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5. We are given with the following set of input-output (x,y) data. x:Temperature (°C) y: Corrosion (mm/yr) 26.6 1.58 26.0 1.45 27.4 1.13 21.7 0.96 Suppose that we want to model the above set of data with a linear model y = ax + b. Since our model may be perfect and there might be some noise in the measurements y, we assume y = ax + b + e, where e is the error in our modeling. a) Write down the matrix structure for this problem using the given model and the input- out data. b) Write down the structure of the solution for the coefficients a and b. You are not required to solve for the unknown parameters in our model but rather the form of the solution using least-squares error method. c) Suppose that the least squares solution for the unknown parameters are a = 0.0691 and b = -0.4761, resulting in ŷ = 0.0691 x – 0.4761. Using this model and the given input-output data, find the squared-error defined as follows e2 = E=1(Vn - n)², where y, is the nth measurement and ŷ, is the output of the model evaluated at the nth input data.

5. We are given with the following set of input-output (x,y) data. x:Temperature (°C) y: Corrosion (mm/yr) 26.6 1.58 26.0 1.45 27.4 1.13 21.7 0.96 Suppose that we want to model the above set of data with a linear model y = ax + b. Since our model may be perfect and there might be some noise in the measurements y, we assume y = ax + b + e, where e is the error in our modeling. a) Write down the matrix structure for this problem using the given model and the input- out data. b) Write down the structure of the solution for the coefficients a and b. You are not required to solve for the unknown parameters in our model but rather the form of the solution using least-squares error method. c) Suppose that the least squares solution for the unknown parameters are a = 0.0691 and b = -0.4761, resulting in ŷ = 0.0691 x – 0.4761. Using this model and the given input-output data, find the squared-error defined as follows e2 = E=1(Vn - n)², where y, is the nth measurement and ŷ, is the output of the model evaluated at the nth input data.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5. We are given with the following set of input-output (x,y) data. x:Temperature (°C) y: Corrosion (mm/yr) 26.6 1.58 26.0 1.45 27.4 1.13 21.7 0.96 Suppose that we want to model the above set of data with a linear model y = ax + b. Since our model may be perfect and there might be some noise in the measurements y, we assume y = ax + b + e, where e is the error in our modeling. a) Write down the matrix structure for this problem using the given model and the input- out data. b) Write down the structure of the solution for the coefficients a and b. You are not required to solve for the unknown parameters in our model but rather the form of the solution using least-squares error method. c) Suppose that the least squares solution for the unknown parameters are a = 0.0691 and b = -0.4761, resulting in ŷ = 0.0691 x – 0.4761. Using this model and the given input-output data, find the squared-error defined as follows e? = E-1(Vn - Pn)?, where y, is the nth measurement and ŷ, is the output of the model evaluated at the nth input data.
Transcribed Image Text:5. We are given with the following set of input-output (x,y) data. x:Temperature (°C) y: Corrosion (mm/yr) 26.6 1.58 26.0 1.45 27.4 1.13 21.7 0.96 Suppose that we want to model the above set of data with a linear model y = ax + b. Since our model may be perfect and there might be some noise in the measurements y, we assume y = ax + b + e, where e is the error in our modeling. a) Write down the matrix structure for this problem using the given model and the input- out data. b) Write down the structure of the solution for the coefficients a and b. You are not required to solve for the unknown parameters in our model but rather the form of the solution using least-squares error method. c) Suppose that the least squares solution for the unknown parameters are a = 0.0691 and b = -0.4761, resulting in ŷ = 0.0691 x – 0.4761. Using this model and the given input-output data, find the squared-error defined as follows e? = E-1(Vn - Pn)?, where y, is the nth measurement and ŷ, is the output of the model evaluated at the nth input data.
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