2  Review


Settling In

  • Sit at a different table today! Introduce yourselves and check in with each other.
  • Catch up on any recent Slack messages you might have missed.
  • Review the solutions and #board-work from the least squares derivations we started last class.




Syllabus Highlights

ImportantReminder

The syllabus can be found here: Course Logistics > Syllabus.



Meet Your Preceptor

Say hi to our preceptor, Nick! 👋

Find a link to his office hours schedule and other info in the syllabus.



Problem Sets

Goals:

  • practice and deepen your understanding of concepts introduced in class
  • get feedback to further guide your learning

Submission Details:

  • Due on Fridays (usually), about every 2 weeks
  • Submit in person at the start of class
  • Typed (using Quarto or LaTeX), with the exception of PS0

Policies:

  • Syllabus - Course Policies - Academic Integrity
    • Working with others is strongly encouraged!
    • Just make sure you write up your final answers on your own and credit any sources (including people!) in the “Resource Reflection” at the end of the assignment.
  • Syllabus - Course Policies - AI
    • Be mindful of your use of AI and try to first use resources specific to our course (including your instructor, preceptor, and classmates!) whenever possible.
    • If you do use AI, make sure you cite it appropriately (in the aforementioned Resource Reflection) and write up your answers in your own words.
    • When in doubt, ask me!
  • Syllabus - Course Policies - Extensions
    • If you can’t meet a deadline, request an extension.
    • Each person in this class will automatically be granted three 3-day extensions (no reason necessary!).

Grading:

  • You’ll get feedback on most, if not all, questions.
    • If we don’t have time to grade all questions, I’ll post solutions!
  • I’ll translate that qualitative feedback into an overall score of pass, attempt, or unable to assess.
    • pass = follow all submission instructions and course policies, effortful attempt on all questions, answers are correct or mostly correct on many (but not necessarily all!) of the questions
    • attempt = submitted, but did not meet all criteria above
    • unable to assess = no submission

Tips:

  • Make time (start early!)
  • Form study groups
  • Come to office hours!


ImportantReminder

Your first problem set, PS0, is due at the start of our next class!



Quizzes, Course Grading System, Etc.

Coming up next time 😃




Calculus Review

We’re going to need some tools from calculus in this class!

Here’s the derivation we started last class:

\[\begin{align*} \frac{\partial}{\partial\beta_0} \sum_{i=1}^n (y_i - [\beta_0 + \beta_1 x_i])^2 &= \sum_{i=1}^n 2(y_i - [\beta_0 + \beta_1 x_i])(-1) \\ & = \sum_{i=1}^n -2y_i + \sum_{i=1}^n 2\beta_0 + \sum_{i=1}^n 2\beta_1 x_i \\ &= -2 n \bar{y} + 2n \beta_0 + 2 \beta_1 n \bar{x} \\ &= 2n(\beta_0 + \beta_1 \bar{x} - \bar{y}) \end{align*}\]

To do this derivation, we need to remember various things about how derivatives work (eg chain rule)!

At other points in the semester, we’ll also compute integrals.



Activity

I’ll pass out paper copies of our calculus review activity now.

  1. Part 1 (on your own): 10 minutes
  2. Part 2 (with your table): 5 minutes
Solutions


Useful Techniques

  • Algebra:
    • \(\log(xy) = \log(x) + \log(y)\)
    • \(\log(x^a) = a \log(x)\)
  • Derivatives:
    • \(\frac{d}{dx} [f(x) + g(x)] = \frac{d}{dx} f(x) + \frac{d}{dx}g(x) = f' + g'\)
    • \(\frac{d}{dx} [f(x) * g(x)] = f' g + f g'\) (product rule)
    • \(\frac{d}{dx} f[g(x)] = f'[g(x)] * g'(x)\) (chain rule)
  • Integrals:
    • finding an antiderivative
    • \(\int [f(x) + g(x)] dx = \int f(x) dx + \int g(x) dx\)
    • \(\int f(x) dx = 1\) if \(f(x)\) is a pdf and we’re integrating it over its support
    • integration by parts

We can keep track of these and others here: Crowd-Sourced Useful Techniques.




Probability Review

Work on PS0 with your table.

Note

This problem set is not designed to be a comprehensive probability review. The focus is on topics that we’ll use during our first unit on estimation.

For a more comprehensive review, check out Chapter 1 in the MATH/STAT 355 Notes. We’ll need other parts of this review later in the semester, and will return to this resource then.




Wrapping Up

After class today, please: