Math 170B HW #8 Partial Solutions
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1. Use Eqns 3.24 and 3.25 on page 162. Remember that the guidepoints are 
   (x_0 + a_0, y_0 + b_0) and (x_1 - a_1, y_1 - b_1).

1a. x(t) = -2t^3 + 3t^2, 
    y(t) = -6t^2 + 6t.

1b. x(t) = -2t^3 + 3t^2,
    y(t) = 12t^3 - 18t^2 + 6t. 


2a. From Pg. 484, the normal equations are:

       5*a_0  -   0.5*a_1 = 4.45,
    -0.5*a_0  +  3.25*a_1 = 2.72.

2b. Solve these to get a_0 = 0.988906, a_1 = 0.989063 so the 
    best fitting line is 

        y = 0.989063x + 0.988906.


Both Questions 3 and 4 require proof to get the answers. If you would like 
to know the reasoning, come to office hours or section.

3.  C = (y_1 + y_2 + ... + y_n)/n is the average (or mean) of the y_i.


4.  C = y_{(n+1)/2} is the median of the y_i (since n is odd!).


5a. From page 486, with m=5, n=2, the normal equations are:

      5*a_0             +   2.5*a_2   =   7.55
              2.5*a_1                 =  -0.025
    2.5*a_0             + 2.125*a_2   =   4.6575

5b. Solve these to get a_0 = 1.00571, a_1 = -0.01, a_2 = 1.00857 so the 
    best fitting quadratic (parabola) is 

        y = 1.00857x^2 - 0.01x + 1.00571.


6,7,8.  MATLAB.