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Linear regression

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Abstract Linear regression plays a fundamental role in statistical modeling. This article provides a step‐by‐step coverage of linear models in the order of model specification, model estimation, statistical inference, variable selection, model diagnosis, and prediction. Computation issues in linear regression and intimately relevant extensions of linear models are also discussed. WIREs Comput Stat 2012, 4:275–294. doi: 10.1002/wics.1198 This article is categorized under: Statistical Models > Linear Models Algorithms and Computational Methods > Least Squares

Geometric illustration of least squares estimator.

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Diagnostic plot of r(−i) vs. hii for the 1987 baseball salary data. The size of the bubble corresponds to Cook's distance Di.

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Partial residual plots.

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Plot of jackknife residuals r(−i) vs. ŷi: (a) the case where all the model assumptions are valid, superimposed with a smooth curve from loess smoothing; and (b) the case with unequal error variances.

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Illustration of shrinkage estimators in the two‐dimensional case: (a) ridge (q = 2) and (b) lasso (q = 1).

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Illustration of the bias‐variance tradeoff.

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Geometric illustration of the F test.

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Statistical Models > Linear Models
Algorithms and Computational Methods > Least Squares

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