We define and discuss the seven assumptions of the Classical Linear Regression Model (CLRM) using simple notation and intuition.
The Seven Assumptions:
I.The regression model is linear, is correctly specified, and has an additive error term
II. The error term has a zero population mean
III. All explanatory variables are uncorrelated with the error term
IV. Observations of the error term are uncorrelated with each other (no serial correlation)
V. The error term has a constant variance (no heteroskedasticity)
VI. No explanatory variable is a perfect linear function of any other explanatory variable(s) (no perfect multicollinearity)
VII. The error term is normally distributed (this assumption is optional but usually is invoked)

The proof that OLS is unbiased (Gauss-Markov Part 1):   • Econometrics Lecture: OLS Unbiased Proof  
The OLS coefficient variance derivation (Gauss-Markov Pt. 2):    • Econometrics Lecture: Derivation of t...  

Link to the excellent Introduction to Econometrics Textbook by AH Studenmund:
https://www.amazon.com/gp/product/933...

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