In a snow geese feeding trial, a model was constructed relating gosling* * weight change (Y), to digestion efficiency (X1) which is measured on a scale from 1 to 10, depending on how well nutrition is absorbed by the goosling, and diet (either plants or duck chow). Using Bi, etc. to represent the coefficients of independent variables, and defining any independent variables you create and use, write out the following: [WRITE OUT THE FULL MODELS IN SINGLE EQUATIONS IN EACH SECTION BELOW, NOT BROKEN DOWN INTO SEPARATE SUB-EQUATIONS] Define your independent variables here a) a first order model that allows for different intercepts but the same slope for each diet b) a first order model that allows for different slopes and intercepts for each diet (c) a first order model that allows for different slopes and the same intercept for each diet