## 3 Machine Learning Models: Results and Interpretation  
Using all the available variables, our modeling approach was always the same, regardless of the specific machine learning method. We did the following: \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|} \hline  & **Min.** & **1 st Quartile** & **Median** & **Mean** & **3 rd Quartile** & **Max.** & **Transformation** \\ \hline
**LEX In-State + LEX** & \(1.01\) & \(1.254\) & \(1.364\) & \(1.383\) & \(1.488\) & \(2.228\) & none \\ \hline
**LEX-Out-State** & \(0.011\) & \(0.266\) & \(0.383\) & \(0.402\) & \(0.513\) & \(1.289\) & none \\ \hline
**Non\_home\_dwell\_time** & \(0\) & \(19\) & \(39\) & \(57.15\) & \(75.62\) & \(284\) & log \\ \hline
**Cases** & \(1\) & \(225\) & \(2318\) & \(14,353\) & \(11,712\) & \(375,575\) & log \\ \hline
**Population Density** & \(0.002\) & \(0.006\) & \(0.015\) & \(0.022\) & \(0.026\) & \(0.121\) & log \\ \hline  & **Bottom** & **Average** & **Top** & & **Political Color Category** & \\ \hline
**Climate Temp Category** & \(870\) & \(2738\) & \(968\) & & Blue & Purple & Red \\ \hline
**Health Rank Category** & \(840\) & \(2773\) & \(963\) & & \(1827\) & \(677\) & \(2072\) \\ \hline
**Days of Week** & **Fri** & **Mon** & **Sat** & **Sun** & **Thu** & **Tue** & **Wed** \\ \hline  & \(664\) & \(631\) & \(670\) & \(676\) & \(652\) & \(637\) & \(646\) \\ \hline \end{tabular}
\end{table} 
Table 2: Descriptive Statistics. Figure 1: Distributions of Numeric and Categorical Variables. * Checked the data quality, checking for outliers, imputing for missing values, and transforming variables to be more Gaussian (Normal) to comply with statistical assumptions;
* Partitioned the dataset randomly into Train (80%) and Test (20%) subsets. Model accuracy was determined by performance on the Test subset;
* Checked for multi-collinearity and target leakage [44]. We tried a variety of machine learning methods in R 3.6.2. The algorithms evaluated in this paper are Multiple Regression [45], Ridge Regression [45], Elastic Net Regression, Generalized Additive Model [46; 47], Gradient Boosted Machine [48], Regression Tree [45], Neural Network [45], and Random Forest [48]. The methods were selected for their known strengths in minimizing Errors of Bias and/or Errors of Variance, i.e., their ability to fit data well on hold-out data, neither underfitting nor overfitting. They also represent the range of algorithms commonly used in machine learning prediction, and they were all available as R packages. We started with Multiple Regression as a traditional baseline method for fitting a model with only linear relationships. We then used more advanced methods to attempt to capture non-linear relationships and improve accuracy even at the cost of greater complexity and diminished interpretability:  
Ridge Regression: variant of linear regression to reduce multi-collinearity and overfitting by using a different estimator, the ridge estimator, which has lower variance than the Ordinary Least Squares estimator. Regularization causes all coefficients to move toward zero, possibly becoming negative. (R package MASS)  
Generalized Additive Model: a nonparametric generalization of linear regression, which allows for nonlinear relationships and coefficient regularization while maintaining interpretability. Although overfitting can occur, regularization and cross-validation help to minimize it. (R package mgcv)  
Regression Tree: a decision tree method, which is non-parametric to allow for non-linear relationships between the predictor variables and the numeric target; the tree structure aids interpretability through discovered rules; simple trees can be rendered and traversed visually, aiding auditability and intuitiveness. (R package rpart)  
Neural Network: generalization of linear regression with hidden layer(s) of nodes between input and output nodes; depending on the number of hidden layers, nodes per layer, and the activation function used to convert inputs to outputs, an arbitrarily complex model can be fit; may result in overfitting.