Answer and give examples to the below questions $1.$ Provide two examples of problems that cannot be solved using linear regression techniques. Explain how non$-$linear methods can be helpful in finding a solution. Provide specific details of the problem setting and model forms.

$2.$ What is the purpose of using interaction terms in a regression analysis? Provide a concrete example from practice.

$3.$ What is the nature of a curvilinear model? Provide an example from practice where such a model can be used.