How to store the name of IV in a list which show non linear behavior ?.......How to understand data is linear or non linear ?

To store the name of the independent variable in a list, you can simply create a list and append the variable name to it. For example:

ind_vars = [] # create an empty list
ind_vars.append('temperature') # append the variable name to the list

To understand whether the data is linear or non-linear, you can use visualization techniques such as scatter plots or line plots to get a sense of the relationship between the independent and dependent variables. If the data points form a straight line when plotted, then the data is likely to be linear. If the data points do not form a straight line, then the data is likely to be non-linear.

In addition to visualization, you can also use statistical tests to determine whether the data is linear or non-linear. For example, you can use the Durbin-Watson test to determine whether there is autocorrelation in the data, which would indicate a non-linear relationship. You can also use polynomial regression to fit a curve to the data and compare the results to a linear model to see which model fits the data better.