Hi, I’m pretty new to Data Science. I have some Data with measurement errors and I want to fit a linear model. using DataFrames using GLM using StatsPlots df = DataFrame(x = [0.0, 0.0669873, 0.25, 0.5, 0.75, 0.933013, 1.0], y = [0.223, 0.291, 0.393, 0.549, 0.73, 0.85, 0.896], u_y = [0.023, 0.024…

As indicated in GLM.jl’s doc above, glm does not handle inverse-variance weighting. For this purpose, you may use LsqFit.jl. using DataFrames, LsqFit, Printf, Plots; gr() df = DataFrame(x = [0.0, 0.0669873, 0.25, 0.5, 0.75, 0.933013, 1.0], y = [0.223, 0.291, 0.393, 0.549, 0.73, 0.85, 0.89…

[image] Okarin99: The confidence interval should get plotted but it is so small that you can’t even see it GLM.jl ’s glm does not interpret the weights wts as inverse variances but as prior frequencies: - `wts::Vector=similar(y,0)`: Prior frequency (a.k.a. case) weights of observations. …

There are two different confidence intervals to consider, the confidence interval for the posterior mean, and the interval for a new measurement. You are talking about the interval for a new measurement, which contains uncertainty about both the mean and the measurement.

So to get the right confidence interval I have to sum up the confidence interval I get from glm with the mean of the measurement errors?

Maybe, but probably not. It really depends on what question you want to answer. Usually, you use measurements to learn about some underlying system, and you postulate that the system behaves according to the model you have identified. You are then typically interested in learning about the posterior…

Weighted linear regression with confidence interval fitted to error bars

General Usage

nilshg May 8, 2021, 6:47am 2

Your question is hopefully answered here Plot the confidence interval for a model fit

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Weighted linear regression with confidence interval fitted to error bars

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