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Measurement error in the independent variable of a regression model leads to biased and inconsistent parameter estimates, which affects the reliability of statistical inference. When the explanatory variable is measured with error, the observed variable differs from the true variable. Suppose the true model is ( Y = \beta_0 + \beta_1 X^* + u ), but instead of observing ( X^* ), we observe ( X = X^* + v ), ___ _____ __________ ______ ___ _________ ______ __________.
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