Why is polynomial regression considered a kind of linear regression? Why is polynomial regression considered a kind of linear regression? 
This is what I mean by polynomial regression. For example, the hypothesis function is
$$h(x; t_0, t_1, t_2) = t_0 + t_1 x + t_2 x^2 ,$$
and the sample points are 
$$ (x_1, y_1), (x_2, y_2), \ldots$$

This is a form of linear regression because it takes the form
$$h(x)=\sum_i t_if_i(x)\;,$$
which is a linear combination of functions $f_i(x)$ and is amenable to a solution using only linear algebra. The non-linearity of the functions $f_i(x)$ doesn't complicate the solution; it enters only in calculating the values $f_i(x_j)$, and everything is then linear in these values. What's important is that the function is linear in the parameters $t_i$; otherwise these need to be determined by non-linear optimization.
