Hello, Need some clarity in the concepts
1.At first, When we see data we’ll look for the trend or pattern of the data.
2. Is there any specific (math or intuition) to find correct polynomial function so that function fits the data (or) just trial and error with higher order degree function
Welcome to the community.
Having an awareness of the shape of the basic polynomial functions (order 2,3) does help in case its a straightforward fit, but beyond that it is better to embark on a trial an erorr process. Prof. Andrew will introduce the concept of Bias and Variance, which further bounds us on either side while we are trying to find the right order of the polynomial regression function.
Later on in the specialization, you will get to see and greatly appreciate the fact that Neural Networks can do this work for us without any prodding - 1. It Saves us a lot of time and 2. The functions that it identifies would almost certainly be a better fit to the data, than if we had manually done it.