Classification And REgression Training
Used to streamline making predictive models
Functions for training and plotting classification and
regression models.

University of Michigan - Ann Arbor

Approach that includes testing all possible combinations of predictor variables and then selecting the best model.
Required packages for R:
1. tidyverse for easy data manipulation and visualization
2. caret for easy machine learning workflow
3. leaps, for computing best subsets regression

Best Subset Selection

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Can also utilize the "install packages" feature in r 
library(tidyverse)
library(caret)
library(leaps)

How do I download packages in R?

Collection of R packages designed for data science - all packages have a shared design of tidy data
Several tools included - the connection s between them serve to make statisticians and data scientists more productive 

What is tidyverse?

What is caret?

Performs an exhaustive search for the best subsets of the variables in x
Used for regression subset selection

What is leaps?

1. Let $$M_0$$ denote the null model, which contains no predictors. This model simply predicts the sample mean for each observation.
2. For k = 1,, 2, ..., p:
(a) Fit all $$\binom{p}{k}$$ models that contains exactly k predictors.
(b) Pick the best among these $$\binom{p}{k}$$ models, and call it $$M_k$$. Here best is defined as having the smallest RSS, or equivalently largest $$R^2$$.
3. Select a single best model from among $$M_0, ..., M_p$$ using cross-validated prediction error, $$C_p$$ (AIC), BIC, or adjusted $$R^2$$.

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