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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.

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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.

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  • $\begingroup$ 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, 2016 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. $\endgroup$ Jun 19, 2016 at 21:59

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