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Welcome to our exploration of polynomial regression, a powerful technique in predictive modeling that elegantly captures non-linear relationships between variables. In the pursuit of understanding data and building robust models, the need often arises to move beyond linear approximations. This is where polynomial regression steps in, allowing us to unveil our datasets’ hidden complexities and nuances.
This blog will explore polynomial regression’s principles, applications, implementation, and nuances. Whether you’re a seasoned data scientist seeking deeper insights or a curious enthusiast eager to grasp advanced regression techniques, this blog will equip you with the knowledge to use polynomial regression effectively in your analytical pursuits.
By the end, you’ll comprehend how polynomial regression works and gain the confidence to wield this technique in your own data analysis and machine learning projects.
Join us as we unravel the intricacies of polynomial regression and unlock its potential to transform how we model and interpret data. Let’s dive in!
Polynomial regression is often considered as a special multiple linear regression.
Here’s why- Polynomial regression is a statistical method of determining the relationship between an independent variable (x) and a dependent variable (y) and modeling their relationship as the nth-degree polynomial.
The relationship of the independent and dependent variables on a graph turns out to be curvilinear with the help of a polynomial equation. Polynomial regression is used when there is no linear correlation between the variables, which explains why it looks more like a non-linear function.
Related read: Regression model: Definition, Types, and Examples
Polynomial regression equation of nth degree can be written as:
Y= b0+a1x+a2x^2+a3x^3+…. anx^n
1. Linear polynomial
2. Quadratic polynomial
3. Cubic polynomial
As you can see, the linear polynomial has a degree of 1, the quadratic polynomial has a degree of 2, and the cubic polynomial has a degree of 3. As the degrees of the polynomial equations increase, the curve better fits the dataset.
The problem with linear regression is that it uses the line of best fit. When we have a dataset and plot it on a graph, there has to be a straight line where the scatterplots lie. But what if we have a dataset that gives us no straight line but a curve? This is when polynomial regression comes in.
The difference between linear regression and polynomial regression is that the line of best fit is a curve in polynomial regression. The scatterplots are scanned for a pattern, and the line (curve) is drawn following that pattern of the points. Another difference is that polynomial regression does not require the data to have a linear relationship between them.
So, when linear regression fails to determine a linear relationship between variables, polynomial regression does it for us.
Related read: How to Calculate Linear Regression
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