Consider the following data. 4 6 1 2 3 5 y 100 25 11 4 Apply the whole modeling process: 1) Consider a modeling assumption and its linearized version Y = AX + B. You may assume that the model is a power function model or an exponential model. 2) Test the suitability of the model assumptions. 3) Develop a model on this basis by determining the model parameters. X 6 7 3 2

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 33EQ
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1.
Consider the following data.
1
2
3
4
y
100 25
11 6
Apply the whole modeling process:
1) Consider a modeling assumption and its linearized version Y = AX + B. You
may assume that the model is a power function model or an exponential model.
2) Test the suitability of the model assumptions.
X
5
6
7
4 3 2
3) Develop a model on this basis by determining the model parameters.
4) Test the suitability of your model by comparing it with the original data.
Calculate the relative error in % for each data point. Comment on the suitability
of your model.
5) Consider the y value at x=2.5. At which x is this value y(x=2.5) reduced by 25%
according to the model?
Transcribed Image Text:1. Consider the following data. 1 2 3 4 y 100 25 11 6 Apply the whole modeling process: 1) Consider a modeling assumption and its linearized version Y = AX + B. You may assume that the model is a power function model or an exponential model. 2) Test the suitability of the model assumptions. X 5 6 7 4 3 2 3) Develop a model on this basis by determining the model parameters. 4) Test the suitability of your model by comparing it with the original data. Calculate the relative error in % for each data point. Comment on the suitability of your model. 5) Consider the y value at x=2.5. At which x is this value y(x=2.5) reduced by 25% according to the model?
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