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A certain experiment produces the data (1, 1.7), (2, 2.9), (3, 3.2), (4, 3.5), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y=B₁x + ₂x². Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price set for the product. a. Give the design matrix and observation vector for the unknown parameter vector ³ = D B₂ b. Find the associated least-squares curve for the data. a. The design matrix is X= The observation vector is y= 1 1 2 4 3 9 4 16 5 25 1.7 2.9 3.2 3.5 3.9 C b. The least-squares curve for the data is given by the function y=x+ (x². (Round to two decimal places as needed.)

A certain experiment produces the data (1, 1.7), (2, 2.9), (3, 3.2), (4, 3.5), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y=B₁x + ₂x². Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price set for the product. a. Give the design matrix and observation vector for the unknown parameter vector ³ = D B₂ b. Find the associated least-squares curve for the data. a. The design matrix is X= The observation vector is y= 1 1 2 4 3 9 4 16 5 25 1.7 2.9 3.2 3.5 3.9 C b. The least-squares curve for the data is given by the function y=x+ (x². (Round to two decimal places as needed.)

Linear Algebra: A Modern Introduction
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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A certain experiment produces the data (1, 1.7), (2, 2.9), (3, 3.2), (4, 3.5), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y=B₁x + ₂x². Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price set for the product. a. Give the design matrix and observation vector for the unknown parameter vector ³ = 4) B₂ b. Find the associated least-squares curve for the data. a. The design matrix is X= The observation vector is y= 1 1 2 4 3 9 4 16 5 25 1.7 2.9 3.2 3.5 3.9 C b. The least-squares curve for the data is given by the function y = x + (x². (Round to two decimal places as needed.)
Transcribed Image Text:A certain experiment produces the data (1, 1.7), (2, 2.9), (3, 3.2), (4, 3.5), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y=B₁x + ₂x². Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price set for the product. a. Give the design matrix and observation vector for the unknown parameter vector ³ = 4) B₂ b. Find the associated least-squares curve for the data. a. The design matrix is X= The observation vector is y= 1 1 2 4 3 9 4 16 5 25 1.7 2.9 3.2 3.5 3.9 C b. The least-squares curve for the data is given by the function y = x + (x². (Round to two decimal places as needed.)
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