What are the various assumptions considered for running a multiple regression? Are these different from the ones considered under simple regression?

Multiple regression analysis is a powerful statistical technique used to examine the relationship between two or more independent variables and a dependent variable. It extends the concepts of simple regression by allowing researchers to assess the influence of multiple predictors on the outcome variable. However, before conducting a multiple regression analysis, several assumptions must be met to ensure the validity and reliability of the results. These assumptions are similar to those in simple regression but are extended to accommodate the complexity introduced by multiple predictors. Let's explore these assumptions in detail and discuss how they differ from those in simple regression.

### Assumptions of Multiple Regression:

#### 1. Linearity:
   - Simple Regression: In simple regression, it is assumed that there is a linear relationship between the independent variable and the dependent variable. The relationship can be represented by a straight line.
   - Multiple Regression: In multiple regression, the linearity assumption extends to multiple predictors. It assumes that the relationship between the independent variables and the dependent variable is linear when all other variables are held constant. This means that changes in the independent variables are associated with constant changes in the dependent variable.

#### 2. Independence:
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