can't knit to pdf because of error(latex)
this is my first time using LaTex for school work and I have no idea whats causing error.... Any help appreciated thank you
[WARNING] Deprecated: --highlight-style. Use --syntax-highlighting instead.
! Missing $ inserted.
<inserted text>
$
l.168 \sum
\emph{\{i=1\}\^{}ne\_i =
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.
Try to find the following text in Question_4.Rmd:
\sum
You may need to add $ $ around a certain inline R expression `r ` in Question.Rmd (see the above hint). See https://github.com/rstudio/rmarkdown/issues/385 for more info.
Error: LaTeX failed to compile Question.tex. See https://yihui.org/tinytex/r/#debugging for debugging tips. See Question.log for more info.
Execution halted
$$
\begin{aligned}
\frac{\partial RSS}{\partial \beta_0}
&= -2\sum_{i=1}^n(y_i-\beta_0-\beta_1x_i)\\
&= -2(\sum_{i=1}^n y_i-\sum_{i=1}^n\beta_0-\beta_1\sum_{i=1}^n x_i)\\
&= -2(n\bar{y}-n\beta_0-n\beta_1\bar{x})\\
&= -2(n\bar{y}-n\beta_0-n\beta_1\bar{x})\\
&= (n\bar{y}-n\beta_0-n\beta_1\bar{x})\\
&= (\bar{y}-\beta_0-\beta_1\bar{x})\\
&= \beta_0 = \bar{y}-\beta_1\bar{x}
\end{aligned}
$$
$$
\begin{aligned}
\frac{\partial RSS}{\partial \beta_1}
&= -2\sum_{i=1}^n x_i(y_i-\beta_0-\beta_1x_i)\\
&= -2(\sum_{i=1}^n x_iy_i-\beta_0\sum_{i=1}^n x_i-\beta_1\sum_{i=1}^n x_i^2)\\
&= -2(\sum_{i=1}^n x_iy_i-n\beta_0\bar{x}-\beta_1\sum_{i=1}^n x_i^2)\\
&= -2(\sum_{i=1}^n x_iy_i-n\bar{x}(\bar{y}-\beta_1\bar{x})-\beta_1\sum_{i=1}^n x_i^2)\\
&= -2(\sum_{i=1}^n x_iy_i-n\bar{x}\bar{y}+n\beta_1\bar{x}^2-\beta_1\sum_{i=1}^n x_i^2)\\
&= \sum_{i=1}^n x_iy_i-n\bar{x}\bar{y}+n\beta_1\bar{x}^2-\beta_1\sum_{i=1}^n x_i^2=0\\
&= \beta_1(\sum_{i=1}^n x_i^2-n\bar{x}^2)
=\sum_{i=1}^n x_iy_i-n\bar{x}\bar{y}\\
&= \beta_1S_{xx}=S_{xy}\\
&= \beta_1=\frac{S_{xy}}{S_{xx}}
\end{aligned}
$$
$$
\sum_{i=1}^ne_i
= \sum_{i=1}^n(Y_i-b_0-b_1X_i)\\
= \sum_{i=1}^nY_i-nb_0-b_1\sum_{i=1}^nX_i\\
= \sum_{i=1}^n(b_0+b_1X_1)-nb_0-b_1\sum_{i=1}^nX_i\\
=0
$$
$$
\begin{aligned}
\sum_{i=1}^n e_iX_i
&= \sum_{i=1}^nX_i(Y_i-b_0-b_1X_i)\\
&= \sum_{i=1}^nX_iY_i-\sum_{i=1}^nX_ib_0-\sum_{i=1}^nb_1X_i^2\\
&= \sum_{i=1}^nX_iY_i-\left(b_0\sum_{i=1}^nX_i+b_1\sum_{i=1}^nX_i^2\right)\\
&= \sum_{i=1}^nX_iY_i-\sum_{i=1}^nX_iY_i\\
&= 0
\end{aligned}
$$