Simple & Multiple Linear Regression

Service Description

Definition: Simple Linear Regression Linear regression is a statistical method that examines the relationship between two variables — one independent variable (X) and one dependent variable (Y) — to determine how changes in the independent variable affect the dependent variable. It assumes a linear (straight-line) relationship between the two. Mathematical Model 𝑌=𝑏0+𝑏1𝑋+𝜀 Where: Y = dependent variable (the outcome or response) X = independent variable (the predictor) 𝑏0 = intercept (value of Y when X = 0) 𝑏1 = slope (rate of change in Y for each unit change in X) ε = error term (random variation not explained by X) Purpose To quantify how one variable influences another. To predict the value of the dependent variable based on the independent variable. Example (Lean Six Sigma context) You might use simple linear regression to predict defect rates (Y) based on temperature settings (X) in a production process. If the regression shows a significant relationship, you can adjust temperature to minimize defects. Output Regression equation (predictive formula) R² (coefficient of determination) – how well X explains Y p-values – whether the relationship is statistically significant Definition: Multiple Linear Regression Multiple linear regression extends simple linear regression by modeling the relationship between one dependent variable (Y) and two or more independent variables (X₁, X₂, X₃, …). It helps understand how several factors together affect an outcome. Mathematical Model Y=b_0+b_1 X_1+b_2 X_2+b_3 X_3+⋯+b_n X_n+ε Where: Y= dependent variable X_1,X_2,X_3,…X_n= independent (predictor) variables b_0= intercept b_1,b_2,…b_n= coefficients showing how each variable influences Y ε= error term Purpose To understand how multiple variables together influence an outcome. To control for confounding effects (how one variable’s impact changes when others are included). To build predictive models for complex, real-world processes. Example (Data Science context) A data scientist uses multiple regression to predict customer satisfaction (Y) based on delivery time (X₁), product quality (X₂), and price (X₃). Each predictor contributes differently, and the model quantifies their combined influence. Output Regression equation with multiple coefficients Adjusted R² – how well all variables together explain Y Significance tests for each variable Multicollinearity diagnostics (checking whether predictors are too closely related)