Linear Regression: Model Assumptions, Fitting, and Diagnostics

Summary

This overview introduces linear regression as a model for a continuous response, expressed as a linear combination of input features plus random error. It explains the role of the intercept and describes the compact matrix representation of the model. The fitting goal is to estimate coefficients that provide a best fit, with Ordinary Least Squares presented as the central method to be developed in the series.

The article lays out a learning path covering exploratory data analysis, OLS and its normal equations, maximum likelihood, stochastic gradient descent, the Gauss-Markov theorem, goodness of fit, identifiability, and generalized and weighted least squares. These topics connect fitting choices to assumptions such as uncorrelated residuals and constant error variance. The piece is a roadmap rather than a worked empirical study: it gives no dataset results or detailed derivations. Its core practical message is that model choice and interpretation require understanding assumptions and diagnostics, not just using a prediction library.

Key ideas

• Linear regression models a continuous response as a linear combination of features and an error term.
• The intercept can be represented by including a constant feature in the design matrix.
• Ordinary Least Squares estimates coefficients by optimizing a criterion of fit.
• Residual correlation and nonconstant error variance can call for alternative fitting methods.
• Exploratory analysis, identifiability checks, and fit diagnostics are part of sound model use.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.