Machine Learning Linear Regression Cost Function Notation

Question

When I see $J(\theta _{0}, \theta _{1}) = ...$ as the result of a single variable cost function in linear regression I think that it is a column vector instead of a scalar. How am I supposed to know it's a scalar?

Answer 1

Why do you think it is a column vector? $J$ is a function that depends on the parameters $\theta_0$ and $\theta_1$. The notation $f(x,y)$ means that $f$ is a function that takes two inputs $x$ and $y$. In your case, with $\theta_0$ and $\theta_1$ you compute the value of $J$.