I would like to understand the difference between the regression lines in black and the regression lines in blue, (slide page 10) below.
In blue : regression lines adjusted for region, plotted separately for N and S regions. In black: region-specific regression lines
Thanks
The "region-adjusted slopes" are almost as useless here as the unadjusted slope:
The region-adjusted slope comes from estimating separate regression of damage on elevation for the Southern region sites only, and the Northern region sites only, and then taking a weighted average of these two estimates (slopes).
That makes an implicit assumption that the actual slope is the same for Southern and Northern sites.*
They aren't, as the "Tree Damage and Elevation - 9" slide shows. For Southern sites the slope can't be distinguished statistically from 0 (95% CI include 0). The slope significantly exceeds 0 for Northern sites (lower limit of 95% CI, 0.06).
I can't tell whether the individual slopes in that last slide were estimated with a model containing an interaction between region and elevation (usually preferable, to get a better estimate of the residual variance) or were from subset analysis by region.
A couple of warnings about this type of analysis.
First, least-squares linear regression typically shouldn't be used with percentage outcomes like these. Although there aren't values close to either 0% or 100% (which can lead to model predictions impossibly below 0 or above 100), we don't know how reliable the percentage values are and whether all sites should be weighted the same as they are here. The reliability of a percentage value depends on the total number of trees evaluated for damage. A better model would work directly with the observed counts of damaged and undamaged trees.
Second, the Southern versus Northern dichotomy ignores the continuous nature of latitude values. Binning a continuous variable is generally not a good idea. This might better be done with a generalized additive model that uses continuous values for both elevation and latitude, with a smoothing function that directly shows the form of the interaction between them.
*From what's shown, I can't tell where the intercepts for those two blue lines came from; the slopes are identical, by construction.
