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\Large
36-617: Applied Linear Models\\
Fall 2022\\
HW03 -- Due Mon Sept 19, 11:59pm
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\item Please turn the homework in online in our course webspace at canvas.cmu.edu.
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\item There is a link to Gradescope in the description of this assignment on Canvas. 
\item You should submit a single pdf to Gradescope. If you need help with this, please see \\ https://www.cmu.edu/teaching/gradescope/index.html.  Also, allow yourself some extra time to create the pdf \& upload it in Gradescope.
\item Don't forget to identify which pages each (part of each) problem appears on in your solitions.  Gradescope allows the TA to grade all the problem 1's together, then all the problem 2's, and so forth.  This leads to more consistent grading and better comments for you.
\item Remember to list who you worked with, on this and every assignment.
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\item Reading:
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\item For this week: Sheather Ch 6 (supplemental: ISLR 3.3.3; G\&H Ch 4)

\item For next week: Sheather Ch 7 (supplemental: ISLR Ch 6; G\&H Ch 4)

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\item There are 4 exercises below.  Remember that data sets will be in the ``0-books'' folder in the files area of our Canvas site (in the ``data-sheather'' subfolder).

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\section*{Exercises}

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\item Sheather, Ch 3 (yes!), pp. 109 ff., \#5. % cars04.csv

\item Sheather, Ch 5, p. 147, \#2. % HoustonChronicle.csv

\item Sheather, Ch 6, pp. 224 ff., \#5.   % pgatour2006.csv
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\item For part (b), feel free to transform variables as needed so that (i) the assumptions of the linear regression model are better satisfied; and (ii) the model is still ``explainable'' to non-statisticians.

\item For part (e): We will discuss variable selection formally next week.  For now, remember that the $t$ statistic for each column $X_j$ of the $X$ matrix tests whether the coefficient $\beta_j$ is significantly different from zero, {\em after including all other columns of $X$ in the model.}

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\item In the folder for this hw assignment you will find a pdf called ``COVID breakthrough rates in England''.  This is a recent article from the medical journal {\em The Lancet}. Note that the article is exactly in IMRAD format, with sections labelled ``Introduction'', ``Methods'', ``Results'' and ``Discussion''. 

The Abstract for this paper has a special form, called a ``structured abstract'', in which there is a short, labelled, paragraph corresponding to each section of the paper.  We will not be writing structured abstracts in our class, but it is good to see the additional information that a structured abstract can contain.  In our class, we will be writing shorter abstracts, consisting of approximately one sentence per section of the paper (so, 4--5 sentences for a paper with 4 sections).  Each sentence highlights the main point of each section, possibly with one extra sentence giving the main resul of the paper.

\comment{  If we were going to convert it to IDMRAD format, we could simply move the portion of the ``Methods'' section before the ``Statistical analysis'' subhead on p. 4 into a new ``Data'' section between ``Introduction'' and ``Methods''.  (You do not have to do this, but it is worth thinking about).
}

\comment{
For our IDMRAD papers we generally will want shorter abstracts, with up to five  sentences, one sentence for each section of the paper.  Here I want you to write two  different abstracts for the paper:
}

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\item Write a one-paragraph abstract with exactly four sentences, one for each section of the paper: Introduction, Methods, Results and Discussion.  Each sentence should highlight the main point of each section, and together the four sentences should tell the story of the paper.  The last sentence should include the main result of the paper (or, if you need a fifth sentence to give the main result, that is fine too).

\comment{

\item Now, imagine that this is an IDMRAD paper, with the data section containing the material before the ``Statistical analysis'' subhead on p. 4 (as described above).  Write a one-paragraph abstract with exactly five sentences, one for each section of the paper: Introduction, Data, Methods, Results and Discussion.  Each sentence should highlight the main point of each section, and together the five sentences should tell the story of the paper.  The last sentence should include the main result of the paper.

}

\item Does the paper appropriately address each of the parts of an IMRAD paper as described the ``IMRAD: What goes into each section'' pdf? (in the hw01 folder in the files area of our Canvas site.)\\[-1em]  

For each section below, either say ``yes this section has the right content'', or say ``no'' and describe what is missing and/or what needs to be moved to another section of the paper or deleted.\\
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% \item Abstract
\item Introduction
\item Methods
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\item Results
\item Discussion
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}


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