Question

(a) Find the least squares linear polynomial approximating $\sqrt{t}$ on $[0,1]$, choosing six different exact data values. (b) How much more accurate is the least squares quadratic polynomial based on the same data? 

   (a) Find the least squares linear polynomial approximating $\sqrt{t}$ on $[0,1]$, choosing six different exact data values. (b) How much more accurate is the least squares quadratic polynomial based on the same data?
Applied Linear Algebra (Undergraduate Texts in Mathematics)
Applied Linear Algebra (Undergraduate Texts in Mathematics)
Peter J. Olver,… 2nd Edition
Chapter 5, Problem 23 ↓

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A simple choice is to use equally spaced points, including the endpoints. Thus, we choose $t_0 = 0, t_1 = 0.2, t_2 = 0.4, t_3 = 0.6, t_4 = 0.8, t_5 = 1.0$.  Show more…

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(a) Find the least squares linear polynomial approximating $\sqrt{t}$ on $[0,1]$, choosing six different exact data values. (b) How much more accurate is the least squares quadratic polynomial based on the same data?
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