docs: improve narrative flow, definition notation, and pronoun clarity (#1118)

* docs: improve narrative flow, definition notation, and pronoun clarity

- Add explicit noun phrases after demonstrative pronouns across subfiles.
- Update mathematical definition equations to use \eqdef.

Co-authored-by: dem-extra1 <112029334+dem-extra1@users.noreply.github.com>

* docs: improve narrative flow, definition notation, and semantic line breaks

- Add explicit noun phrases after demonstrative pronouns across subfiles.
- Update mathematical definition equations to use \eqdef.
- Enforce semantic line breaks on updated lines to satisfy check-new-line-breaks CI.

Co-authored-by: dem-extra1 <112029334+dem-extra1@users.noreply.github.com>

* docs: use the semantic estimator macro in def-estimated-risk-score

Addresses optional finding 2 from the claude-review on PR #1118:
collapse the hand-composed LHS into the single semantic macro that
already exists for it.

The reviewer suggested the \h... form; CLAUDE.md's "Estimator
indirection" rule prefers the \e... family in new/touched content, so
this uses \ehazfactorf. Both expand identically -- verified by
rendering old and new side by side:

  old: \hat\theta_{{\lambda}}\mathopen{}\left(\tilde{x}\right)
  new: \hat{\theta_{{\lambda}}}\mathopen{}\left(\tilde{x}\right)

The RHS \hvb is left alone: migrating it is a 43-site corpus-wide
change, tracked as #1119.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

---------

Co-authored-by: google-labs-jules[bot] <161369871+google-labs-jules[bot]@users.noreply.github.com>
Co-authored-by: Douglas Ezra Morrison <demorrison@ucdavis.edu>
Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Author: 3 people

_subfiles/Linear-models-overview/_exr-prac-linreg-score.qmd

@@ -68,7 +68,7 @@ $$
 \sum_{i=1}^n x_i y_i = \beta_0\sum_{i=1}^n x_i + \beta_1\sum_{i=1}^n x_i^2
 $$
 
-These are the **normal equations**,
+These equations are the **normal equations**,
 whose solution gives the OLS/MLE estimators
 $\hat\beta_0$ and $\hat\beta_1$.
 

_subfiles/Linear-models-overview/_sec_compare_lm_glm_deviance.qmd

@@ -144,7 +144,7 @@ $$
 = \sum_{k=1}^q \sum_{i: \vx_i = \vx_k} (y_i - \bar{y}_k)^2
 $$
 
-This is nonzero whenever any covariate pattern has replicates with
+This within-group residual sum of squares is nonzero whenever any covariate pattern has replicates with
 different response values.
 The Gaussian deviance relative to the saturated model is therefore:
 

_subfiles/Linear-models-overview/_sec_linreg_coef_sampling_dist.qmd

@@ -25,7 +25,7 @@ $$
 
 :::{.notes}
 
-These are all results you have hopefully seen before.
+These distribution properties are all results you have hopefully seen before.
 
 :::
 

_subfiles/Linear-models-overview/_sec_linreg_diag_conditional_resid.qmd

@@ -5,7 +5,7 @@ If our Gaussian linear regression model is correct, the residuals $\resid_i$ and
 -   a mean of 0
 -   a constant variance
 
-This should be true **for every** value of $x$.
+This mean and variance structure should be true **for every** value of $x$.
 
 ---
 

_subfiles/Linear-models-overview/_sec_linreg_diag_cooks_distance.qmd

@@ -15,7 +15,7 @@ the **Cook's distance** for observation $i$ is
 
 $$
 D_i
-= \frac{\tp{(\hvb_{(-i)} - \hvb)}
+\eqdef \frac{\tp{(\hvb_{(-i)} - \hvb)}
 \tp{\mX}\mX
 (\hvb_{(-i)} - \hvb)}{p\,\hs^2}
 $$ {#eq-cooks-distance-def}

_subfiles/Linear-models-overview/_sec_linreg_diag_marginal_resid.qmd

@@ -18,7 +18,7 @@ rstandard(bw_lm2)
 ```
 
 ::: notes
-These are nearly the same.
+These residual vectors are nearly identical.
 Any differences are from numerical rounding.
 
 :::

_subfiles/glms/_sec_model_fitting_process.qmd

@@ -36,7 +36,7 @@ We will treat EDA as a "step 0" that precedes these four steps.
 > and are they nominal or ordinal?
 >
 > 2. What is the shape of the distribution?
-> This can be examined using frequency tables,
+> This shape can be examined using frequency tables,
 > dot plots,
 > histograms
 > and other graphical methods.

_subfiles/proportional-hazards-models/_def-estimated-risk-score.qmd

@@ -8,6 +8,6 @@ After fitting the model,
 we estimate it by the **estimated risk score**,
 which substitutes the fitted coefficients $\hvb$ for $\vb$:
 
-$$\hat\hazfactor\paren{\vx} = \expf{\dprod{\vx}{\hvb}}$$
+$$\ehazfactorf{\vx} \eqdef \expf{\dprod{\vx}{\hvb}}$$
 
 :::

_subfiles/proportional-hazards-models/_def-risk-score.qmd

@@ -7,7 +7,7 @@ with coefficient vector $\vb$,
 the **risk score** (also called the **hazard multiplier** or **partial hazard**)
 for a subject with covariate vector $\vx$ is:
 
-$$\hazfactorf{\vx} = \expf{\reglincomb}$$
+$$\hazfactorf{\vx} \eqdef \expf{\reglincomb}$$
 
 :::
 

_subfiles/proportional-hazards-models/_sec_coxph-adjust_ties.qmd

@@ -83,7 +83,8 @@ averages the results for the six possible orderings of the failures.
 
 But we don't know the order they failed in, so instead of reducing the
 denominator by one risk coefficient each time, we reduce it by the same
-fraction. This is Efron's method.
+fraction.
+This fractional reduction approach is Efron's method.
 
 ::: smaller
 $$\left(\frac{\theta_1}{\theta_R+\theta_1+\theta_2+\theta_3}\right)