solve linear set of equations of matrix via mrdivide and compute confidence intervals in matlab

To solve a linear set of equations of a matrix using mrdivide operator and compute confidence intervals in Matlab, you can follow the steps below:

Define the linear system of equations in matrix form: Ax = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector.
Use mrdivide operator (\) to solve for x in the equation Ax = b: x = A\b.

Here's an example code snippet:


main.m
% Step 1: Define the linear system
A = [2, 1; 3, 2];
b = [4; 8];

% Step 2: Solve for x using mrdivide (\)
x = A\b;

% Step 3: Compute confidence intervals
confidence = 0.95; % desired confidence level
n = size(A, 1); % number of equations
p = size(A, 2); % number of variables

residuals = b - A*x; % compute residuals
sigma = norm(residuals) / sqrt(n - p); % estimate of standard deviation

% Calculate t value for given confidence level and degrees of freedom
t = tinv(1 - (1 - confidence) / 2, n - p);

% Compute confidence intervals for each variable
ci = [x - t * sigma, x + t * sigma];

% Display the results
disp('Solution for x:');
disp(x);
disp('Confidence Intervals:');
disp(ci);
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In this example, we define a 2x2 coefficient matrix A and a 2x1 constant vector b. Then we solve the linear system using mrdivide operator (\) and compute the confidence intervals using the formula: ci = [x - t * sigma, x + t * sigma], where t is the critical value from the t-distribution for the desired confidence level and sigma is the estimated standard deviation of the residuals.