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ANSC*6370 - QG and Animal Breeding
Fall 03 - Assignment 6

Below is an example data set for a spline regression exercise. In a spline function, inclusion of one of the x-variables depends on the value of another variable. In this example x₂ is included only if x₁ is greater than 7, then x₂ = x₁ - 7, otherwise, x₂=0. The number 7 is called a knot, a point in the curve where the shape changes direction. Below are the data and model equation:

$$y_{i} = a \ + \ b_{1}x_{1} \ + \ b_{2}x_{1}^{2} \ + \ b_{3}x_{2}^{2} \ + \ e_{i},$$

where

$${\bf y} = \left( \begin{array}{r} 147 \\ 88 \\ 202 \\ 135 \\ ... ...n{array}{r} a \\ b_{1} \\ b_{2} \\ b_{3} \end{array} \right).$$

where .

1.

Construct and solve the ordinary least squares equations.

2.

Give the basic AOV table, and R² value.

3.

Test the following hypotheses using the general linear hypothesis method, and summarize the results in the AOV table.

(a)

a = 250.

(b)

4.

Repeat the analysis without x₂² in the model. Compare the two models using $-2log(p({\bf y}\mid{\bf\theta}))$.