Polynomial regression might seem different from linear regression at first glance, but it’s still considered a linear model. Why? It all comes down to how the model parameters are used.

Linear in Parameters: In polynomial regression, the model remains linear in terms of its coefficients. Even if we include terms like squared or cubic versions of the input variable, the relationship with the parameters stays linear.

Transformed Features: Instead of treating the data as simple inputs, polynomial regression transforms the original input features (e.g., turning an input into its squared or cubic form). However, the relationship between the coefficients and the target variable remains linear.

Optimization Stays Linear: The method for estimating the coefficients, such as Ordinary Least Squares, remains the same because the relationship with the parameters does not become non-linear.

Non-Linear Model? If a regression model involves coefficients in non-linear ways, such as multiplying them together or applying complex functions to them, it’s no longer considered linear regression.