If any of the assumptions of linear regression are violated, the model may not be reliable to use for either inference or prediction. For example, if the observations are not independent or the residuals exhibit non-constant variance, the parameter estimates may not be accurate representations of the actual phenomenon occurring. If multicollinearity is not addressed, significant effects might not be identified, and the estimate of the magnitude and direction of the inference can be off. If the relationship between x and y is not linear, the fitted equation will likely underfit the data, and the model will suffer from high bias. Finally, if outliers or high leverage points are present and not dealt with, the model will likely not be a good representation of the general relationship between the predictor and target, and be poorly calibrated to predict future observations.
What are potential problems encountered in Linear Regression?
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