Practice of Statistics in the Life Sciences
Practice of Statistics in the Life Sciences
4th Edition
ISBN: 9781319013370
Author: Brigitte Baldi, David S. Moore
Publisher: W. H. Freeman
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Chapter 28, Problem 28.1AYK
To determine

To write a population regression model that describe this setting and explain in words what each β in your model means.

Expert Solution & Answer
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Explanation of Solution

In the question, it is given that suppose that the number y of new birds that join a colony this year has the same straight line relationship with the percent x1 of returning birds in colonies for two different bird species. An indicator variable shows which species we observe; x2=0 for one and x2=1 for the other. Let us consider the population regression model be as:

  μy=β0+β1x1+β2x2

Where the number y is new birds that join a colony this year, x1 isthe percent of returning birds in colonies and the indicator x2 is the different species of bird returning with x2=0 for one and x2=1 for the other. So, for the one species with x2=0 for one, the model becomes,

  μy=β0+β1x1+β2x2=β0+β1x1+β2(0)=β0+β1x1

And for the other species with x2=1 for the other, the model becomes:

  μy=β0+β1x1+β2x2=β0+β1x1+β2(1)=β0+β1x1+β2=(β0+β2)+β1x1

And in these we can see that the slope that describes how the number of new birds that join a colony this year as percent x1 varies is β1 . The intercept differ: β0 for the one species and (β0+β2) for the other species. So, β2 is of particular interest because it is the fixed change between one and the other species of new birds that join a colony this year.

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