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Intro to Econometric Theory \linebreak
Heinz School, Carnegie Mellon University \linebreak
90-906, Spring 2003-4 \linebreak
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Homework \#3
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Consider the hospital cost data described on the datasets page
of the course website.  Suppose we are interested in understanding
the costs of hospital care in California.
We are going to model these data with the following CNLRM:

  \begin{equation}
  \mathrm{cost}_i = \beta_1 + \beta_2 \mathrm{days}_i 
                  + \beta_3 \mathrm{visits}_i + \epsilon_i
                  \nonumber
  \end{equation}

Analysis of these data appears in the file hwk3.lst available
on the homework page of the course website.  The analysis was
generated with SAS from the program hwk3.sas also available
on the course website.


\begin{enumerate}
\item Interpret $\beta_2$.
\item Interpret $\hat{\beta}_2$.
\item Interpret 207.82
\item Form a 95\% confidence interval for the marginal cost of
      an outpatient visit.
\item Test, at the 1\% confidence level, the hypothesis that 
      the marginal cost of an inpatient day is one fifth the
      marginal cost of an outpatient visit.
\item What is $X'X$?  (hint: first prove that 
      $X'X = (N-1)\hat{V}(X) + N \overline{X} \overline{X}'$)
\item When there is a constant in the model, what do the first
      row and the first column of $X'X$ contain?
\end{enumerate}

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