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Assignment 3: How systems learn

 
a) zero-th order
b) linear 
c) quadratic
d) cubic
e) starting with data row 1, select every 4th from the 39 points, so you have
   only 10 points.  fit these with a polynomial of order 9.
 
f) consider both the JEE rank and the age as determining variables for the
   CPI.  Using a linear and a quadratic function, do you find any reduction
   in error from the uni-variate cases (b,c)?
 
Turn in:
webpage at your-area/hw3/1.html, containing
i) the equation of each hypothesis function in a-d
ii) the graphs for each hypothesis 
iii) the residual error in each case
iv) give a comparative table of the values of the coefficients in a-d. 
    What do you observe about the coefficients as the order increases,
    particularly in case (e)? 
v) results of (f)
vi) Given these investigations, which of these functions you would rather
    choose and why.

Long years ago we made a tryst with destiny, and now the time comes when we shall redeem our pledge, not wholly or in full measure, but very substantially. At the stroke of the midnight hour, when the world sleeps, India will awake to life and freedom. A moment comes, which comes but rarely in history, when we step out from the old to the new, when an age ends, and when the soul of a nation, long suppressed, finds utterance.

 
a) Estimate the probability of each letter a-z based on its frequency in
   this text. 
b) Compute the entropy of this distribution? 
c) Choose a longer text and see if the distributions and
   entropies tally. 

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