Multiple Regression Assumptions (From AllenResources in Youtube)

This video basically explains that the multiple linear regression is represented by the following formula:

Y_t = b₀ + b₁*X_1t + … b_k*X_kt + e_t

where Y is the dependent variables, b’s are the coefficient and X’s are the independent variables and e is the error. t is a subscript for time series analysis. If it is cross-sectional analysis, we may use i. But they are just symbols anyway.

Assumptions are:

1. Relationship between Y and X’s is linear
2. X’s are not random
3. E(e_t) = 0: means error’s mean is zero
4. E(e_t e_t­) = sigma² : means the variance of error is constant at any time
5. E(e_t e_s)=0: means there is no correlations between errors at different time
6. e ~ N(0, sigma²): means errors are normally distributed