Consider the data in the following table: x-1 -0.96 -0.86 -0.79 0.22 0.50 0.93 y-1 -0.151...

 

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Consider the data in the following table: x-1 -0.96 -0.86 -0.79 0.22 0.50 0.93 y-1 -0.151 0.894 0.986 0.895 0.500 -0.306 (a) Written: Which pair of points would you use to estimate y(0.75) using a linear interpo- lation? Estimate y(0.75) via linear interpolation using your chosen points. (b) MATLAB: Using appropriate MATLAB commands and scripts, construct an exact poly- nomial fit, a quadratic least-squares fit, and a cubic spline fit (with MATLAB's default not- a-knot conditions) to the above data. Estimate y(0.75) according to each method of curve fitting. Plot the original data, the two-point linear fit from question 4, part (a), the exact polynomial, least-squares quadratic and the cubic spline on the same graph using appopriate line styles. (c) Written: With reference to the graph generated for part (b), which curve (or curves) best reflect the general shape of the data (giving reasons)? Consider the data in the following table: x-1 -0.96 -0.86 -0.79 0.22 0.50 0.93 y-1 -0.151 0.894 0.986 0.895 0.500 -0.306 (a) Written: Which pair of points would you use to estimate y(0.75) using a linear interpo- lation? Estimate y(0.75) via linear interpolation using your chosen points. (b) MATLAB: Using appropriate MATLAB commands and scripts, construct an exact poly- nomial fit, a quadratic least-squares fit, and a cubic spline fit (with MATLAB's default not- a-knot conditions) to the above data. Estimate y(0.75) according to each method of curve fitting. Plot the original data, the two-point linear fit from question 4, part (a), the exact polynomial, least-squares quadratic and the cubic spline on the same graph using appopriate line styles. (c) Written: With reference to the graph generated for part (b), which curve (or curves) best reflect the general shape of the data (giving reasons)?