LS Fit Using Orthogonal Polynomials over the Data Interval

   One can make the vectors or functions used to compute the fit coefficients more symmetrical if one defines a set of orthogonal polynomials on the interval covered by the data. The data for the 9 sets of measurements covered the interval [0,2]. We can start by setting p₀=1 and letting p₁=ax+b. When we integrate the product of the two polynomials over the interval [0,2] and set it equal to zero, we are left with one undetermined constant so to be more definite we can choose the coefficients so they are small integers. We then get p₁=x-1. Setting p₂=ax²+bx+c and setting the integrals of the products of p₂ with the other two polynomials equal to zero we are again left with one undetermined coefficient which we can again set be equal to small integers. And we get 

p₂=3x²-6x+2.

  Using the same formula for λ we get the following results.

The λ functions look more symmetrical but the accuracy of the fit doesn't seem to be improved.