<h1 id="linear-regression">Linear Regression<a aria-hidden="true" class="anchor-heading icon-link" href="#linear-regression"></a></h1>
Assume that the response is a linear function of the inputs.
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>W</mi><mi>T</mi></msup><mi>X</mi><mo>+</mo><mi>ϵ</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>D</mi></munderover><mrow><msub><mi>w</mi><mi>j</mi></msub><msub><mi>x</mi><mi>j</mi></msub></mrow><mo>+</mo><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">y(x) = W^TX + \epsilon = \sum_{j=1}^{D}{w_jx_j} + \epsilon</annotation></semantics></math>y(x)=WTX+ϵ=j=1∑D​wj​xj​+ϵ</div>
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math>ϵ is the residual error between our linear predictions and the actual answer.
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi></mrow><annotation encoding="application/x-tex">W</annotation></semantics></math>W is the model's weight vector.

Linear Regression


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