Fix math display

exercises/jsp.md

@@ -1,7 +1,13 @@
-Exercise: Junior School Project
+---
-================
+title: "Exercise: Junior School Project"
-Nora Wickelmaier
+author: "Nora Wickelmaier"
-2025-06-20
+output:
+  md_document:
+    variant: gfm
+    preserve_yaml: true
+kramdown:
+  math_engine: mathjax
+---
 
 Load the Junior School Project collected from primary (U.S. term is
 elementary) schools in inner London in R. You might need to install the
@@ -71,11 +77,11 @@ aggregate(gcraven ~ school, dat, mean) |> head()
     ## 5      5  5.075722e-16
     ## 6      6  0.000000e+00
 
-3.  Create a plot with `lattice::xyplot()` with `gcraven` on the
+3.  Create a plot with `lattice::xyplot()` with `gcraven` on the x-axis
-    $x$-axis and `math` on the $y$-axis and one panel for each school.
+    and `math` on the y-axis and one panel for each school. Use
-    Use `type = c("p",    "g", "r")`. You can also use `ggplot2` if you
+    `type = c("p",    "g", "r")`. You can also use `ggplot2` if you want
-    want to. What would be your conclusion about the need for
+    to. What would be your conclusion about the need for school-specific
-    school-specific slopes based on this plot?
+    slopes based on this plot?
 
 <img src="jsp_files/figure-gfm/unnamed-chunk-7-1.png" style="display: block; margin: auto;" />
 
@@ -108,9 +114,11 @@ aggregate(gcraven ~ school, dat, mean) |> head()
                                 &~~~ + \beta_{4}\,mraven_i + \beta_{5}\,(gcraven_{ij} \times mraven_{i})\\
                                 &~~~ + \upsilon_{0i} + \upsilon_{1i}\,gcraven_{ij} + \varepsilon_{ij}
     \end{align*}
-    $$ with
+    $$
-    $\boldsymbol\upsilon \sim N(\boldsymbol 0, \boldsymbol{\Sigma}_\upsilon)$
+
-    i.i.d., $\varepsilon_{ij} \sim N(0, \sigma^2)$ i.i.d.
+    with
+    $$\boldsymbol\upsilon \sim N(\boldsymbol 0, \boldsymbol{\Sigma}_\upsilon)$$
+    i.i.d., $$\varepsilon_{ij} \sim N(0, \sigma^2)$$ i.i.d.
 
 5.  Interpret the parameters of the model: