Examine closely the system of equations that result when you fit the quadratic in Proble...

Examine closely the system of equations that result when you fit the quadratic in Problem 3. Suppose c2 = 0. What would be the corresponding system of equations? Repeat for the cases c1 = 0 and c3 = 0. Suggest a system of equations for a cubic. Check your result. Explain how you would generalize the system of Equation (3.4) to fit any polynomial. Explain what you would do if one or more of the coefficients in the polynomial were zero.

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Derive the equations that minimize the sum of the squared deviations between a set of data points and the quadratic model y = c₁x² + c₂x + c₃. Use the equations to find estimates of c₁, c₂, and c₃ for the following set of data.

Compute D and d_max to bound c_max. Compare the results with your solution to Problem 3 in Section 3.2.

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3.2.3: For the following data, formulate the mathematical model that minimizes the largestdeviation between the data and the model y = c₁x² + c₂x + c3. If a computer code is available, solve for the estimates of c₁, c₂, and c₃.