MathLiveOrdinary least squares estimator (matrix form)
Gives the vector of regression coefficients that minimizes the sum of squared residuals in a linear regression model. It is used whenever a linear model y = X beta + error is fitted to data and X has full column rank.
\hat{\beta} = (X^{\top}X)^{-1}X^{\top}yWhat the symbols mean
| estimated coefficient vector | |
| design matrix of regressors, n by p, including a column of ones for the intercept | |
| vector of observed responses, length n | |
| transpose of the design matrix |
About this formula
- FieldStatistics
- TopicLinear regression
- LevelUniversity
- Also calledOLS estimator matrix form, least squares coefficient estimate, normal equations solution, linear regression coefficients formula, beta hat OLS, OLS formula
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