here is myLinReg needed to solve this problem function [a,E] = myLinReg(x,y) % [a,E] = myLinReg(x,y) % calculate the linear least squares regression to data given in x,y % Input % x: column vector of measured x data to fit % y: column vector of measured y data to fit % Output % a: vector of coefficients for the linear fit y = a(1)+a(2)*x % E: error of the fit = sum of the residual square % define a as a 2 entry vector a = zeros(2,1); n = length(x); % determine number of data points if n ~= length(y) fprintf ('Error: the length of data vectors x and y must be the same\n') a(:) = realmax(); E = realmax(); % set a and E to real max return end % calculate and store sum terms Sx = sum(x); Sy = sum(y); Sxx = sum(x.*x); Sxy = sum(x.*y); % Calculate linear equation coefficients a(1) = (Sxx*Sy-Sxy*Sx)/(n*Sxx-Sx*Sx); % a0 coefficient a(2) = (n*Sxy-Sx*Sy)/(n*Sxx-Sx*Sx); % a1 coefficient % Calculate the error of the fit E = sum((y-(a(2)*x+a(1))).^2); end
here is myLinReg needed to solve this problem function [a,E] = myLinReg(x,y) % [a,E] = myLinReg(x,y) % calculate the linear least squares regression to data given in x,y % Input % x: column vector of measured x data to fit % y: column vector of measured y data to fit % Output % a: vector of coefficients for the linear fit y = a(1)+a(2)*x % E: error of the fit = sum of the residual square % define a as a 2 entry vector a = zeros(2,1); n = length(x); % determine number of data points if n ~= length(y) fprintf ('Error: the length of data vectors x and y must be the same\n') a(:) = realmax(); E = realmax(); % set a and E to real max return end % calculate and store sum terms Sx = sum(x); Sy = sum(y); Sxx = sum(x.*x); Sxy = sum(x.*y); % Calculate linear equation coefficients a(1) = (Sxx*Sy-Sxy*Sx)/(n*Sxx-Sx*Sx); % a0 coefficient a(2) = (n*Sxy-Sx*Sy)/(n*Sxx-Sx*Sx); % a1 coefficient % Calculate the error of the fit E = sum((y-(a(2)*x+a(1))).^2); end
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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here is myLinReg needed to solve this problem
function [a,E] = myLinReg(x,y)
% [a,E] = myLinReg(x,y)
% calculate the linear least squares regression to data given in x,y
% Input
% x: column vector of measured x data to fit
% y: column vector of measured y data to fit
% Output
% a: vector of coefficients for the linear fit y = a(1)+a(2)*x
% E: error of the fit = sum of the residual square
% define a as a 2 entry vector
a = zeros(2,1);
n = length(x); % determine number of data points
if n ~= length(y)
fprintf ('Error: the length of data vectors x and y must be the same\n')
a(:) = realmax(); E = realmax(); % set a and E to real max
return
end
% calculate and store sum terms
Sx = sum(x); Sy = sum(y);
Sxx = sum(x.*x); Sxy = sum(x.*y);
% Calculate linear equation coefficients
a(1) = (Sxx*Sy-Sxy*Sx)/(n*Sxx-Sx*Sx); % a0 coefficient
a(2) = (n*Sxy-Sx*Sy)/(n*Sxx-Sx*Sx); % a1 coefficient
% Calculate the error of the fit
E = sum((y-(a(2)*x+a(1))).^2);
end
![**Developing a MATLAB Function for Least Squares Regression**
In this tutorial, you will learn how to develop a MATLAB function, `myFit`, designed to find the best fit for the function \( y(x) = \frac{1}{(mx^3 + b)} \) using a set of given data points \((x_i, y_i)\). This will involve applying least squares regression techniques.
**Function Requirements:**
- The function `myFit` should take two column vectors, `x` and `y`, as input arguments. These vectors represent the data points used in the fitting process.
- **Output:** The function should return two scalar values, `m` and `b`, which are the parameters for the function \( y(x) = \frac{1}{(mx^3 + b)} \).
**Procedure:**
1. **Set Up Regression:**
- To perform the linear least squares regression, utilize the function call:
```
[a, ~] = myLinReg(...)
```
- Inside your function, declare `a` as a global variable:
```
global a;
```
- This should be the first line in your `myFit` function to ensure proper usage of the global variable.
2. **Implementing myFit:**
- The function should correctly interact with the regression function `myLinReg`, performing operations to adjust the parameters `m` and `b` for the best fit.
By following these instructions, you will be able to create a MATLAB function that efficiently fits a curve to the given dataset using linear regression techniques. This skill is commonly applied in data analysis and computational modeling across various scientific and engineering fields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa3769d6-5bdb-4366-8adb-dd8310df7605%2F40f710ce-211b-49f4-a708-efa559f50b80%2Fcvlm9_processed.png&w=3840&q=75)
Transcribed Image Text:**Developing a MATLAB Function for Least Squares Regression**
In this tutorial, you will learn how to develop a MATLAB function, `myFit`, designed to find the best fit for the function \( y(x) = \frac{1}{(mx^3 + b)} \) using a set of given data points \((x_i, y_i)\). This will involve applying least squares regression techniques.
**Function Requirements:**
- The function `myFit` should take two column vectors, `x` and `y`, as input arguments. These vectors represent the data points used in the fitting process.
- **Output:** The function should return two scalar values, `m` and `b`, which are the parameters for the function \( y(x) = \frac{1}{(mx^3 + b)} \).
**Procedure:**
1. **Set Up Regression:**
- To perform the linear least squares regression, utilize the function call:
```
[a, ~] = myLinReg(...)
```
- Inside your function, declare `a` as a global variable:
```
global a;
```
- This should be the first line in your `myFit` function to ensure proper usage of the global variable.
2. **Implementing myFit:**
- The function should correctly interact with the regression function `myLinReg`, performing operations to adjust the parameters `m` and `b` for the best fit.
By following these instructions, you will be able to create a MATLAB function that efficiently fits a curve to the given dataset using linear regression techniques. This skill is commonly applied in data analysis and computational modeling across various scientific and engineering fields.
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