Polynomiregressiomalli

polynomial regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables as an nth degree polynomial. Unlike linear regression which fits a straight line, polynomial regression can capture more complex, curved relationships in data. The model can be expressed as y = β₀ + β₁x + β₂x² + ... + βₙxⁿ + ε, where β represents coefficients and ε is the error term. This approach is particularly useful when data shows a nonlinear pattern that cannot be adequately captured by a simple linear model. Polynomial regression is widely applied in various fields including economics, engineering, and social sciences for trend analysis, forecasting, and modeling phenomena with natural curvature. However, it's important to avoid overfitting by selecting an appropriate polynomial degree, as higher-degree polynomials may fit the training data well but perform poorly on new data. Cross-validation techniques are often employed to determine the optimal polynomial degree for a given dataset.