# Comparison of two least-squares optimization problems

I have come across two least square minimization problems. The first one is:

$$\min_{\beta\in \mathbb{R}} \lvert y_j-x_j\beta\rvert, \quad \text{where}\ j = 1, \dots, n.$$

Here $$y$$ is the dependent random variable and $$x$$ is the independent random variable.

What does $$\beta$$ mean when $$x_{j} = 1$$?

The second minimization problem is:

$$\min_{\beta\in \mathbb{R}}\lvert y_j - x_j\beta \rvert ^2.$$

What's the difference between these two minimization problems? Which one is a better option?

• Could you please use MathJax and define your variables? The question is not answerable in this fashion. – Jan May 18 at 16:39
• I'm so sorry I will try to update. I have never used MathJax before. But I will try to figure out – Ana May 18 at 16:42
• Also, what is "it" when you write "What does it say..."? Maybe you should provide a reference. Furthermore, you have five open questions, three from today. It would be a good idea to respond to/accept the answers given there before asking again and again new questions. – Jan May 18 at 16:44
• I have updated. I am quite new and am still trying to figure out everything. Thanks for your feedback – Ana May 19 at 0:08
• how do I close a question? I tried to respond saying thanks but it didn't work? I up voted. what else do I have to do? can you please kindly let me know? In terms of MathJax, I am very new to these. It is impossible for me to figure out how to operate MathJax in a few hours. I do understand MathJax is preferable and I do understand the way I posted the very initial post was not the right way. But I am trying my best to make sure to learn as fast as possible with the limited time I have in life (trust me life is not just maths for me - being a mum of two kids, a full time job and studies – Ana May 19 at 6:35