DS-Lecture-5----Multiple Regression.pptx

Multilinear regression is a statistical technique used to model the relationship between multiple independent variables and a dependent variable. It extends the concept of simple linear regression, which deals with only one independent variable, to scenarios where there are multiple predictors influencing the outcome. In multilinear regression, each independent variable is assigned a coefficient that represents its contribution to the dependent variable, allowing for the prediction of the outcome based on a combination of these predictors.

The primary objective of multilinear regression is to find the best-fitting linear equation that describes the relationship between the independent variables and the dependent variable. This equation takes the form:

\[Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_nX_n + \varepsilon\]

Where:
- \(Y\) is the dependent variable,
- \(X_1, X_2, ..., X_n\) are the independent variables,
- \(\beta_0, \beta_1, \beta_2, ..., \beta_n\) are the coefficients (also known as regression coefficients or parameters) representing the strength and direction of the relationship between each independent variable and the dependent variable,
- \(\varepsilon\) is the error term representing the difference between the observed and predicted values.

To determine the values of the coefficients, the method of least squares is commonly employed in multilinear regression. This method minimizes the sum of the squared differences between the observed and predicted values, effectively finding the line that best fits the data.

Multilinear regression is widely used in various fields such as economics, finance, social sciences, and engineering for predictive modeling, forecasting, and understanding the relationships between variables. It provides insights into how changes in one or more independent variables affect the dependent variable, enabling better decision-making and hypothesis testing.

However, multilinear regression has limitations, particularly when assumptions such as linearity, independence of errors, and homoscedasticity are violated. Additionally, multicollinearity, where independent variables are highly correlated, can lead to unreliable coefficient estimates. Despite these challenges, multilinear regression remains a powerful and versatile tool in the statistical analysis toolkit, offering valuable insights into complex data relationships.

1. DS 5002 Data Science: Tools & Techniques Regression-II Simple Linear Regression Multiple Linear Regression Fall 2023 Dr. Kashif Zafar