Linear Regression

This lesson focuses on creating linear regression models using tidymodels. Linear regression is often considered a foundational tool for modeling relationships and is commonly used in various fields of data science. Linear regression is also an excellent way to get familiar with the tidymodels interface because we can focus on the basics rather than some of the more complex issues that come up with more advanced models.

There are several pros and cons to linear regression models that are important to consider when choosing this approach. The primary benefits of linear regression models center around their interpretability—they’re relatively straightforward and transparent, so they can tell a clear story about the relationships between inputs and outputs. However, that also means they’re less flexible and struggle to capture more complex patterns in the data, such as complex interactions between input variables that impact the outcome.

Advantages

• Simplicity: Linear regression models are relatively simple and easier to interpret than more complex models. The relationship between the predictor variables and the response variable is expressed in a linear equation, making it intuitive to understand and explain.

• Interpretable coefficients: The coefficients in linear regression models provide valuable insights into the magnitude and direction of the relationship between the predictors and the response variable. They can help identify the most influential predictors and quantify their impact on the outcome.

• Model transparency: Linear regression models are transparent regarding model assumptions and the underlying mathematics. Assumptions—such as linearity, independence of errors, and homoscedasticity—can be checked and validated, allowing a better understanding of the model’s behavior.

• Computational efficiency: Linear regression models are computationally efficient, particularly when dealing with large datasets. They can be trained and applied relatively quickly, making them suitable for scenarios where time is a constraint.

Disadvantages

• Limited flexibility: Linear regression models assume a linear relationship between the predictors and the response variable. This assumption might not always hold, especially when dealing with complex or nonlinear relationships.

• Sensitivity to outliers: A significant and often under-recognized issue is that linear regression models are sensitive to outliers, which can significantly impact the model’s coefficients and predictions. Outliers can distort the linear relationship and lead to less accurate results. Preprocessing techniques or robust regression methods may be needed to handle outliers effectively.

• Limited capturing of complex patterns: Linear regression models may struggle to capture complex patterns or interactions between predictors. They assume a linear additive relationship between the predictors and the response, which may not adequately represent the underlying complexities in the data.

• Violation of assumptions: Linear regression models rely on certain assumptions, such as linearity, independence of errors, and normality of residuals. Breaches of these assumptions can affect the model’s performance and lead to biased or unreliable estimates.