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.

equation 3.4

Data from problem 3

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.

Transcribed Image Text:

MI m m @ x +b2 * = 2 xy i=l i=l i=l m yi m a xi + mb = i=l izl