Hello, world

Everything on this page is plain HTML. The math is MathML that pandoc generates at build time, and the plot is an SVG file made by R.

Inline math: $f(x) = \frac{1}{\sigma\sqrt{2\pi}}\, e^{-(x-\mu)^2 / 2\sigma^2}$.

Display math:

$$\hat{\beta} = (X^\top X)^{-1} X^\top y$$

An aligned derivation:

$$\begin{aligned} \operatorname{Var}(\hat\beta) &= (X^\top X)^{-1} X^\top \operatorname{Var}(y)\, X (X^\top X)^{-1} \\ &= \sigma^2 (X^\top X)^{-1} \end{aligned}$$

set.seed(1)
x <- rnorm(100)
y <- 0.5 * x + rnorm(100, sd = 0.7)
par(mar = c(4, 4, 1, 1))
plot(x, y, pch = 19, col = "#0b5e7466", las = 1)
abline(lm(y ~ x), lwd = 2)