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# SMAT - Linear Models Course

Exercise set 6

I have almost done with showing the other parts, but I am struggling with the last part of the third one to deduce the relationship between beta and beta hat.

I would be grateful if anyone can give me a piece of help to make me proceed on.

Posted by Sungyeon Hong at 0:56
Vertical projection and orthogonal projection?

The lecture note remarks that they are different, but could anyone explain about their difference exactly?

Posted by Sungyeon Hong at 17:46
In exercise set 2

Despite the kind explanations in the answer sheet, I am not sure how to calculate the part (a) of the 4th exercise.

Could you let me know some more detail?

Posted by Sungyeon Hong at 16:35
In the exercise set 5

For the parts (a) and (b) in the 4th exercise of set 5, I have to describe the first p elements and the rest (n-p) elements of each fixed value \hat{\tilde{y}} and I have done computing it, but I am afraid if I do not have any idea of how to describe them.

And for the part (c), could anyone help a bit more for me to think further on?

Posted by Sungyeon Hong at 0:06
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
Regarding a terminology

Is there any difference between a regression model and a fitted model?

Posted by Sungyeon Hong at 13:28
Regression references

Some of you have asked me for recommended references regarding general statistics and regression models. My personal recommendation would be to consult the following books:

- For general introductory statistics up to and including linear regression: G. Casella, R.L. Berger, Statistical Inference, 2nd ed., Duxbury Press, 2002.

- For an accessible introduction to linear regression models (especially LASSO and Ridge regression): Chapter 3 of The Elements of Statistial Learning available as pdf at http://www-stat.stanford.edu/~tibs/ElemStatLearn/

- For a detailed treatment of essentially all important aspects of regression models: N.R. Draper, H.S. Smith. Applied regression analysis, 3rd ed., Wiley, 1998. (Note that the 3rd edition is a significant update of the earlier editions.)

- For a concise, yet detailed treatment of linear regression: Chapter 8 of A.C. Davison, Statistical models, Cambridge University Press, 2003.

Posted by Mikael Kuusela at 16:30
Exercise 4 #2

For the second problem in Exercise set 4, is it right to use the table of "cement heat evolution" from the lecture slide?

I wonder why we have only three variables for x's: x1, x2, and x3.

To be more specific, what are x's in this case?

There might be something I misunderstand, but I hope someone would be able to help me.

Posted by Sungyeon Hong at 16:50
Regarding the problem 1(d) in Exercise Set 3

Hi, I have been solving the homework problem 1 from Exercise Set 3, but I am not sure what I am going to use to prove the last part (d).

Is everyone doing well with this?

Posted by Sungyeon Hong at 21:53