- Eight students took tests in mathematics and physics. The marks for each student are given in the table below where \(m\) represents the mathematics mark and \(p\) the physics mark.
| \multirow{2}{*}{} | Student |
| | \(A\) | B | \(C\) | D | \(E\) | \(F\) | G | \(H\) |
| \multirow{2}{*}{Mark} | \(m\) | 9 | 14 | 13 | 10 | 7 | 8 | 20 | 17 |
| \(p\) | 11 | 23 | 21 | 15 | 19 | 10 | 31 | 26 |
A science teacher believes that students' marks in physics depend upon their mathematical ability. The teacher decides to investigate this relationship using the test marks.
- Write down which is the explanatory variable in this investigation.
- Draw a scatter diagram to illustrate these data.
- Showing your working, find the equation of the regression line of \(p\) on \(m\).
- Draw the regression line on your scatter diagram.
A ninth student was absent for the physics test, but she sat the mathematics test and scored 15 .
- Using this model, estimate the mark she would have scored in the physics test.