a X y The following data is given -2 -1 1.5 3.2 0 4.5 1 3.4...

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a X y The following data is given -2 -1 1.5 3.2 0 4.5 1 3.4 a x²+b = 2 2 that best fit (1) (5 point) Determine the coefficients a and b in the function f(x) the data. What is the corresponding value of the squares of the residuals or Sp Σi (yi -f(x;))²? Here, we introduce the coefficient of determination r² = St-Sr, where = St St = Σi(y₁ - y)² and y is the arithmetic mean of y₁. Calculate ². (2) (5 points) Determine the coefficients of the quadratic polynomial that best fit the data using the polynomial regression. Check your answer with the MATLAB predefined function polyfit. Calculate S, and r². (3) (5 points) Plot the original data in circular marker (O), the fitted data in (1) in red solid line, and the fitted data in (2) in blue solid line in one figure. Which fit do you think better between (1) and (2)? Explain your answer. a X y The following data is given -2 -1 1.5 3.2 0 4.5 1 3.4 a x²+b = 2 2 that best fit (1) (5 point) Determine the coefficients a and b in the function f(x) the data. What is the corresponding value of the squares of the residuals or Sp Σi (yi -f(x;))²? Here, we introduce the coefficient of determination r² = St-Sr, where = St St = Σi(y₁ - y)² and y is the arithmetic mean of y₁. Calculate ². (2) (5 points) Determine the coefficients of the quadratic polynomial that best fit the data using the polynomial regression. Check your answer with the MATLAB predefined function polyfit. Calculate S, and r². (3) (5 points) Plot the original data in circular marker (O), the fitted data in (1) in red solid line, and the fitted data in (2) in blue solid line in one figure. Which fit do you think better between (1) and (2)? Explain your answer.

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