Thread by @Sachintukumar

Day 60 of #100DayswithMachineLearning

Topic - Polynomial Regression in ML

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Polynomial regression is type of regression analysis where relationship between independent variable(s) and dependent variable is modeled as an nth-degree polynomial function.

It is an extension of simple linear regression which assumes linear relationship between the variable

In polynomial regression, the polynomial function takes the form:

y = β₀ + β₁x + β₂x² + ... + βₙxⁿ

where:

y represents the dependent variable,

x represents the independent variable,

β₀, β₁, β₂, ..., βₙ are the coefficients that determine the shape and behavior of the polynomial curve,

n represents the degree of the polynomial.

To perform polynomial regression, you would typically follow these steps:

1) Collect your data: Gather a set of data points with both the independent variable and the dependent variable values.

2) Choose the degree of the polynomial: Decide the degree of the polynomial function that best fits your data. A higher degree allows the polynomial to capture more complex relationships, but it can also lead to overfitting

3) Formulate the regression equation: Based on the chosen degree, construct the polynomial regression equation by assigning appropriate coefficients to each term

4) Estimate the coefficients: Use a regression algorithm (e.g., ordinary least squares) to estimate the values of the coefficients that minimize the sum of squared differences between the predicted values and the actual values.

5) Evaluate the model: Assess the goodness of fit of the polynomial regression model by examining statistical measures such as R-squared, adjusted R-squared, and root mean squared error (RMSE). These metrics provide insights into how well the model fits the data.

6) Make predictions: Once you have a satisfactory model, you can use it to make predictions by plugging in new values of the independent variable into the regression equation @AnalyticsVidhya

analyticsvidhya.com/blog/2021/07/a…

It's worth noting that polynomial regression can be sensitive to degree chosen and may be prone to overfitting if a high degree is selected without proper justification. Therefore, it's important to balance the complexity of the model with its generalizability to unseen data

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