I Linear regression and random variables

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Linear regression models utilize a finite set of data (x, y) to estimate population parameters, with the goal of determining the best fit line through ordinary least squares (OLS). In this context, Y is treated as a random variable, while X is typically considered fixed without random errors. The regression model is expressed as y = β1x + β0 + ε, where ε represents the error term, assumed to follow a normal distribution. The discussion emphasizes that the regression estimates the conditional mean of Y given X, rather than predicting specific values of Y. Overall, the interpretation of regression results hinges on whether the model includes a random component and how the variables are treated within the statistical framework.
  • #31
DrDu said:
Of course outliers are an issue! But first one has to define what an outlier is. An outlier may violate ##E(\epsilon_i)=0##. OLS is sensitive to this, it is not a robust method. A single outlier of this kind may lead to a slope estimate arbitrary far away from the true one.
Yes. My point was that I should not worry about outliers at other ##x## values where the expected values of the estimators are concerned since it is the entire distribution at those ##x## values that determine those estimator expected values.
 

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