用MATLAB实现简单的线性回归

目录

一、损失函数CostFunction

二、梯度下降算法gradientDescent

三、直线回归

四、绘图效果

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致歉：公示的推导要用到LATEX，但我不太会，所以.......

一、损失函数CostFunction

function J=myCostFunction(X,y,theta)
    m=size(y,1)
    yhat=X*theta;
    delta=yhat-y;
    delta=delta.^2;
    dsum=sum(delta)%对列向量求和
    J=dsum/(2*m)
end

二、梯度下降算法gradientDescent

function theta=gradientDescent(X,y,theta,alpha,iter)
    m=size(y,1);
    for i=1:iter
        yhat=X*theta;
        error=yhat-y;
        delta=1/m * (X'*error);
        theta=theta-alpha*delta;
end

三、直线回归

function myLinearRegression()
    data=load('ex1data1.txt');
    x=data(:,1); %这是数据X
    y=data(:,2); %这是数据Y
    figure,axis equal ,scatter(x,y,'r*');
    m=size(y,1)
    %n=length(y)
    X=[ones(m,1),x]
    theta=[0;0]%两行一列的矩阵
    J=myCostFunction(X,y,theta)

    iter=1500;
    alpha=0.01;
    theta=gradientDescent(X,y,theta,alpha,iter);

    xval=max(x);
    X=1:0.1:xval;
    
    XX=[ones(size(X,2),1),X'];
    YY=XX*theta;

    
    hold on
    scatter(X,YY,'ko');

end

 1、size（）

m=size(y,1) 求y列向量的行数

2、theta=[0;0]

生成2*1的矩阵

>> theta=[0;0]

theta =

     0
     0

四、绘图效果

五、用二次曲线实现回归

%% 这个是主函数 
function LinearTest()
    % 装入数据
    data = load('ex1data1.txt');
    % figure, scatter(data(:,1), data(:,2));
    x = data(:,1);
    y = data(:,2);
    X = [ones(size(x,1), 1),x];
    t = eye(97,1);%生成单位矩阵
    for i=1:97
        t(i,1)=X(i,2)*X(i,2);
    end
    X = [X,t];
    theta = zeros(3,1);
    % J = costF(X, y, theta);
    iter = 1500;
    alpha = 0.0001;
    theta = gradientD(X, y, theta, alpha, iter);
    pre = X*theta;
    figure, scatter(data(:,1), data(:,2));
hold on
% scatter(x, pre,'go');
xval = max(x);
X = 1:0.1:xval;
XX = [ones(size(X,2), 1),X', X'.^2];
prenew = XX*theta;
plot(X,prenew);
% plot(x,pre, 'rx', 'MarkerSize', 10)
end

function J = costF(X, y, theta)
    prediction = X*theta;
    k1 = (prediction - y);
    k2 = k1.^2;
    csum = sum(k2);
    J = csum/size(y,1)*0.5;
end

function theta = gradientD(X, y, theta, alpha, iter)
    for i = 1:iter
        
        pre = X*theta;
        m = size(y, 1);
        error = (pre - y)/m;
        pJ = 1/m*(X'*error);
        theta = theta - alpha*pJ
    end
end