The Hitchhiker's Guide to Linear Models + A Primer in Optimization

This book aims to get straight to the point, and the only thing I assume here is that you have used spreadsheets at some point and that you are motivated to estimate linear models in R. Here I do not assume that you know how to install R or the basics of the R programming language.

This books contains no proofs. I tried to replace those with multiple examples consisting in analyzing my own experiments, such as throwing a tennis ball and measuring the time it takes to hit the ground from different heights, and another where I got two thermometers and measured the temperature outside a building at the same time of the day on different days.

ISBN: 978-1-7380675-0-3

This tiny book presents the theory behind Karush-Kuhn-Tucker (KKT) conditions and how to solve minimization and maximization problems for differentiable functions defined on Rⁿ subject to a finite number of equality and inequality constraints. I tried to explain KKT conditions and duality beyond just solving the Lagrangian. I worked on direct explanations about the Hyperplane Separation Theorem, Farkas' Lemma, and the Envelope Theorem to connect mathematical notions to well-known micro results such as Roy's Identity and Shepard's Lemma for a straightforward interpretation of KKT multipliers as "shadow prices" and how changes in budgets and prices affect optimal decisions.

The goals are:

• Cover what I consider are some gaps between Varian (1992) and/or Jehle (2011) compared to Mas-Colell (1995).
• Provide a concise reference for students by presenting the results using consistent notation and terminology.
• Provide a basis for more advanced topics in optimization, such as convex analysis and variational calculus.