Creating Regression Models to Predict Data Responses

Before we look at any code, we should understand a little about the math behind a regression model. As mentioned, regression models can have multiple input variables, or features, but for this article, we will use a single feature for simplicity. Regression analysis involves making a guess at what type of function would fit your dataset the best, whether that be a line, an nth degree polynomial, a logarithmic function, etc. Regression models assume the dataset follows this form: Here, x and y are our feature and response at observation i, and e is an error term. The goal of the regression model is to estimate the function, f, so that it most closely fits the dataset (neglecting the error term). The function, f, is the guess we make about what type of function would best fit our dataset.