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?



$\theta$ 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 interpretations of the intercept and slope parameters are different, hence the different subscripts.

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.

  • $\begingroup$ no, he did not use $\Theta$ $\endgroup$ – Jodast Oct 16 at 17:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.