Double subscript and superscript

Question

I have tried several approach and search for similar cases but I couldn't make this working.

As you can see the highlighted yellow looks improper and wrong. I would like to fix the following issues

1. make the subscript and superscript smaller

2. remove the space between sigma and its subscript

3. when I add sigma with subscript beta in the denominator they look like multiplication

I used the following code

$\beta_1,\frac{\sigma^2_{\epsilon}}{S_{xx}}$ and $\sigma^2_{\beta_i}$ and $\frac{\hat{\beta}_i-\beta_i}{\sigma_{\beta_i}}$

Answer 1

I don't have the reputation to post an image, but here's a link to a picture of one approach

More details below ~~

Hope this helps!

Answer to 1)

Let's use the expression \sigma^2_{\beta_i}. The answers should apply within \frac as well.

A couple of ways to reduce the size -- compare these

% what we're starting from
$\sigma^2_{\beta_i}$

We can add an extra subscript layer using THAT, to get a smaller subscript (which auto-scales subsubscripts, like i here).

$\sigma^2_{\!_{\beta_i}}$

Or we can use \mathsmaller from the relsize package:

$\sigma^2_{\mathsmaller{\beta_i}}$

This combo seems to work well:

$\sigma^{\mathsmaller{2}}_{\!_{\beta_i}}$

Answer to 2)

You can reduce space with an easy but kind of stupid hack (google for scaling negative space) -- just use \hspace{}.

Compare the starting point

% what we're starting from
$\sigma^2_{\beta_i}$

To beta-i with negative space:

\sigma^2_{\hspace{-.05in}\beta_i}$

Answer to 3)

Put these two together, and you get:

% what we're starting from
$\sigma^2_{\beta_i}$

% what we end up with
$\sigma^{\mathsmaller{2}}_{\hspace{-.05in}\!_{\beta_i}}$

Answer 2

You can scale via \scalebox{<factor>} and/or raise via \raisebox{<height>}. Some horizontal adjustment is possible via \! (for more, see What commands are there for horizontal spacing?).

\documentclass{article}

\usepackage{graphicx}

\begin{document}

$\beta_1,\frac{\sigma^{\scalebox{.7}{$\scriptscriptstyle 2$}}_{\!\epsilon}}{S_{xx}}$ and 
$\sigma^2_{\beta_i}$ and 
$\frac{\hat{\beta}_i-\beta_i}{\sigma_{\!\raisebox{-.1ex}{\scalebox{.7}{$\scriptscriptstyle \beta_i$}}}}$

\end{document}