Week 5 Linear Regression Modeling.pdf

25/02/2024 Linear Regression Modeling in Data Mining In the Context of Business Introduction to Linear Regression Linear regression is a statistical technique...

25/02/2024 Linear Regression Modeling in Data Mining In the Context of Business Introduction to Linear Regression Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. Dependent Variable is continuous Independent Variables: Continuous Categorical Ordinal Binary Conversion to the appropriate type of data is required to ensure the linear regression model performs accordingly. 1  25/02/2024 Linear Regression Equation The general form of the linear regression equation for a single independent variable is: Y = ß0 + ß1X1 + e Where: Y = Dependent variable X1 = Independent variable ß0 = Intercept ß1 = Coefficient of X1 e = Error term Business Context of Linear Regression Linear regression is widely used in business for various purposes, including: - Sales forecasting - Customer segmentation - Price optimization - Risk assessment - Marketing effectiveness analysis 2  25/02/2024 Walkthrough Example: Multiple Linear Regression Let's consider a business example where we want to predict the sales revenue of a retail store based on multiple factors such as advertising spending, store size, and location. We can use multiple linear regression to build a model that predicts sales revenue (Y) based on the following independent variables (X): - Advertising spending - Store size - Location The multiple linear regression equation for this example would be: SalesRevenue = ß0 + ß1(Advertising) + ß2(Size) + ß3(Location) + e Implication of Linear Regression in Business Predictive Modelling Predict future demand for products or services based on historical data. E.g. inventory management, production planning, and setting sales targets. Analyze and improve business operations Inference to Relationships Risk Assessment Help in predicting maintenance requirements for machinery (preventing downtime). Decision Support Strategic Decision-Making: Analyzing historical data and trends, businesses can make informed strategic decisions (e.g. entering new markets, launching new products, or changing business operations) Customer Insights and Segmentation Understanding customer behaviour, preferences, and segmentation can be enhanced using linear regression to analyse sales data and customer feedback 3  25/02/2024 Linear Regression-Limitation Linear regression does have several limitations that are important to consider when applying it in practice: Assumption of Linearity: Assumption that there is a linear relationship between the independent and dependent variables. This isn't always the case in real-world business scenarios where relationships can be non-linear. Increasing advertising spending initially leads to a significant increase in sales, but after a certain point, further increases in advertising spend have a diminishing return. Influence of Outliers: Sensitive to outliers in the data. Outliers can significantly affect the slope and intercept of the regression line, leading to inaccurate predictions or interpretations Analyzing the relationship between store size and sales (with one store is exceptionally large and has unusually high sales) Multicollinearity: common in business data, where multiple factors can be interrelated. In cases where independent variables are highly correlated with each other, linear regression can produce unreliable coefficient estimates. A real estate company is using linear regression to predict house prices based on features like square footage, number of bedrooms, and number of bathrooms (these features are often correlated i.e. larger houses tend to have more bedrooms and bathrooms Overfitting and Underfitting: Data can be overfitted when they include too many independent variables. Conversely, they can underfit if important variables are omitted or if the model is too simplistic for complex data structures. Overfitting: A financial services firm builds a linear regression model to predict stock prices using a large number of economic indicators Underfitting: A small business uses linear regression to forecast sales using only the time of year (ignoring factors like marketing efforts, economic conditions, and competitor actions. Remember that statistical models, including linear regression, provide limited insights and should be supplemented with domain knowledge and expert judgment. Conclusion Linear regression modelling is a powerful tool for businesses to analyse relationships between variables and make informed decisions. By understanding the principles of linear regression and applying them in the context of business while understanding its limitations, organisations can gain valuable insights and improve their operations. 4