# Regression with Independent variables accuracy rates

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.

• What do you specifically mean by "accurate a%" ? – Matthew Gunn Jun 12 '16 at 6:48
• – Ashe Jul 11 '16 at 18:51

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.