7.1.1 Multiple Linear Regression¶

Objective: Transition from simple linear regression to multiple linear regression, expanding the analysis to include multiple independent variables affecting a single dependent variable.
Overview: This session introduces multiple linear regression (MLR), exploring its theoretical foundation, model construction, and applications in business analytics.

Definition: Multiple linear regression (MLR) extends simple linear regression by allowing the dependent variable to be influenced by multiple independent variables.

Model Parameters: Discussion on estimating the coefficients that best fit the data using the least squares method.
Error Term Assumptions: Maintaining assumptions from simple linear regression, such as the expectation of the error term being zero, ensuring unbiased estimates.

Data Collection: Gathering data from various sources like ERP systems or government census data, focusing on both primary and secondary sources.
Data Preprocessing: Addressing data quality, handling missing data, and transforming variables as necessary.
Descriptive Analytics: Using statistics and visualization to understand data properties and the relationships between variables.
Modeling Strategy: Selecting the appropriate independent variables, ensuring they are independent of each other to avoid multicollinearity.
Model Development: Formulating the regression equation and estimating parameters using Ordinary Least Squares (OLS).
Model Diagnostics: Performing tests for statistical significance (F-test and T-test) and checking for multicollinearity, normality of residuals, and heteroscedasticity.
Model Validation: Using measures like \(R^2\), Adjusted \(R^2\), Mean Absolute Percentage Error, and Root Mean Square Error to assess model performance on validation datasets.

Real-World Example: Discusses how MLR can be applied to enhance predictions in scenarios where multiple factors influence a business outcome, such as predicting sales based on pricing, advertising spend, and economic conditions.

Model Implementation: The final steps involve deploying the model in a real-world setting, monitoring its performance, and making necessary adjustments based on ongoing results.
Continuous Learning: Emphasizes the iterative nature of model development and the importance of continual learning and adaptation in business statistics.

Advanced Topics: The course will continue to explore deeper aspects of regression analysis, including interaction effects among variables and more complex statistical methods to handle data challenges.