Homework Problem 4, Due Friday Fri. Sept. 18
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(a) Write a function  "SimLin" with the following 
inputs and outputs:

       INPUTS:
xvec = either NULL (the default) or a fixed numeric vector 
          (of arbitrary length)
simx = vector of (mean,sd,length) parameters for a normally 
          distributed SIMULATED vector   xvec , to be used 
	  in case  xvec  is NULL
errsd = error standard deviation to be used in simulating yvec
coef  = vector with 2 components (intercept,slope) to be used 
	  in simulating yvec

       OUTPUT: a list containing all the (named) components xvec,
simx, errsd, coef from the INPUTs, together with a component yvec
which is a vector of the same length as xvec , simulated to 
follow the simple linear regression model
            yvec[i] = coef[1] + coef[2]*xvec[i] +  epsilon[i] 
where epsilon is a pseudo-random normally distributed vector of the
same length as xvec, with mean 0 and standard deviation  errsd.

(b) Test your function in creating some datasets of moderately
large size (say, 300), and show that it is working properly by
calculate some appropriate summary statistics (means, covariances, 
residuals, histograms or whatever: the choice is yours).

[The working R lines and outputs for part (b) are restricted to
1/2 page AT MOST. You may, and probably should, submit a few clearly
written lines of text to explain what you are calculating and why it
indicates that the simulated linear-regression function is working.]