Questions about multiple regression and polynomial regression

Hello everyone,

I have some questions regarding “Multiple Regression” and “Polynomial Regressions.” Here are my queries:

  1. In multiple regression, what is the shape of the cost function? In a single-variable scenario, the format resembles a bowl of soup. How does it differ in multiple regression? Is the cost function drawn for each variable separately?
  2. Concerning polynomial regression, I comprehend the examples in the machine learning specialization (week2), such as the y = cos(x) instance. However, these examples typically involve a single variable. If the model incorporates multiple variables, like in the case of predicting house prices using features such as size and bedrooms, should we analyze the distribution of each feature with the target y firstly to know how the model will be?

e.g., size as polynomial, others as linear? How do we determine the overall format of the model? Could it be something like “f = w1x1 + w2x² + w3*x2 + b”?

Your insights on these matters would be greatly appreciated.

Thank you.

If by multiple regression you mean multi-output network then yes you have multiple cost functions.

In polynomail regression with many variables it just mean many dimensions involved, its good to normalize data in general for all variables involved.