1 A random sample of wheat seedlings is planted and their growth is measured. The table shows their average growth, \(y \mathrm {~mm}\), at half-day intervals.
| Time \(t\) days | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| Average growth \(y \mathrm {~mm}\) | 0 | 7 | 21 | 33 | 45 | 56 | 62 |
- Draw a scatter diagram to illustrate these data.
- Calculate the equation of the regression line of \(y\) on \(t\).
- Calculate the value of the residual for the data point at which \(t = 2\).
- Use the equation of the regression line to calculate an estimate of the average growth after 5 days for wheat seedlings. Comment on the reliability of this estimate.
It is suggested that it would be better to replace the regression line by a line which passes through the origin. You are given that the equation of such a line is \(y = a t\), where \(a = \frac { \sum y t } { \sum t ^ { 2 } }\).
- Find the equation of this line and plot the line on your scatter diagram.