Hey #SciTwitter/ #StatsTwitter. My brain is quarantine-mushed, help me out. I& #39;m tryna get reliable trendlines through data w/ measurement errors. See sample plot: Big outliers skew a linear regression, but a weighted regression (W=1/errorbars) gets better results. Yay! BUT...

...I don& #39;t think WLS gets what I really need. Case in point: The exact same datasets, one with much-larger error bars. Weighted regressions give the same answers with nearly-identical p-vals (<0.001), EVEN THO I& #39;m far more uncertain of any "real" trend w/ the orange data.

If the weights are all the same, it doesn& #39;t matter to a weighted-linear regression what they are. Points just are weighted relative to each other even if huge errors could bury actual trends, and/or suggest "false-positive" trends. What stats model do I really need here?