Collaborative Filtering: Why not Linear Regression

I just got finished with the Collaborative Filtering Algorithm video. I am a little confused as to why linear regression cannot be used to learn parameters. What I mean is that if you are given w and b and ratings (y), isn’t optimizing for x just the same process with (basically) the same cost function to minimize?

For the movie-rating example, if you are given parameters w and b for one user, why is it that you cannot learn features for the movie with linear regression in the way I mentioned above? Is it merely because it will not generalize well to new users?

Yes collaborative filtering can be viewed as linear regression.

The difference though is that the training data is in the output, and it’s a matrix of users and ratings. You’re trying to learn both the weights and features that give the best matching model.