Linear least squares minimizes over a vector . Its normal equations for linear least squares are ; geometrically is the orthogonal projection of onto the range of .
This is an orthogonal projection interpretation of linear least squares. The best affine predictor has slope covariance divided by predictor variance and intercept chosen to match means.
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Linear least squares is a statistical method used to find the best-fitting linear relationship between a dependent variable and one or more independent variables. The goal of linear least squares is to minimize the sum of the squares of the differences (residuals) between the observed values and the values predicted by the linear model.