From c2c2f5d64bcdd0342fe14ab0fc663c9be830cb98 Mon Sep 17 00:00:00 2001 From: Pierre-Edouard Portier Date: Mon, 14 Mar 2022 13:29:43 +0100 Subject: [PATCH] =?UTF-8?q?correction=20erreur=20sur=20un=20slide=20(d?= =?UTF-8?q?=C3=A9riv=C3=A9e=20en=20fn=20de=20beta)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 02_moindres_carres_slides.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/02_moindres_carres_slides.Rmd b/02_moindres_carres_slides.Rmd index d56599d..750857f 100644 --- a/02_moindres_carres_slides.Rmd +++ b/02_moindres_carres_slides.Rmd @@ -36,7 +36,7 @@ $$ # Moindres carrés -- Annuler la dérivée selon $\mathbf{X}$ de la fonction convexe $\|\mathbf{X}\boldsymbol\beta-\mathbf{y}\|^2_2$ +- Annuler la dérivée selon $\boldsymbol\beta$ de la fonction convexe $\|\mathbf{X}\boldsymbol\beta-\mathbf{y}\|^2_2$ - $\|\mathbf{X}\boldsymbol\beta-\mathbf{y}\|^2_2 = \boldsymbol\beta^T\mathbf{X}^T\mathbf{X}\boldsymbol\beta - 2\boldsymbol\beta^T\mathbf{X}^T\mathbf{y} + \mathbf{y}^T\mathbf{y}$ - $\mathbf{0} = 2\mathbf{X}^T\mathbf{X}\boldsymbol\beta - 2\mathbf{X}^T\mathbf{y} \quad \equiv \quad \mathbf{X}^T\mathbf{X} \boldsymbol\beta = \mathbf{X}^T\mathbf{y}$ - $\hat{\boldsymbol\beta} = \left(\mathbf{X}^T\mathbf{X}\right)^{-1}\mathbf{X}^T\mathbf{y}$