A multiple regression model is an extension of the simple linear regression model that allows for more than one explanatory variable. It can be specified as: [ Y_i = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \dots + \beta_k X_{ki} + u_i \quad \text{for } i = 1, 2, \dots, n ] where (Y_i) is the dependent variable for observation (i), (X_{1i}, X_{2i}, \dots, X_{ki}) are the values of (k) explanatory variables for the same observation, (\beta_0, \beta_1, \dots, \beta_k) are the parameters to be estimated, and (u_i) is the stochastic error term capturing the effects of all factors on (Y_i) that are not included among the explanatory variables. The error term (u_i) in the classical multiple regression model is assumed to satisfy the following conditions: 1. Zero mean: (E(u_i) = 0). This implies that the error term has no systematic component and does not bias the conditional expectation of (Y_i). 2. Homoscedasticity: (Var(u_i) = \sigma^2) for all (i). This means the variance of the error term is constant across all observations. 3. No autocorrelation: (Cov(u_i, u_j) = 0) for (i \neq j). Errors are uncorrelated across observations. 4. Normality (for maximum likelihood estimation): (u_i \sim N(0, \sigma^2)). The error terms are normally distributed, which is particularly important for inference and for using the maximum likelihood method efficiently. 5. Exogeneity: (E(u_i|X_{1i}, X_{2i}, \dots, X_{ki}) = 0). The errors are uncorrelated with the explanatory variables, ensuring that the regressors