Regression with error in the dependent var.

For the data set pictured below, I want test the significance of a simple linear regression. The slope and intercept are highly significant with x-y data points only. However, there is substantial known measurement error for the dependent variable.

I believe that I need to include this measurement error in the calculation of p values for the slope and intercept. Is that true? If so, does anyone know how to include it in regression analysis for common statistical software (SPSS, r, or minitab)? Thank you.

plot example.png
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TS Contributor
In Minitab, use Orthogonal regression. This is designed for error in both independent and dependent variables.


Ambassador to the humans
It does partially depend on what your actual goal is. What do you want to do? Make inferences or make predictions?


Omega Contributor
Can you define what you mean by measurement error and how it is caused and how you know its magnitude? Do you have a validation set where a gold standard is applied?


Active Member
@SunnyDays Simple linear regression assumes that there is random error in the dependent variable, in particular that the y_i|x_i are normally distributed with constant variance. Did you mean to say that there is measurement in error in the indepndent variable?