Polynomial regression expands the linear regression model by adding polynomial terms to the equation. For example, a second-degree polynomial regression model is represented as:
Here, \( y \) is the dependent variable, \( x \) is the independent variable, \( \beta_0, \beta_1, \) and \( \beta_2 \) are coefficients, and \( \epsilon \) is the error term. By including higher-order terms, the model can more accurately fit the non-linear trends common in nanotechnology data.
