6. The Principal of a school believes that more students are absent on days when the temperature is lower. Over a two-week period in December she records the percentage of students who are absent, \(A \%\), and the temperature, \(T ^ { \circ } \mathrm { C }\), at 9 am each morning giving these results.
| \(T \left( { } ^ { \circ } \mathrm { C } \right)\) | 4 | \({ } ^ { - } 3\) | \({ } ^ { - } 2\) | \({ } ^ { - } 6\) | 0 | 3 | 7 | \({ } ^ { - } 1\) | 3 | 2 |
| \(A ( \% )\) | 8.5 | 14.1 | 17.0 | 20.3 | 17.9 | 15.5 | 12.4 | 12.8 | 13.7 | 11.6 |
- Represent these data on a scatter diagram.
You may use
$$\Sigma T = 7 , \quad \Sigma A = 143.8 , \quad \Sigma T ^ { 2 } = 137 , \quad \Sigma A ^ { 2 } = 2172.66 , \quad \Sigma T A = 20.7$$
- Calculate the product moment correlation coefficient for these data and comment on the Principal’s hypothesis.
- Find an equation of the regression line of \(A\) on \(T\) in the form \(A = p + q T\).
- Draw the regression line on your scatter diagram.