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Polynomial regression is often considered as a special multiple linear regression. Why? Let us understand – polynomial regression is a statistical method of determining the relationship between an independent variable (x) and a dependent variable (y) and model their relationship as the nth degree polynomial.
The relationship of the independent and dependent variable on a graph turns out as a curvilinear relationship with the help of a polynomial equation. Polynomial regression is used when there is no linear correlation between the variables. Hence, it explains why it looks more like a non-linear function.
Conducting exploratory research seems tricky but an effective guide can help.
Polynomial regression equation of nth degree can be written as:
Y= b0+a1x+a2x^2+a3x^3+…. anx^n
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 degree of the polynomial equations goes up, the curve better fits the dataset.
The problem with linear regression was, it uses the line of best fit. Meaning, when we have a dataset and we 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 but a curve? This is when polynomial regression comes in.
The difference between linear regression and a 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 is drawn (curve) following that pattern of the points. Another difference is, polynomial regression does not make it compulsory for 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.