work on Ch11

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diff --git a/01-intro.html b/01-intro.html
diff --git a/10-mlm-review.qmd b/10-mlm-review.qmd
@@ -924,7 +924,8 @@ homogeneity of the variances and covariance matrices $\mathbf{S}_i$, I show only
 #| out-width: "90%"
 #| fig-cap: Bivariate data ellipses for pairs of the three responses, showing the means, correlations and variances for the three groups.
 colors <- scales::hue_pal()(3) |> rev()  # match color use in ggplot
-covEllipses(cbind(caring, play, emotion) ~ group, data=Parenting,
+covEllipses(cbind(caring, play, emotion) ~ group, 
+  data=Parenting,
   variables = 1:3,
   fill = TRUE, fill.alpha = 0.2,
   pooled = FALSE,
@@ -1090,7 +1091,7 @@ or, expressed in terms of the variables,
 \begin{bmatrix} \beta_{0,\text{anx}} \\ \beta_{0,\text{dep}} \end{bmatrix} +
 \begin{bmatrix} \beta_{1,\text{anx}} \\ \beta_{1,\text{dep}} \end{bmatrix} \text{grade} +
 \begin{bmatrix} \beta_{2,\text{anx}} \\ \beta_{2,\text{dep}} \end{bmatrix} \text{grade}^2 \\
-& + \cdots
+& + \cdots +
 \begin{bmatrix} \beta_{5,\text{anx}} \\ \beta_{5,\text{dep}} \end{bmatrix} \text{grade}^5
 \end{eqnarray*} {#eq-AH-mod2}
 

diff --git a/11-mlm-viz.qmd b/11-mlm-viz.qmd
@@ -45,19 +45,20 @@ knitr::include_graphics("images/dogfood-quartet.png")
 
 
 
-* In data space, each group is summarized by its **data ellipse**, representing the means and covariances.
+* In data space (a), each group is summarized by its **data ellipse** (b), representing the means and covariances.
 
-* Variation against the hypothesis of equal means can be seen by the $\mathbf{H}$ ellipse in the **HE plot**, representing the data ellipse of the fitted values. Error variance is shown in the $\mathbf{E}$ ellipse,
+* Variation against the hypothesis of equal means can be seen by the $\mathbf{H}$ ellipse in the **HE plot** (c), representing the data ellipse of the fitted values. Error variance is shown in the $\mathbf{E}$ ellipse,
 representing the pooled within-group covariance matrix, $\mathbf{S}_p$ and the data ellipse of the residuals from the model.
+For the dogfood data, the group means have a negative relation: longer time to start eating is associated with a smaller amount eaten.
 
 * The MANOVA (or Hotelling's $T^2$) is formally equivalent to a **discriminant analysis**, predicting
 group membership from the response variables which can be seen in data space. (The main difference is 
 emphasis and goals: MANOVA seeks to test differences among group means, while discriminant analysis aims
 at classification of the observations into groups.)
 
 * This effectively projects the $p$-dimensional
-space of the predictors into the smaller **canonical space** that shows the greatest differences among
-the groups.
+space of the predictors into the smaller **canonical space** (d) that shows the greatest differences among
+the groups. As in a biplot, vectors show the relations of the response variables with the canonical dimensions.
 
