3. Consider the points (-1, 1), (0, 0), (1, 2), (3, 0), (4,1). We will try to fit poly- nomials to these data. You may u

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3 Consider The Points 1 1 0 0 1 2 3 0 4 1 We Will Try To Fit Poly Nomials To These Data You May U 1 (179.62 KiB) Viewed 34 times

3. Consider the points (-1, 1), (0, 0), (1, 2), (3, 0), (4,1). We will try to fit poly- nomials to these data. You may use the provided Google colab notebook to answer this question. (1) Write down the corresponding least squares problem. (2) For each degree d € {1,2,...,6}, find the best degree d polynomial that fits the data (write your answer in the form pa(y) = xo+x₁Y+ ··· +xayd. Then plot the residuals against the degrees. ● ● - (3) Consider a new data point (ye, b6) (5,-1). Use the polynomial models found in part (2) to give predictions (i.e. values of those polynomials at y = 5) for this new data point. Which model gives the best prediction?