Multiple-regression analysis was used to model the abundance y of an individual bird species in transects in the United Kingdom (Journal of Applied Ecology, Vol. 32, 1995). Three of the independent variables used in the model, all field boundary attributes, are
1. Transect location (small pasture field, small arable field, or large arable field)
2. Land use (pasture or arable) adjacent to the transect
3. Total number of trees in the transect
a. Identify each of the independent variables as a quantitative or qualitative variable.
b. Write a first-order model for E(y) as a function of the total number of trees.
c. Add main-effect terms for transect location to the model you wrote in part b. Graph the hypothesized relationships of the new model.
d. Add main-effect terms for land use to the model you came up with in part c. In terms of the β's of the new model, what is the slope of the relationship between E(y) and number of trees for any combination of transect location and land use?
e. Add terms for interaction between transect location and land use to the model you arrived at in part d. Do these interaction terms affect the slope of the relationship between E(y) and number of trees? Explain.
f. Add terms for interaction between number of trees and all coded dummy variables to the model you formulated in part e. In terms of the β's of the new model, give the slope of the relationship between E(y) and number of trees for each combination of transect location and land use.