I have a linear regression model predicting Y from X1 and X2. However, from separate analysis in the past, the independent variables X1 and X2 are known to be accurate a% and b%.

Is there a way to predict Y by accommodating the accuracy rates of the independent variables? Any references (book or articles) you can point is very much appreciated.


Assuming that

the independent variables X1 and X2 are known to be accurate a% and b%

means that $X1 = aZ1$ and $X2 = bZ2$ where $Z1$ and $Z2$ are the true values of the independent variables without measurement error, and $a$ and $b$ are known, then you can simply compute $Z1$ and $Z2$ and use those as the predictors in your model.

  • $\begingroup$ Thanks for clarifying, Robert. I don't have Z2 and Z2. The a and b are old estimates from a old sample. In the current sample, i only have X1 and X2 and don't know their accuracy rates. However, it is reasonable to assume that the accuracy rates are same. Since the sample is different, i have a aggregate estimate of accuracy rate and I am wondering if i can use these aggregate estimates somehow in the model.... maybe as weights? $\endgroup$ – dexter2323 Jun 18 '16 at 19:40
  • $\begingroup$ Even if the samples are different (though presumably from the same population ?) since a and b are the same you just compute Z1= X1/a and likewise for Z2. $\endgroup$ – Robert Long Jun 19 '16 at 21:59

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