A simple curve that often makes a good model for the variable costs of a company, as a function of the sales level x, has the form y = B1x + B2x² + B3x³ There is no constant term because fixed costs are not included. a. Give the design matrix and the parameter vector for the linear model that leads to a least-squares fit of the equation above, with data (х1. У), .... (%,. Ул) b. [M] Find the least-squares curve of the form above to fit the data (4, 1.58), (6, 2.08), (8, 2.5), (10, 2.8), (12,3.1), (14, 3.4), (16, 3.8), and (18, 4.32), with values in thousands. If possible, produce a graph that shows the data points and the graph of the cubic approximation.
A simple curve that often makes a good model for the variable costs of a company, as a function of the sales level x, has the form y = B1x + B2x² + B3x³ There is no constant term because fixed costs are not included. a. Give the design matrix and the parameter vector for the linear model that leads to a least-squares fit of the equation above, with data (х1. У), .... (%,. Ул) b. [M] Find the least-squares curve of the form above to fit the data (4, 1.58), (6, 2.08), (8, 2.5), (10, 2.8), (12,3.1), (14, 3.4), (16, 3.8), and (18, 4.32), with values in thousands. If possible, produce a graph that shows the data points and the graph of the cubic approximation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A simple curve that often makes a good model for the variable costs of a company, as a function of the sales level x, has
the form
y = B1x + B2x² + B3x³
There is no constant term because fixed costs are not included.
a. Give the design matrix and the parameter vector for the linear model that leads to a least-squares fit of the equation
above, with data
(х1. У), .... (%,. Ул)
b. [M] Find the least-squares curve of the form above to fit the data
(4, 1.58), (6, 2.08), (8, 2.5), (10, 2.8), (12,3.1), (14, 3.4), (16, 3.8), and (18, 4.32),
with values in thousands. If possible, produce a graph that shows the data points and the graph of the cubic
approximation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4569841f-2406-4655-8d10-364346eb225f%2F35a108c0-b747-47ae-916b-0fd51da8649d%2Fjsz3sle.png&w=3840&q=75)
Transcribed Image Text:A simple curve that often makes a good model for the variable costs of a company, as a function of the sales level x, has
the form
y = B1x + B2x² + B3x³
There is no constant term because fixed costs are not included.
a. Give the design matrix and the parameter vector for the linear model that leads to a least-squares fit of the equation
above, with data
(х1. У), .... (%,. Ул)
b. [M] Find the least-squares curve of the form above to fit the data
(4, 1.58), (6, 2.08), (8, 2.5), (10, 2.8), (12,3.1), (14, 3.4), (16, 3.8), and (18, 4.32),
with values in thousands. If possible, produce a graph that shows the data points and the graph of the cubic
approximation.
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