Now, use ks functionality to calculate a 3D kernel estimate of the density based on the 1000

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Now, use ks functionality to calculate a 3D kernel estimate of the density based on the 1000 generated observations. Ensure that the returned object contains the vector of 99 sensible contour levels. Replot the point cloud of (a) in a new RGL device and then make two separate calls to contour3d as follows

i. The first should superimpose the theoretical contour at an α level of 0.5 from (b) only. Use the same color and opacity as you did in (b).

ii. The second should draw the isosurface at the 50th percentile as estimated from the point-specific KDE surface. Make it red and reduce the opacity to 20 percent.

Here are my results from (b) on the left and (c) on the right. Note that the appearance of your KDE isosurface will vary because of the random generation of the 1000 data points, which dictate the final estimate.

The MASS package has another data set you’ve not yet met. The Boston data frame object contains a number of descriptive observations concerning house prices in suburbs of Boston, Massachusetts, in the 1970s (Harrison and Rubinfeld, 1978). Load the MASS package and inspect the help file ?Boston to learn about the present variables.