of nitrogen fertilizer applied, \(x \mathrm {~kg} / \mathrm { hectare }\), and the average yield of maize, \(y\) tonnes/hectare, in 5 experimental plots are given in the table below.

1. Draw a scatter diagram to illustrate these data.
2. Calculate the equation of the regression line of \(y\) on \(x\).
3. Draw your regression line on your scatter diagram and comment briefly on its fit.
4. Calculate the value of the residual for the data point where \(x = 30\) and \(y = 2.5\).
5. Use the equation of the regression line to calculate estimates of average yield with nitrogen fertilizer applications of
   (A) \(45 \mathrm {~kg} / \mathrm { hectare }\),
   (B) \(150 \mathrm {~kg} /\) hectare.
6. In a plot where \(150 \mathrm {~kg} /\) hectare of nitrogen fertilizer is applied, the average yield of maize is 8.7 tonnes/hectare. Comment on this result.