Question: Exercise 1.2 gives the age \(x_{1}\), measured in years, as well as the selling price \(x_{2}\), measured in thousands of dollars, for \(n=10\) used cars. These data are reproduced as follows:

1. Use the results of Exercise 1.2 to calculate the squared statistical distances \(\left(\mathbf{x}_{j}-\overline{\mathbf{x}}\right)^{\prime} \mathbf{S}^{-1}\left(\mathbf{x}_{j}-\overline{\mathbf{x}}\right), \bar{j}=1,2, \ldots, 10\), where \(\mathbf{x}_{j}^{\prime}=\left[x_{j 1}, x_{j 2}\right]\)
2. Using the distances in Part a, determine the proportion of the observations falling within the estimated \(50 \%\) probability contour of a bivariate normal distribution.
3. Order the distances in Part a and construct a chi-square plot.
4. Given the results in Parts \(\mathrm{b}\) and \(\mathrm{c}\), are these data approximately bivariate normal? Explain.

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