How bad can heteroscedasticity be before causing problems? I have two questions about heteroscedasticity in multiple regressions.    


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*According to my trusty textbook (Using Multivariate Statistics 2007, p.127), it says that deviations from heteroscedasticity only reduce that statistical power of a test, rather than inflating the type I error rate (is this true?)

*I wanted to know if there were any guidelines about how to judge effect sizes for heteroscadisticity and how much is a bad effect size for it to matter (with N=187). Because I use two categorical variables, luckily my residual/predicted plot is in two distinct clumps that I can analyse (see below):

 A: It is true that heteroscedasticity reduce your power (see: Efficiency of beta estimates with heteroscedasticity), but it can also inflate type I errors.  Consider the following simulation (coded in R):  
set.seed(1044)                          # this makes the example exactly reproducible
b0 = 10                                 # these are the true values of the intercept
b1 = 0                                  #  & the slope
x  = rep(c(0, 2, 4), each=10)           # these are the X values
hetero.p.vector = vector(length=10000)  # these vectors are to store the results
homo.p.vector   = vector(length=10000)  #  of the simulation

for(i in 1:10000){                      # I simulate this 10k times
  y.homo   = b0 + b1*x + rnorm(30, mean=0, sd=1)  # these are the homoscedastic y's

  y.x0     = b0 + b1*0 + rnorm(10, mean=0, sd=1)  # these are the heteroscedastic y's
  y.x2     = b0 + b1*2 + rnorm(10, mean=0, sd=2)  #  (notice the SDs of the error
  y.x4     = b0 + b1*4 + rnorm(10, mean=0, sd=4)  #   term goes from 1 to 4)
  y.hetero = c(y.x0, y.x2, y.x4)

  homo.model         = lm(y.homo~x)               # here I fit 2 models & get the
  hetero.model       = lm(y.hetero~x)             #  p-values
  homo.p.vector[i]   = summary(homo.model)$coefficients[2,4]
  hetero.p.vector[i] = summary(hetero.model)$coefficients[2,4]
}
mean(homo.p.vector<.05)    # there are ~5% type I errors in the homoscedastic case
# 0.049                    #  (as there should be)
mean(hetero.p.vector<.05)  # but there are ~8% type I errors w/ heteroscedasticity
# 0.0804

Linear models (such as multiple regression), tend to be fairly robust, though.  In general, a rule of thumb is that you are OK as long as the largest variance is not more than four times the lowest variance.  This is a rule of thumb, so that should be taken for what it's worth.  However, notice that in the simulation above, in the heteroscedastic model, the highest variance is $16\times$ the smallest variance ($4^2=16$, vs $1^2 = 1$) and the resulting type I error rate is $8\%$ instead of $5\%$.  
