Question

A scientist is researching whether or not birds of prey exposed to pollutants lay eggs with thinner shells. He collects a random sample of eggs 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

1. Explain why a linear model may be appropriate to describe the relationship between p and t. [3 marks]
2. Obtain the linear regression line of t on p. [4 marks]

Answer 1

Solution

We will use excel to find the solution

a.Explain why a linear model may be appropriate to describe the relationship between p and t.

We will plot scatter plot to check there is any relationship between t & p

From the scatter plot we have evidence that there is positive and linear relationship between t & p.

And we will also find correlation between t & p

	p	t
p	1
t	0.94576	1

So we can see that the correlation between p and t is 0.94576 which indicates that they are positively correlated.

So scatter plot and correlation coefficient we have strong evidence that t & p have linear relationship.

b.Obtain the linear regression line of t on p.

So we have regression equation

t = 0.317p + 0.740