3. A scientist is researching whether or not birds of prey exposed to pollutants lay eggs with thinner shells. He collects a random sample of egg shells from each of 6 different nests and tests for pollutant level, \(p\), and measures the thinning of the shell, \(t\). The results are shown in the table below.
| \(p\) | 3 | 8 | 30 | 25 | 15 | 12 |
| \(t\) | 1 | 3 | 9 | 10 | 5 | 6 |
[You may use \(\sum p ^ { 2 } = 1967\) and \(\sum p t = 694\) ]
- Draw a scatter diagram on the axes on page 7 to represent these data.
- Explain why a linear regression model may be appropriate to describe the relationship between \(p\) and \(t\).
- Calculate the value of \(S _ { p t }\) and the value of \(S _ { p p }\).
- Find the equation of the regression line of \(t\) on \(p\), giving your answer in the form \(t = a + b p\).
- Plot the point ( \(\bar { p } , \bar { t }\) ) and draw the regression line on your scatter diagram.
The scientist reviews similar studies and finds that pollutant levels above 16 are likely to result in the death of a chick soon after hatching.
- Estimate the minimum thinning of the shell that is likely to result in the death of a chick.
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