Explain the assumptions underlying the multiple linear regression model.

In the context of Applied Regression Analysis, understanding the assumptions underlying the multiple linear regression (MLR) model is crucial for ensuring the validity, reliability, and interpretability of the results derived from the model. The MLR model is a statistical technique used to explain the relationship between one dependent variable (also known as the response variable) and two or more independent variables (predictors or explanatory variables). The fundamental goal is to model this relationship in a linear form and use it for prediction, inference, or both.

The standard form of the MLR model is:

$$
Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \cdots + \beta_kX_k + \varepsilon
$$

Here,

* $Y$ is the dependent variable,
* $X_1, X_2, \ldots, X_k$ are independent variables,
* $\beta_0, \beta_1, \ldots, \beta_k$ are the regression coefficients,
* $\varepsilon$ is the error term representing unobserved influences.

For valid estimation and inference in the MLR model using Ordinary Least Squares (OLS), several assumptions must be satisfied. Each assumption serves a specific purpose, either to ensure unbiased _______ ____ _________ ________ _____ ________ ___ ___ _______.
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