a. Rewrite the data points (2,1), (4,2), (8,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be theassociated design matrix. Why are the columns of X orthogonal?b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y =B₁ + B₁x²,where x = x-5.75.The associated design matrix, X, is1 - 1.752.253.251the entries in one column are all 1 and the entries in the other column sum to 0.(Simplify your answer. Use ascending order.)B.Therefore, the columns of X are orthogonal becauseb. Write the normal equations for the data from part (a). Select the correct choice below and fill in the answerboxes within your choice.(Simplify your answer.)O A. [Bo B₁] =Bo421-0

Here we have to find the associated matrix.

a. Rewrite the data points (2,1), (4,2), (8,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal? b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y =B₁ + B₁x², where x =x-5.75. The associated design matrix, X, is the entries in one column are all 1 and the entries in the other column sum to 0. (Simplify your answer. Use ascending order.) B. 1 -1.75 1 2.25 1 3.25 b. Write the normal equations for the data from part (a). Select the correct choice below and fill in the answer boxes within your choice. (Simplify your answer.) O A. Po P₁] = B1 Therefore, the columns of X are orthogonal because Bo B₁

a. Rewrite the data points (2,1), (4,2), (8,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal? b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y =B₁ + B₁x², where x =x-5.75. The associated design matrix, X, is the entries in one column are all 1 and the entries in the other column sum to 0. (Simplify your answer. Use ascending order.) B. 1 -1.75 1 2.25 1 3.25 b. Write the normal equations for the data from part (a). Select the correct choice below and fill in the answer boxes within your choice. (Simplify your answer.) O A. Po P₁] = B1 Therefore, the columns of X are orthogonal because Bo B₁

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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