What are the assumptions required for linear regression? What if some of these assumptions are violated?

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The assumptions are as follows:

  1. The sample data used to fit the model is representative of the population
  2. The relationship between X and the mean of Y is linear
  3. The variance of the residual is the same for any value of X (homoscedasticity)
  4. Observations are independent of each other
  5. For any value of X, Y is normally distributed.
    Extreme violations of these assumptions will make the results redundant. Small violations of these assumptions will result in a greater bias or variance of the estimate.