Polynomial Regression

Describing Polynomial Regression

• Polynomial regression is a regression method where the relationship between the independent variable $X$ and the dependent variable $Y$ is modelled as an $n^{th}$ degree polynomial in $X$
• Polynomial regression is used when there is a non-linear relationship between the response variable and a predictor variable
• As we use lower degrees of polynomials, we don’t observe high oscillations of the curve around the data
• In other words, a quadratic function will have one hump, a cubic function will have two humps, etc.
• Polynomial regression models are usually fit using the method of least squares

Mathematics behind Polynomial Regression

• Polynomial regression fits a nonlinear relationship between the value of $X$ and the corresponding conditional mean of $Y$, denoted $E[Y|X]$
• Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function $E[Y|X]$ is linear in the unknown parameters that are estimated from the data
• For this reason, polynomial regression is considered to be a special case of multiple linear regression

References

• Polynomial Regression Wiki
• Polynomial Regression Examples