What type of regression is used when the response variable is modeled as an nth degree polynomial of the input feature?

The type of regression used when the response variable is modeled as an nth degree polynomial of the input feature is called Polynomial Regression.

Here are the steps to perform Polynomial Regression:

1. Data Collection: Collect the data that you want to create a regression model for. This data should include your input feature and the response variable.

2. Choose Degree of Polynomial: Decide on the degree of the polynomial regression. The degree of the polynomial is the highest power of the input feature in the polynomial equation. The degree is represented as 'n' in your question.

3. Create Polynomial Features: Transform the input feature into polynomial features. For example, if your input feature is 'x' and you chose a 2nd degree polynomial, you would create the features x and x^2.

4. Fit Model: Use a regression algorithm (like Linear Regression) to fit your model to the data. This will find the coefficients (or parameters) of the polynomial that result in the best fit to your data.

5. Evaluate Model: Evaluate the performance of your model. This could be done through methods like cross-validation or by splitting your data into a training set and a test set, and evaluating the performance on the test set.

6. Use Model: Once you are satisfied with your model's performance, you can use it to make predictions on new data.