Polynomial regression is a valuable extension of linear regression, particularly when dealing with datasets that exhibit non-linear relationships between variables. While linear regression assumes a straight-line connection between the predictor and response variables, polynomial regression uses polynomial equations to capture the curvature and non-linearity present in the data. This flexibility allows us to model complex phenomena more accurately. By selecting an appropriate polynomial degree, we can strike a balance between underfitting (oversimplification) and overfitting (overcomplication) of the data. In essence, polynomial regression empowers us to better understand and predict outcomes in situations where linear models fall short.
The choice between a linear or polynomial model depends on the nature of the data and the underlying relationships. If the data exhibits a linear pattern, a simple linear regression model may suffice, as it’s more interpretable and computationally efficient. However, when there are clear indications of non-linear patterns or curvature in the data, opting for polynomial regression can yield superior results. The challenge lies in selecting the right polynomial degree, as excessively high degrees can lead to overfitting. Therefore, it’s crucial to analyze the data, experiment with different degrees, and employ techniques like cross-validation to determine whether a linear or polynomial model is the better fit for a given dataset.
For the given diabetes dataset the r square produced by polynomial regression model than a multiple linear regression model is not much better .