# In a linear regression hypothesis equation, what does each symbol represent?

So I've been watching Andrew Ng's machine learning lectures, and I'm on a video about univariate linear regression. He was talking about how a Hypothesis takes an input and predicts an output, like a typical function we learn in math class such as $$f(x) = mx + b$$, where f is a function with input x that outputs a line with a slope of m and a y-intercept of b. However, Ng said that the general hypothesis equation in linear regression is $$h_\theta(x) = \theta_o + \theta_1 x$$. I get that this is a function h of input x, and it looks like $$\theta_1 x$$ is equivalent to $$mx$$ while $$\theta_o$$ is equivalent to $$b$$, but why use all the thetas instead of the other variables? Is $$\theta_1$$ a slope like $$m$$? Why use theta multiple times? What is the meaning of the subscripts?

Thanks!

$$\theta$$ is a common variable in statistics. We usually see $$\theta$$ as an angle in trig and physics long before we see its use in statistics, but $$\theta$$ is just the variable of choice in statistics for an unknown parameter.
$$\theta_0 = b$$
$$\theta_1 = m$$
The reason there is a $$\theta$$ subscript on $$h_{\theta}$$ is because $$\theta$$ without a subscript is a set of all $$(\theta_0,\theta_1) \in \mathbb{R}^2$$. (Did he, by any chance, use a capital theta, $$\Theta$$?) What this means is that the equation is a valid regression equation for any values of $$\theta_0$$ and $$\theta_1$$. This is for technical reasons when it comes to hypothesis testing.
• no, he did not use $\Theta$ – Jodast Oct 16 at 17:32