While estimating a regression model you found that the explanatory variable is measured with certain error. Specify the model. What are its consequences on the parameters?

When estimating a regression model where the explanatory variable is measured with error, it introduces a situation commonly referred to as errors-in-variables or measurement error. The classical linear regression model assumes that the explanatory variables are measured without error. However, in real-world scenarios, this is often not the case, and measurement error in the explanatory variable can lead to biased and inconsistent estimates of the parameters.

Model Specification

Let’s consider a simple linear regression model with one explanatory variable XX and a dependent variable YY. The true relationship between YY and XX is given by:

Y=β0+β1X+uY = \beta_0 + \beta_1 X + u

where:

• YY is the dependent variable,
• XX is the explanatory variable,
• β0\beta_0 and β1\beta_1 are the intercept and slope coefficients, respectively,
• uu is the error term.

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