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One area of machine learning that I don’t have a lot of practice in is polynomial regression.
Polynomial regression is a form of linear regression in machine learning where the relationship between the independent variable (feature) and the dependent variable (target) is modelled as an nth-degree polynomial. In other words, instead of fitting a straight line to the data, polynomial regression fits a polynomial curve to capture more complex and non-linear relationships between the variables.
The general form of a polynomial regression equation of degree n is:
y = β₀ + β₁x + β₂x² + β₃x³ + … + βₙxⁿ + ε
where:
y is the dependent variable (target) we want to predict.
x is the independent variable (feature).
β₀, β₁, β₂, …, βₙ are the coefficients of the polynomial terms. They represent the weights of each degree of the feature in the regression model.
ε is the error term, representing the difference between the predicted values and the actual values.
Polynomial regression can capture more complex relationships between variables compared to simple linear regression, making it a useful tool for dealing with data that does not follow a straight line. It can also be used to fit data with curvature or data points that exhibit non-linear trends.
To perform polynomial regression, the data points are transformed by adding polynomial features to the original input features. For example, if the original feature is x, polynomial regression may include additional features such as x², x³, and so on up to the desired degree. Then, a linear regression model is used to estimate the coefficients of the polynomial terms.
It’s important to note that while polynomial regression can provide a better fit to the data, using a high degree polynomial can lead to overfitting, especially when the dataset is small. Therefore, it’s crucial to choose an appropriate degree for the polynomial that balances the model’s complexity and its ability to generalise to new data.
To summarise, polynomial regression is a technique used in machine learning to…