# Regression models' results: reporting them as means or medians?

I have a zero-inflated and extremely positively-skewed outcome variable - lottery wins in dollars. Thus, I use two-part analysis, since adjusting is also needed: one for positive values (lognormal regression) and the second for non-zero probability (logistic regression/bernoulli).

I have found that presenting the results of these two regressions in one plot makes the interpretation really simple: you can see the probability of winning (x-axis) together with the received amount of money (in case you won).

The plot looks like this:

• y-axis outcome variable values come from a lognormal model

• x-axis outcome variable values come from a logistic regression/bernoulli model (I report them as probabilities, not odds-ratios).

It's well known practice that crude non-normal data should be reported as median (IQR/min-max/quantiles/percentiles). However, if these values come from regression analysis, should I report them as means or medians in this graph? Does regression "convert" these variables to "normally distributed" variables?

• Why should skewed data be reported using median instead of mean? I do think that people often mean the halfway point (median) when they talk about an average value, but if you’re doing technical work involving means, you probably mean an expected value or estimated expected value.
– Dave
Commented Sep 29, 2020 at 11:04
• How does the two axes relate to each other? What exactly are the models you mention? "Means or medians" or what? Why can't you just label those as "regression predictions"?
– Tim
Commented Sep 29, 2020 at 12:05
• I edited the beginning of the initial post a bit to make things a bit more clear. And the question remains the same: should I use means or medians. Commented Sep 29, 2020 at 12:45
• The only grounds I can see for talking about medians here are if you use quantile regression to model how median outcomes vary with the predictors. Commented Sep 29, 2020 at 12:57
• Thanks! Thus, it would be fine to report Y and X values as means? Commented Sep 29, 2020 at 13:17