2. A researcher thinks there is a link between a person's height and level of confidence. She measured the height \(h\), to the nearest cm , of a random sample of 9 people. She also devised a test to measure the level of confidence \(c\) of each person. The data are shown in the table below.
| \(h\) | 179 | 169 | 187 | 166 | 162 | 193 | 161 | 177 | 168 |
| \(c\) | 569 | 561 | 579 | 561 | 540 | 598 | 542 | 565 | 573 |
[You may use \(\Sigma h ^ { 2 } = 272094 , \Sigma c ^ { 2 } = 2878966 , \Sigma h c = 884484\) ]
- Draw a scatter diagram to illustrate these data.
- Find exact values of \(S _ { h c } S _ { h h }\) and \(S _ { c c }\).
- Calculate the value of the product moment correlation coefficient for these data.
- Give an interpretation of your correlation coefficient.
- Calculate the equation of the regression line of \(c\) on \(h\) in the form \(c = a + b h\).
- Estimate the level of confidence of a person of height 180 cm .
- State the range of values of \(h\) for which estimates of \(c\) are reliable.