ggplot

This post is primarily to give the basic overview of principal components analysis (PCA) for dimensionality reduction and regression. I wanted to create it as a guide for my regression students who may find it useful for their projects. First, let’s note the two main times that you may want to use PCA - dimensionality reduction (reducing variables in a dataset) and removing colinearity issues. These are not exclusive problems, often you want to do both.

One of the classic assumptions of the linear regression models is that, conditioned on the explanatory variables, the response variable should be normally distributed. While teaching this the other day, I had a flash of insight into how to visualize this - ridge-line plots! Data I’ve been using Matloff’s Statistical Regression and Classification book, which uses the mlb dataset from his freqparcoord package. This has data on heights, weights, ages, positions, and teams of over 1000 major league baseball players.

When I lived in Tacoma, I was running quite a bit. Since I moved away my training has become much more irregular, but I thought it would be interesting to take the Tacoma data from my current Garmin Forerunner 220 a take a look. Data Prep The Garmin stores data in .fit format, but gpsbabel can translate to a nicely structured GPX file, which is what I’ll start with here.

Recently some diversity stats have been circulated around the College of Idaho, and as new Idahoan I wondered about the general diversity (or lack thereof) in Idaho. I remembered seeing this post a while back about mapping in R, so I went to work. Shapefiles First, we need shapefiles for both the Idaho country boundaries and census tracts, which will give finer detail for data. These can be downloaded from the [US Census Bureau] (https://www.

Introduction Recently a student in another course came to my office looking for someone “who could explain the Monte Carlo simulation” to her. I was caught a bit off-guard since (a) it was 10 minutes before my geometry class and (b) there is no single Monte Carlo simulation. After a brief discussion, I found out she wanted to predict stock prices using Monte Carlo simulation, but she thought that the Monte Carlo simulation provided the prediction - she couldn’t say how the actual predictions were being made which is the crucial part.

This is the second part of two posts about using ggplot to visualize geometric transformations in the complex plane. Inversions For this post we’ll focus on inversions, having already covered rotations, translations, and reflections. An inversion can be thought of as a reflection across a circle, the the inside of the circle gets flipped to fill the plane outside the circle and the outside is flipped into the circle. This is a more complicated transformation, both to visualize and to perform mathematically, but is essential to geometry.

I’m currently teaching a Geometry course, and wished there was an easy way to illustrate geometric transformations for my students. I’m sure they’ll agree I’m not a great artist. Since R is my preferred way to draw any picture, I thought “Let’s use GGPlot to show transformations!” For those not versed in geometry, we would like to easily visualize translations (shifts along a vector), rotations, and dilations of points (or collections of points) in the complex plane.