How to plot decision boundary for logistic regression in MATLAB?

I am trying to run logistic regression on a small data set. I present the full code below:

    %% Plotting data
    x1 = linspace(0,3,50);
    mqtrue = 5;
    cqtrue = 30;
    dat1 = mqtrue*x1+5*randn(1,50);
  
    x2 = linspace(7,10,50);
    dat2 = mqtrue*x2 + (cqtrue + 5*randn(1,50));
    
    x = [x1 x2]'; % X
    
    subplot(2,2,1);
    dat = [dat1 dat2]'; % Y
    
    scatter(x1, dat1); hold on;
    scatter(x2, dat2, '*'); hold on;
    classdata = (dat>40);

    %% Compute Cost and Gradient
    
    %  Setup the data matrix appropriately, and add ones for the intercept term
    [m, n] = size(x);
    
    % Add intercept term to x and X_test
    x = [ones(m, 1) x];
    
    % Initialize fitting parameters
    initial_theta = zeros(n + 1, 1);
    
    % Compute and display initial cost and gradient
    [cost, grad] = logistic_costFunction(initial_theta, x, dat);

    % Plot Boundary
    plotDecisionBoundary(initial_theta, x, dat);
    %% Predict and Accuracies
    
    % Compute accuracy on our training set
    p = predict(initial_theta, x);
    fprintf('Train Accuracy: %f\n', mean(double(p == dat)) * 100);

I then proceed to compute gradient and cost:

logistic_costFunction.m

-----------------------

    function [J, grad] = logistic_costFunction(theta, X, y)
    
    % Initialize some useful values
    m = length(y); % number of training examples
    
    grad = zeros(size(theta));
    
    H = sigmoid(X*theta);
    T = y.*log(H) + (1 - y).*log(1 - H);
    J = -1/m*sum(T);
    
    % ====================Compute grad==================
    
    for i = 1 : m
    	grad = grad + (H(i) - y(i)) * X(i,:)';
    end
    
    grad = 1/m*grad;
    
    end

sigmoid.m

    function g = sigmoid(z)
    % Computes thes sigmoid of z
    
    g = zeros(size(z));
    
    g = 1 ./ (1 + (1 ./ exp(z)));
    
    end

plotDecisionBoundary.m

----------------------

    function plotDecisionBoundary(theta, X, y)
    %PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
    %the decision boundary defined by theta

    if size(X, 2) <= 3
        % Only need 2 points to define a line, so choose two endpoints
        plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
    
        % Calculate the decision boundary line
        plot_y = (theta(2).*plot_x + theta(1));
    
        % Plot, and adjust axes for better viewing
        plot(plot_x, plot_y)
        
        % Legend, specific for the exercise
        legend('Admitted', 'Not admitted', 'Decision Boundary')
        axis([30, 100, 30, 100])
    else
        % Here is the grid range
        u = linspace(-1, 1.5, 50);
        v = linspace(-1, 1.5, 50);
    
        z = zeros(length(u), length(v));
        % Evaluate z = theta*x over the grid
        for i = 1:length(u)
            for j = 1:length(v)
                z(i,j) = mapFeature(u(i), v(j))*theta;
            end
        end
        z = z'; % important to transpose z before calling contour
    
        % Plot z = 0
        % Notice you need to specify the range [0, 0]
        contour(u, v, z, [0, 0], 'LineWidth', 2)
    end
    hold off
    
    end

I get no errors, even though I haven't verified if the logistic regression is actually working. I then proceed to plot and predict accuracy.

predict.m

---------

    function p = predict(theta, X)
    %   p = PREDICT(theta, X) computes the predictions for X using a 
    %   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
    
    p = (sigmoid(X*theta) >= 0.5);
    
    end

After running the main script I get an empty plot:

Workspace:

Any suggestions on how I can plot the decision boundary line correctly?

Answer 1

[An Liu]

maybe your axis is not fit your data

you need to change the axis range in plotDecisionBoundery function

function plotDecisionBoundary(theta, X, y)

...

% Legend, specific for the exercise

legend('Admitted', 'Not admitted', 'Decision Boundary')

axis([30, 100, 30, 100])->change here

...

end

[Suresh Subbanarahari]

An liu, thanks for your reply. I had similar issue and could adjust to see the values. Any suggestion to check on why it always shows a straight line which is not an expected decision boundary.

[Samet Oran]

because your code needs to arrange "cost function" The cost value that 0.6931 the first iteration result. It needs to reduce. The link will help you;

https://www.youtube.com/watch?v=hHtooSGdtjc&t=403s

Answer 2

[waleed qaisrani]

Chage your "plot_y" in your "Plot Decision Boundary" Function

From this:

plot_y = (theta(2).*plot_x + theta(1));

To this:

plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));

[shino aabe]

did'nt helped for me @waleed qaisrani