Problem 1 (40 pts): P(x) function values against x values were obtained experimentally as follows: Polynomial Regression Expression A simple polynomial is often used as an empirical correlation equation. This can be written in general form as: P(x)=a0+a1x+a2x2+a3x3++anxn Here a0an are the parameters, also called coefficients, to be determined by regression, and n is the degree of the polynomial. Typically, when using the least-squares objective function, the degree of polynomial that provides the best data correlation is chosen. a) Assuming x is the independent variable and P is the dependent variable, relate (obtain a set of equations with 3 unknowns) the data using the 2 nd Order Polynomial Regression method. (15 pts) (Correct solution set up is 6 pts and each parameter is 1 pts, total 9 pts) b) Solve a set of equations with 3 unknowns using one of the Cramer, Gaussian Elimination, Gauss-Jordan or Inverse Matrix Methods. (15 Marks) (Correct solution set up is 6pts and each value is 3 pts, total 9 pts) c) Calculate the error between 2nd Order Polynomial Equation and experimental data for each 7 data points. (10 Marks) (each value is 1.5 pts, total 10pts )