# ISyE 6416 Homework 1; Regression in R solution

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Original Work ?

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## Problem Description.

The attached data set (w logret 3automanu.txt) includes weekly log returns of three auto manufacturers: Toyota Motor Corp., Ford Motor Corp., and GM. Treat the log returns of GM as response
and log returns of Toyota and Ford as predictors. Fit a linear regression model in R. Perform necessary
model diagnostics. Is linear regression a useful tool for this data set? Do you need to do any model
selection?

Write a report to a banker who thinks that linear regression can be utilized, so that he can use
the log returns of Toyota and Ford to interpret the log returns of GM. Your conclusion can go either
way. Your justification should be convincing.

Report Writing. You may imagine that you are actually writing a short conference paper. See more
on the next page.

Hewitt, J. (Winter 2004). First Impressions: Writing a Good Abstract. The Communication Factor (Newsletter of the
Cain Project in Engineering and Professional Communication at Rice University), p. 2.

First Impressions: Writing a Good Abstract
Because an abstract often determines if a published paper or dissertation will be read or ignored, a writer needs to
pack persuasive information into a few words.
If an abstract answers the Seven Key
Questions in the box to the right, it is
likely to be complete and enticing.
A single sentence may answer or
signal the answer to more than one of
the seven questions. For example,
Importance, Contribution, and
Application may well be covered in
the same few words, and a clear
elucidation of the problem may well
include other aspects.

Seven Key Questions
1. Clear Focus. Does the abstract make clear what work needed to be
done, what problem needed to be solved?
2. Method(s). What method(s) were applied to address the problem? Why
these particular methods?

4. Context. How does this work fit in with other work in the field?
5. Results. What, specifically, are the results? What evidence is given to
convince us of those results?

6. Unique Contribution. What does this work report that is new?
7. Possible Applications. In what ways might this work be useful, either
theoretically or practically?

Annotated Sample Abstract
This abstract is from “Directional Hypercomplex Wavelets for Multidimensional Signal Analysis and Processing”
by Wai Lam Chan, Hyeokho Choi, and Richard G. Baraniuk, all in the ECE Department at Rice. The sentences are
numbered for easier reference in the comments below.

Abstract
1. We extend the wavelet transform
to handle multidimensional signals
that are smooth save for singularities
along lower-dimensional manifolds.
2. We first generalize the complex
wavelet transform to higher
dimensions using a multidimensional
Hilbert transform. 3. Then, using the
resulting hypercomplex wavelet
transform (HWT) as a building block,
we construct new classes of nearly
shift-invariant wavelet frames that
are oriented along lower-dimensional
subspaces. 4. The HWT can be
computed efficiently using a 1-D
dual-tree complex wavelet transform
along each signal axis. 5. We
demonstrate how the HWT can be
used for fast line detection in 3-D.

Comments on Each Sentence in the Abstract
1. Instead of writing the all-too-common passive construction, “The wavelet
transform is extended to handle…,” these authors take possession of and
responsibility for the work with the opening word, “We.” (Those
authors who cannot bring themselves to use “we” even in a multipleauthor paper could use “This paper extends” as an alternative.)

The verb
“extend” not only precisely says what the work does, but also signals
context. Clearly, this paper is based on specific prior work on “the
wavelet transform” and expands possible applications of the earlier work
to specific multidimensional signals. The problem is defined;
applications are signaled. As one student said, “There’s a lot riding on
that word extend,” and he’s right. Consider what would be lost if the
word were the more common (and imprecise) “study” or “discuss.”

2. “First” clearly signals to the reader that there will be more than one step in
the method. The rest of the sentence gives details about what was done
and links the sentence with the “multidimensional” in the title and in the
first sentence.

3. This second step in the sequence is clearly signaled and then precisely
defined. Though the details are left for the body of the paper, enough is
given here to illustrate the actual process.

4. The shift to passive voice works here because it includes the reader as a
possible user of this new any computer-driven research project, in which
saving time translates to “saving money.”

5. “Demonstrate“ clearly signals results, evidence, and applications, as well
as suggesting importance of the work. Repetition of “HWT” reinforces
what has newly been added to the field, and “for fast line detection in 3-
D” illustrates the promise of the title or a “multidimensional ” application
of the wavelet transform.

Verb choice in the five sentences illustrates a powerful writing technique. Extend, generalize, construct, computed,
and demonstrate are precise and varied. Each verb signals an exact action necessary for the persuasive progression
of the argument.

In summary, this brief abstract defines the focus of the paper, suggests its context, identifies and applies the methods
used, shows why those methods work, gives specific results that echo the promise of the title, indicates what is new,
and in the final sentence signals evidence for possible applications of this new technique. Impressive and persuasive
in only 95 words!