OLS minimizes squared differences
Ordinary least squares
OLS minimizes squared differences
The Gauss–Markov theorem states that OLS estimators are the best linear unbiased estimators (BLUE) when certain assumptions hold true. This theorem guarantees the efficiency of OLS estimators in linear regression models.
Example
Consider a dataset with observed values (y) and predicted values (ŷ) from a linear regression model. The OLS method calculates the best-fitting line by minimizing the squared differences (y - ŷ)².
Remember this
Understanding OLS is crucial for accurate parameter estimation and model fitting in linear regression analysis.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Related concepts
Regularization (mathematics)
L1 regularization results in sparse solutions
Finite element method
Why does a straight-line guess fail in complex terrain?
t-SNE preserves local structure
Can we see the hidden patterns in a cloud of data points?
ill-conditioned matrices cause numerical instability: small input changes → large output changes
Small changes can lead to huge errors in math
the reverse process learns: p_θ(x_{t-1}|x_t)
Can we trace back the roots of life?
Principal component analysis
Eigenvectors point along maximum variance
Swipe through 100 ML concepts daily
Open Pocket Polymath