History
The least squares method was first published by which famous French mathematician?
Adrien-Marie Legendre.
Card 1 of 259. Answer: Adrien-Marie Legendre.
Adrien-Marie Legendre.
Card 1 of 259. Answer: Adrien-Marie Legendre.
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Adrien-Marie Legendre. He published the method of least squares in 1805, in an appendix to his book on determining the orbits of comets. Least squares fits a model by choosing the parameters that minimize the sum of squared residuals, Σ (yᵢ − ŷᵢ)².
Carl Friedrich Gauss published his own treatment in 1809 in Theoria motus corporum coelestium and claimed he had used the method since 1795, starting one of the best-known priority disputes in mathematics. Historians such as Stephen Stigler think Gauss probably had it first, but Legendre has priority of publication. Robert Adrain also published it in the United States around 1808. Gauss also gave it a probabilistic justification by assuming normally distributed errors.
For a straight line the slope is b = Σ (xᵢ − x̄)(yᵢ − ȳ) / Σ (xᵢ − x̄)², and in general β̂ = (XᵀX)⁻¹Xᵀy. Interviewers ask why squared errors: they are differentiable, give a unique closed-form solution, and match maximum likelihood under Gaussian noise. The cost is sensitivity to outliers.