[R-sig-ME] pooled within-cluster regression line

[Simon Harmel]

Dear All,

Top panel of Figure 3 of this open access paper (see **link below**) shows
3 clusters of datapoints, each with five datapoints.

The authors note:

> "The dotted line represents the regression of well-being (y) on workload
(x) within each cluster (i.e., the pooled within-cluster regression,
Beta_w)".

Say I have the hypothetical data blow with 3 clusters (`group`). How can I
find and draw the **the pooled within-cluster, $\beta_w$** regression line?

THE LINK: (
https://www.researchgate.net/publication/6274186_Centering_Predictor_Variables_in_Cross-Sectional_Multilevel_Models_A_New_Look_at_An_Old_Issue
)

## R code: ---------------------------------------------------
  set.seed(2)
  pop_mean <- 80
  n_groups <- 3
  groups <- gl(n_groups, 5)
  x <-rnorm(length(groups), 55, 15)
  Z <-model.matrix(~groups-1)
  group_means <-rnorm(n_groups, 0, 2.5)
  y <- pop_mean + -.3*x + Z%*%group_means + rnorm(length(groups), 0, 2)
  data <- data.frame(y, groups, x)

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