Suppose that you wish to fit the model
Chapter 12, Problem 37SE(choose chapter or problem)
Suppose that you wish to fit the model
\(Y=\beta_{0}+\beta_{1}+\beta_{2} x^{2}+z\)
to a set of data points. If the
points are to be allocated at the design points
, and
1, what fraction should be assigned to each value of so as to minimize \(V\left(\widehat{\beta}_{2}\right)\)? (Assume that
is large and that \(k_{1} k_{2}\), and \(k_{3}, k_{1}+k_{2}+k_{3}=1\), are the fractions of the total number of observations to be assigned at
, and 1 , respectively.)
equation transcription:
Text transcription:
Y=beta{0}+\beta{1}+beta{2} x^{2}+z
V(widehat{\beta}{2})
k{1} k{2}
k{3}, k{1}+k{2}+k{3}=1
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