gplot2.tidyverse.org/reference/labs.html">labs</a></span><span class="op">(</span>y <span class="op">=</span> <span class="st">"LS level-1 residuals"</span>, 
       title <span class="op">=</span> <span class="st">"LS residuals against standardized LRT score"</span><span class="op">)</span></code></pre></div>
<p>The smoother shows that standardized LRT scores might not be linearly related to GCSE exam scores. Likelihood ratio tests (not shown) confirm that quadratic and cubic terms for <code>standLRT</code