Polynomial regression is a type of regression analysis used to model the relationship between a dependent variable and one or more independent variables. Unlike simple linear regression, which fits a straight line, polynomial regression fits a curve by using polynomial equations. This allows for capturing more complex relationships in the data. In polynomial regression, the independent variable is raised to a power, creating a polynomial equation of the form y = a + b_1x + b_2x^2 + ... + b_nx^n. The coefficients a and b are determined through a process called least squares estimation, which minimizes the difference between the observed and predicted values.