Why don't the dimensions in this linear regression equation match up? I'm going through an article on linear regression, and they give the following formula for computing estimates:



The convention is that all vectors are column vectors. So if n is the number of samples and m is the number of parameters, hw(x) has dimensions n x 1, wT has dimensions 1 x m, and x has dimensions n x m. The problem is that these dimensions don't work out for matrix multiplication.

Where have I gone wrong here?
My guess is that $x$ here refers to a single datapoint with shape $m$x$1$. So $h_w(x)$ and $w^Tx$ both have shape $1$. In the case of multiple datapoints given as a matrix $X$ of shape $n$x$m$, the equation becomes:

$h_w(X) = Xw$