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Question:

How does this notation using theta mean a line(ar function)?

Explanation:

I'm taking Andrew Ng's Machine Learning course on Coursera. He often uses math notation without explaining it. He says...

We're going to represent h as follows. And we will write this as h (subscript theta) (x) equals theta (subscript one) plus theta (subscript one) of x. (see first green line of right of image below)

enter image description here

"h" above means hypothesis in machine learning but would commonly be called a function in math.

What I am really confused by and hoping for help understanding is ...

what does "theta (subscript one) plus theta (subscript one) of x" mean?

how does it represent a line or linear function?

I don't yet understand the correlation.

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A more popular form of a straight line would be $$y=mx+c$$

Here $\theta_0$ corresponds to $c$ which is the intercept.

and $\theta_1$ corresponds to $m$ which is the gradient.

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  • $\begingroup$ Wow! It took me a while to understand your answer but it's really elegant. Thank you. So c is the intercept because when x = 0, y = c. and m is the gradient because m determines the slope. Cool. $\endgroup$ – Axle Max Sep 2 '18 at 7:20
  • $\begingroup$ 2 more questions: 1. Is theta used here for a reason? Or is it a convention of some kind? 2. Is the use of Theta here a reference to the polar coordinate system or is it just coincidence? $\endgroup$ – Axle Max Sep 2 '18 at 7:22
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    $\begingroup$ it is just a symbol, it is not relevant to polar coordinate. another common notation is $\beta$ for this setting. They are parameters that we have to estimate in this setting. $\endgroup$ – Siong Thye Goh Sep 2 '18 at 11:42

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