Building upon the foundations of statistical inference and data description, this chapter introduces methods for modeling relationships between variables using regression analysis. We begin with the most fundamental technique: simple linear regression.

You will learn how to define the simple linear regression model mathematically, often represented as $y = \beta_0 + \beta_1 x + \epsilon$. We will cover the method of least squares for estimating the model parameters ($\beta_0$ and $\beta_1$) to find the best fit line through the data. Key aspects include interpreting the meaning of these estimated coefficients in practical terms and evaluating the model's performance using common metrics like R-squared ($R^2$) and Mean Squared Error (MSE).

Furthermore, we will discuss the essential assumptions underlying linear regression that are necessary for valid inference. The chapter provides an overview of extending these concepts to multiple linear regression, where more than one predictor variable is used. Finally, practical examples will demonstrate how to implement, fit, and assess regression models using Python libraries such as Statsmodels and Scikit-learn.