Statistical modeling/Milk offtake

The first step in the analysis of the milk offtake data is to try and fit a regression equation with a term to describe a common slope for the pattern and a term to allow separate intercepts on the y-axis for the two locations. We can do this by adding a parameter for LOCATION to that for AGEC. The model can be written algebraically in the form:

      y_i = a + bx_i + L_j + e_i

where y_i and x_i are the milk offtake and the age of calf, respectively, for cow i (i =1, ..., 164), where L_j (j=1, 2) is a parameter that describes the location where the cow resides with reference to a constant a, and where e_i is the residual term.

The location parameter L_i signifies that the regression lines for the two locations cross the y-axis at a + L₁ and a + L₂, respectively.

• With the algebraic constraint L₁ + L₂ = 0, this reduces to a + L₁ and a − L₁, respectively.
• With the algebraic constraint L₁ = 0, this reduces to a and a + L₂, respectively.

GenStat uses the second constraint.