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@jemoka / Jemoka Knowledge Base / wiki/concepts/linear_regression.md
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--- title: "[redirect] Linear Regression" type: concept related: [Linear Predictor, House Price Prediction] source: https://www.jemoka.com/posts/kbhlinear_regression/ confidence: high status: active --- See Linear Regression example: house price prediction 1 dimension We want to predict sales price from feet above ground. \begin{equation} h(x) = \theta_{0} + \theta_{1} x \end{equation} This makes: \(h : \mathbb{R} \to \mathbb{R}\). and the \(\theta = \qty(\theta_{0}, \theta_{1})\) are what we call parameters or weights. d dimensions \begin{equation} h(x) = \theta_{0} + \sum_{j=1}^{d}\theta_{j}x_{j} \end{equation} but this is like clumsy, so if we come up with a special feature \(x_0 = 1\), we can just make it the linear model it is: \begin{equation} h(x) = \theta^{T} x \end{equation} so note: this is d features but we have d+1 dimensions for the output.