 <!--
 ```{r}
@@ -89,7 +90,14 @@ knitr::include_graphics("images/arcmanov.png")
 
 
 For more complex models such as MANOVA with multiple factors or multivariate multivariate regression,
-there is one $\mathbf{H}$ ellipse for each term in the model. ...
+there is one sum of squares and products matrix (SSP), and therefore one
+$\mathbf{H}$ ellipse for each term in the model. For example, in a two-way MANOVA design with the model
+formula `(y1, y2) ~ A + B + A*B` and equal sample sizes in the groups, the total sum of squares accounted for by the model is
+\begin{align*}
+\mathbf{SSP}_{\text{Model}} & = \mathbf{SSP}_{A} + \mathbf{SSP}_{B} + \mathbf{SSP}_{AB} \\
+                            & = \mathbf{H}_A + \mathbf{H}_B + \mathbf{H}_{AB} \period
+\end{align*}
+
 
 ## HE plot construction
 
@@ -116,9 +124,14 @@ puts this on the same scale as the \E ellipse.
 I refer to this as _effect size scaling_, because it is similar to an effect size index used in
 univariate models, e.g., $ES = (\bar{y}_1 - \bar{y}_2) / s_e$ in a two-group, univariate design.
 
-This is illustrated in ...
+### Example: Iris data
+
+**TODO**: Introduce the iris data earlier. Where???
+
+@fig-iris-HE1 shows two views of the relationship between sepal length and sepal width for the iris data. ...
 <!--
 ```{r}
+#| eval: false
 op <- par(mar = c(4, 4, 1, 1) + .5,
           mfrow = c(1, 2))
 col <-c("blue", "darkgreen", "brown")
@@ -143,6 +156,15 @@ par(op)
 ```
 -->
 
+```{r}
+#| label: fig-iris-HE1
+#| out-width: "100%"
+#| fig-cap: "Iris data: Data ellipses and HE plot"
+knitr::include_graphics("images/iris-HE1.png")
+```
+
+
+### Significance scaling
 
 The geometry of ellipsoids and multivariate tests allow us to go further with another re-scaling of the $\mat{H}$ ellipsoid
 that gives a _visual test of significance_ for any term in a MLM.
@@ -164,6 +186,17 @@ where $\text{df}_1 = \max(p, \text{df}_h)$ and $\text{df}_2 = \text{df}_h + \tex
 For these data, the HE plot using
 significance scaling is shown in the right panel of \figref{fig:heplot-iris1}.
 
+```{r}
+#| label: fig-iris-HE2
+#| out-width: "100%"
+#| fig-cap: "HE plots for sepal width and sepal length in the iris dataset. Left: effect scaling of the $\\mathbf{H}$ magtrix; right: significance scaling"
+knitr::include_graphics("images/iris-HE2.png")
+```
+
+
+### Contrasts
+
+### HE plot matrices
 
 ## Canonical discriminant analysis {#sec-candisc}
 

diff --git a/R/iris/iris-HE.R b/R/iris/iris-HE.R
@@ -78,3 +78,7 @@ heplot(iris.mod, hypotheses=hyp, fill=TRUE,
 # vary label position and fill.alpha
 heplot(iris.mod, hypotheses=hyp, fill=TRUE, fill.alpha=c(0.3,0.1), col=c("red", "blue"), 
        lty=c(0,0,1,1), label.pos=0:3)
+
+pairs(iris.mod,
+      fill=TRUE, fill.alpha=c(0.3,0.1)
+)
diff --git a/bib/pkgs.bib b/bib/pkgs.bib
@@ -34,7 +34,8 @@ @Manual{R-broom
 }
 
 @Manual{R-candisc,
-  title = {candisc: Visualizing Generalized Canonical Discriminant and Canonical Correlation Analysis},
+  title = {candisc: Visualizing Generalized Canonical Discriminant and Canonical
+Correlation Analysis},
   author = {Michael Friendly and John Fox},
   year = {2024},
   note = {R package version 0.9.0},
@@ -44,7 +45,7 @@ @Manual{R-candisc
 @Manual{R-car,
   title = {car: Companion to Applied Regression},
   author = {John Fox and Sanford Weisberg and Brad Price},
-  year = {2024},
+  year = {2023},
   note = {R package version 3.1-3},
   url = {https://r-forge.r-project.org/projects/car/},
 }
@@ -89,14 +90,6 @@ @Manual{R-corrplot
   url = {https://github.com/taiyun/corrplot},
 }
 
-@Manual{R-datasauRus,
-  title = {datasauRus: Datasets from the Datasaurus Dozen},
-  author = {Colin Gillespie and Steph Locke and Rhian Davies and Lucy {D'Agostino McGowan}},
-  year = {2024},
-  note = {R package version 0.1.8},
-  url = {https://github.com/jumpingrivers/datasauRus},
-}
-
 @Manual{R-datawizard,
   title = {datawizard: Easy Data Wrangling and Statistical Transformations},
   author = {Indrajeet Patil and Etienne Bacher and Dominique Makowski and Daniel Lüdecke and Mattan S. Ben-Shachar and Brenton M. Wiernik},
@@ -316,14 +309,6 @@ @Manual{R-knitr
   url = {https://yihui.org/knitr/},
 }
 
-@Manual{R-langevitour,
-  title = {langevitour: Langevin Tour},
-  author = {Paul Harrison},
-  year = {2024},
-  note = {R package version 0.7},
-  url = {https://logarithmic.net/langevitour/},
-}
-
 @Manual{R-lattice,
   title = {lattice: Trellis Graphics for R},
   author = {Deepayan Sarkar},
@@ -359,9 +344,9 @@ @Manual{R-marginaleffects
 
 @Manual{R-MASS,
   title = {MASS: Support Functions and Datasets for Venables and Ripley's MASS},
-  author = {Brian Ripley and Bill Venables},
+  author = {Brian Ripley},
   year = {2024},
-  note = {R package version 7.3-61},
+  note = {R package version 7.3-60.0.1},
   url = {http://www.stats.ox.ac.uk/pub/MASS4/},
 }
 
@@ -638,7 +623,7 @@ @Book{car2019
   year = {2019},
   publisher = {Sage},
   address = {Thousand Oaks {CA}},
-  url = {https://www.john-fox.ca/Companion/},
+  url = {https://socialsciences.mcmaster.ca/jfox/Books/Companion/},
 }
 
 @Misc{correlationPackage,
@@ -865,17 +850,6 @@ @InCollection{knitr2014
   note = {ISBN 978-1466561595},
 }
 
-@Article{langevitour2023,
-  title = {langevitour: Smooth Interactive Touring of High Dimensions, Demonstrated with scRNA-Seq Data},
-  author = {Paul Harrison},
-  journal = {The R Journal},
-  year = {2023},
-  volume = {15},
-  number = {2},
-  pages = {206-219},
-  doi = {10.32614/RJ-2023-046},
-}
-
 @Book{lattice2008,
   title = {Lattice: Multivariate Data Visualization with R},
   author = {Deepayan Sarkar},