b. Find the associated least-squares curve for the data. y=x+x² (Round to two decimal places as needed.) c. If a machine learned the curve you found in (b), what output would it provide for an input of x=6? y= (Round to two decimal places as needed.) A certain experiment produces the data (1, 1.8), (2, 2.8), (3, 3.3), (4, 3.6), and (5, 4.1). Describe the model that produces a least-squares fit of these points by a function of the form y=B+x+B2x2. 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 to be set for the product. Answer parts (a) through (c) below. a. Give the design matrix, the observation vector, and the unknown parameter vector. Choose the correct design matrix X below. O A. 1 2 3 4 5 149 16 25 O B. 1 1 2 4 3 9. 4 16 5 25 The observation vector is y = Choose the correct form of the parameter vector ẞ below. O A. B₁ B₂ Ba Ba B5 O B. 0 B₁ B₂ Loupio for the data ○ C. 1 1 1 ○ D. 1 1 1 1 1 1 2 3 4 149 16 25 55 124 139 14 16 1525 ○ C. X ○ D. B₁ +2 12

b. Find the associated least-squares curve for the data. y=x+x² (Round to two decimal places as needed.) c. If a machine learned the curve you found in (b), what output would it provide for an input of x=6? y= (Round to two decimal places as needed.) A certain experiment produces the data (1, 1.8), (2, 2.8), (3, 3.3), (4, 3.6), and (5, 4.1). Describe the model that produces a least-squares fit of these points by a function of the form y=B+x+B2x2. 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 to be set for the product. Answer parts (a) through (c) below. a. Give the design matrix, the observation vector, and the unknown parameter vector. Choose the correct design matrix X below. O A. 1 2 3 4 5 149 16 25 O B. 1 1 2 4 3 9. 4 16 5 25 The observation vector is y = Choose the correct form of the parameter vector ẞ below. O A. B₁ B₂ Ba Ba B5 O B. 0 B₁ B₂ Loupio for the data ○ C. 1 1 1 ○ D. 1 1 1 1 1 1 2 3 4 149 16 25 55 124 139 14 16 1525 ○ C. X ○ D. B₁ +2 12

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

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