Homework Problem 17, Due Wednesday March 17.
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Using read.table, load into Splus the dataset Dset17.asc 
from the Data directory of the course web-page

http://www.math.umd.edu/~evs/s798c/Data

(i) Using "lm", fit a normal linear regression model: 

       Y_i ~  N(b0 + b1* X1_i + b2*X3_i, sigma^2) 

using an ordinary linear regression model with scalar 
intercept a, error-variance sigma^2, and 2-dim regression 
coefficients b, altogether giving 4-dim unknown parameter.

(ii) Recover the maximum likelihood estimates of the 
parameters  a,b, sigma^2 by applying nlmin or nlminb to 
the negative log-likelihood of the model. Regard the X1 
and X3 columns as fixed, and the Y_i variables as 
independent with the given `working' model. (Actually 
the data were simulated from a similar linear regression 
model with transformed X1 and X3 and another variable X2, 
omitted here.)

(iii) Get confidence intervals, in any way you like, 
for each of the coefficients  (b0, b1, b2) based on 
assuming the `working' model you fitted is the correctly 
specified model.

(iv) Get confidence intervals for each of b0, b1, b2 
using the `robust' or `sandwich' version of the 
asymptotic variance matrix for the MLE's. Note that 
your alternative calculations of Iobs for this 
`sandwich' must involve the sigma^2 parameter as well !