POLYNOMIAL REGRESSION

What is Polynomial Regression?
 In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. The polynomial regression fits into a non-linear relationship between the value of X and the value of Y. The Polynomial regression is also called as multiple linear regression models. The Polynomial regression model has been an important source for the development of regression analysis .
For designing a polynomial regression model, we are taking real data of India’s Coronavirus cases per day.

We shall use polynomial regression on this dataset. For that we have a generalised matrix representation of polynomial regression for any degree polynomial.

This is the matrix representation of polynomial regression for any degree polynomial. For our dataset, we are taking 2nd degree polynomial regression or Quadratic regression.

Using this we will find the quadratic equation for this data to fit. Here ,

 n=no. of samples

 X = independent variables 

Y= dependent variables 

c0=c1=c2= Coefficients,

Calculation:

So we got, C0=34.491228070175

 C1=-7.60034176349965 

C2=0.9896331738437

Conclusion: From the above design it is clear that the polynomial regression is correctly prepared. By observing both 2nd degree regression we can conclude that a curve fits the data best as the degree of polynomial increases