C3_W3 (MLE: Linear Regression): Why do we assume points around the line are in normal distribution while calculating likelihood

Course Q&A Math for Machine Learning Probability & Statistics for Machine Learning &...
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Normal distributions are extremely common in natural systems. So it’s a good assumption.

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Hi @GORRELA_SRI_SATYA_VE good question. This came from statistics, there are some assumptions about linear regression model that you need to meet for creating a model.

  1. Linearity: The relationship between X and the mean of Y is linear.
  2. Homoscedasticity: The variance of residuals is the same for any value of X.
  3. Independence: Observations are independent of each other.
  4. Normality: For any fixed value of X, Y is normally distributed.

In this case, we need to assume that for each value of X, Y is normally distributed, that happens to be on the line we set, but we made this assumption before actually plotting the linear regression model.