Question

a. how many nightingales would sarah expect to find with 6 oak trees?
b. if sarah observed 4 nightingales on the plot with 6 oak trees, what would the residual be?
c. imagine where the upper and lower boundary lines. what are their equations
interpret the correlation coefficient

Explanation:

Step1: Substitute \(x = 6\) into the regression equation \(y=mx + b\)

Given \(m = 0.52469\) and \(b=1.88525\), the regression equation is \(y = 0.52469x+1.88525\).
When \(x = 6\), \(y=0.52469\times6 + 1.88525\)

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Step2: Calculate the residual

The formula for the residual \(e=y_{observed}-y_{predicted}\).
We know \(y_{observed} = 4\) and \(y_{predicted}\approx5\) (from part a).
So \(e = 4 - 5=- 1\)

Answer:

a. Sarah would expect to find approximately \(5\) nightingales.
b. The residual is \(-1\)