I'm trying to determine whether an unweighted or weighted regression would be more suitable for my data.
I have variables X and Y, both are measured variables but X has very small errors while Y has quite large errors. This is because Y is calculated from an average of 5 measurements - so the error bars are including repeatability of these values from our analytical instrument.
I initially thought weighted regression would work because it would treat data points with smaller errors as more important, giving more weight to Y values with smaller standard deviations (so that data points that were more reproducible by the instrument are more reliable).
However I've been warned against using weighted linear regressions because they are ideal for data that has large errors on both X and Y variables, is this statement true?
I'm also worried about choosing the regression method because I get very different p values from the two regressions. With the weighted regression my p value is <0.001, but with the unweighted regression my p value is ~0.5, which completely changes my interpretation. I'm trying to understand what's causing this much difference in p values with the different regression methods and what regression would be best for my data.
Any insight would be appreciated!