1. Foundational Theory of Linear Regression
Ordinary Least Squares (OLS) Regression is a precise, statistical method used to separate mixed costs. Instead of guessing a visual line of best fit or relying on just two data points, regression analysis mathematically calculates a line that minimizes the sum of the squared differences (errors) between the actual data points and the regression line.
2. Interpreting the Statistical Outputs
The Intercept (a)
The point where the line crosses the Y-axis, representing the total fixed cost for the period.
The X-Variable Coefficient (b)
The slope of the line, which represents the variable cost per unit of activity.
Coefficient of Determination (R²)
A statistical metric that measures the explanatory power of the model, ranging from 0.0 to 1.0. An R² value of 0.92 means that 92% of the variance in total costs is directly driven by changes in the activity level (X). The remaining 8% is caused by random operational factors.
The t-Statistic and p-Value
Tests whether the relationship between the cost and the activity level is statistically reliable. A p-value below 0.05 indicates a high level of significance, proving that the chosen activity metric is a valid driver of the cost.
3. Multiple Regression Frameworks
Simple regression uses a single activity driver (X). In complex business setups, managers use Multiple Regression to model costs based on several independent variables at the same time:
Y = a + b_1X_1 + b_2X_2 + b_3X_3 “
- Example: Total factory delivery cost (Y) can be modeled more accurately by analyzing delivery miles driven (X₁), the weight of cargo moved (X₂), and local fuel price fluctuations (X₃) simultaneously.