In the context of linear regression we are trying to solve a very simple problem. Given a sequence of pairs of points $((x_1, y_1) \dots (x_n, y_n))$ we are trying to find the polynomial that best fits these points with respect to a loss function (least squares is very commonly used in these cases). Essentially we are trying to come up with a function of the form:

$y = \beta_0 x^0 + \beta_1 x + \beta_2 x^2 + \dots \beta_k x^k$## Linear Regression

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