lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

correcting typos

Browse Source
This commit is contained in:
Morten Hjorth-Jensen
2023-09-04 08:13:39 +02:00
parent 2a445d0f02
commit 25cf50425a
9 changed files with 73 additions and 85 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/Projects/2023/Project1/html/Project1.html
+3 -5
View File
@@ -417,11 +417,9 @@ Give a
critical discussion of the three methods and a judgement of which
model fits the data best.
</p>
<p>v</p>
<h3 id="part-d-paper-and-pencil-part">Part d): Paper and pencil part </h3>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_blank">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>).</p>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_blank">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>). The exercise is also part of the weekly exercises for week 37.</p>
<p>The assumption we have made is
that there exists a continuous function \( f(\boldsymbol{x}) \) and a normal distributed error \( \boldsymbol{\varepsilon}\sim N(0, \sigma^2) \)
@@ -466,7 +464,7 @@ $$
\mbox{Var}(\boldsymbol{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
$$
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \). .
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \).
A given parameter \( \beta_j \) is given by the diagonal matrix element of the above matrix.
</p>
<h3 id="part-e-bias-variance-trade-off-and-resampling-techniques">Part e): Bias-variance trade-off and resampling techniques </h3>
@@ -540,7 +538,7 @@ $$
\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
$$
<p>The answer to this exercise should be included in the theory part of the report.
<p>The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.
Explain what the terms mean and discuss their interpretations.
</p>