Estimating the density of X_i for the dataset:
Spending per high-school student (X_i) and graduation rates (Y_i)
  for 50 states
Table 8.6 p380 in Hollander and Wolfe 1999
 
Data:
    1.   7971   65.5      26.   3998   79.6
    2.   7151   62.3      27.   3943   85.4
    3.   6564   77.4      28.   3919   69.1
    4.   6230   84.9      29.   3858   77.3
    5.   5471   74.4      30.   3840   65.9
    6.   5329   69.8      31.   3794   76.3
    7.   5207   78.7      32.   3786   74.0
    8.   5201   74.1      33.   3744   61.1
    9.   5051   88.3      34.   3691   71.9
   10.   5017   71.7      35.   3623   75.8
   11.   4989   78.4      36.   3608   65.3
   12.   4789   73.0      37.   3519   88.3
   13.   4747   84.9      38.   3434   61.0
   14.   4692   73.6      39.   3408   64.6
   15.   4462   74.7      40.   3368   66.7
   16.   4457   74.1      41.   3249   79.6
   17.   4386   90.9      42.   3138   61.4
   18.   4369   75.6      43.   3093   71.7
   19.   4246   74.4      44.   3068   69.3
   20.   4246   87.3      45.   3011   69.0
   21.   4164   77.1      46.   2989   77.2
   22.   4149   71.6      47.   2718   74.9
   23.   4124   85.8      48.   2667   75.4
   24.   4092   58.0      49.   2548   66.9
   25.   4076   80.2      50.   2454   79.4

X-values (n=50):
   2454   2548   2667   2718   2989   3011   3068   3093   3138   3249
   3368   3408   3434   3519   3608   3623   3691   3744   3786   3794
   3840   3858   3919   3943   3998   4076   4092   4124   4149   4164
   4246   4246   4369   4386   4457   4462   4692   4747   4789   4989
   5017   5051   5201   5207   5329   5471   6230   6564   7151   7971
 
 
Estimating the density f_X(x) for bandwidths:
   h=10
   h=50
   h=200
   h=500

Approximating Int(0,10000) by Sum(1,10000):
  Int = Int(0,10000) f(x)dx    Intsq = Int(0,10000) f(x)^2 dx
  Intsqsc is after scaling (0,10000) --> (0,1)
 
  h= 10    Int=1.0000   Intsq=0.00074016    Intsqsc=7.4016
  h= 50    Int=1.0000   Intsq=0.00035331    Intsqsc=3.5331
  h=200    Int=1.0000   Intsq=0.00029768    Intsqsc=2.9768
  h=500    Int=1.0000   Intsq=0.00025865    Intsqsc=2.5865