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# SMAT - Linear Models Course

Question about 4th lecture
I have a problem with the 4th lecture, concerning the slide with the graph showing an important covariate left out. I didnt get if on this graph there is or not a linear relationship between x3 and the residuals ? So when should we have included a variable that we did not ? And about the residuals, are they computed with the model or with all the explanatories ? Thank you very much !
Posted by Morgane Ferrara at 16:49
Some questions

Hi,

I have some problems understanding these parts of the course/exercises

1) In series 12, why is the density of y_j, g(y_j-x_j^T beta), where g() is the denstiy of epsilon_j, my guess would be that y_j-x_j^T beta = epsilon_j but then why do they have different density functions ? Or are they actually the same "modulo a shift" ?

2)On the slides about Robust/Resistent Regression: M-estimation as Weighted Regression : when taking the derivative with respect to gamma, why is there still x_i^T  in the sum with psi, since according to the chain rule we take the transpose of x_i^T ?

Posted by Jean-Claude Ton at 0:13

Hello,

In week6, slide 3 page3, when computing delta for the 3 different cases, I don't understand the calculation that results to the bias in the wrong model and to 0 (no bias) for the correct and true model.. What am I missing?

Jérémy

Posted by Jeremy Gotteland at 18:00
Ridge regression
Hi, I don't really understand how you compute the parameter gamma in the Ridge regression (set 7/8/9). I know that it's equivalent to solve the minimization problem, but how can you solve this problem? Thanks, Jad
Posted by Jad Abou-Moussa at 14:21
Anova

Hi,

I'm just wondering if for each step of the anova method we must have independant column to be able to compute the matrix H?

Thanks!

Posted by Jad Abou-Moussa at 21:22
MGF in the first lecture slide

In the lecture slide of Week 1, there are seven properties of Gaussian vectors and the first one is about the MGF. It is written that M_Y(u) =exp{ μ^T u + 1/2 u^T Ω u}, but isn't it u^T μ for the first term of the exponent? Or it doesn't matter because they have the same value, I mean, μ^T u = u^T μ?

Posted by Sungyeon Hong at 23:37
Indépendance de ||e||^2 et ||e_1-e||^2

Hello,

J'aurais une petite question. Cela concerne http://smat.epfl.ch/courses/Regression/Slides/week5_ht.pdf , sur la 7ème slide (démonstration de la deuxième propriété). Je ne comprends pas, pourquoi est-ce qu'on doit montrer (pour montrer l'indépendance) que :

(H_1-H)H(\sigma^2 I)(I-H)^T=0

(en fait, c'est surtout le sigma^2I que je ne comprend pas.

Merchi beaucoup et bonne journée,

J.

Posted by Julien Duvanel at 11:12
VIF et coefficient de détermination

Pour ceux qui se demandent comment on montre

$VIF_j = 1/(1- R_j^2)$

j'ai trouvé la réponse (cf. pdf) dans le livre "Methods and Applications of Linear Models" de R. R. Hocking

Posted by Shahin Tavakoli at 15:35
Isosurfaces elliptiques?

Bonjour à tous,

Est-ce que quelqu'un (Shahin, par exemple) sait pourquoi on définit les isosurfaces au début du cours, quelle est leur utilité et quelle est la signification (conceptuelle) d'isosurface elliptiques ?

Merci

Posted by Christophe-Aschkan Mery at 19:26