Regression Analysis
Regression analysis is a statistical method for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, focusing on the relationship between a dependent variable and one or more independent variables.
Where y is the dependent variable, x₁ to xₚ are independent variables, β₀ is the intercept, β₁ to βₚ are coefficients, and ε is the error term.
Regression Results
R-squared
Goodness of fit
Adjusted R-squared
Adjusted for predictors
Standard Error
Residual standard error
Observations
Number of data points
Coefficients
| Variable | Coefficient | Std. Error | t-statistic | VIF |
|---|
Analysis of Variance (ANOVA)
| Source | Sum of Squares | Degrees of Freedom | Mean Square | F-value |
|---|
Prediction
Regression Examples in Industrial Engineering
Production Example
Predict production output based on machine runtime and operator experience.
X: Runtime (hrs), Experience (years)
y: Output (units)
Example data:
X: 8,2; 10,3; 12,1; 14,5; 16,4
y: 100, 120, 110, 150, 140
Quality Control Example
Predict defect rate based on temperature and pressure settings.
X: Temperature (°C), Pressure (psi)
y: Defect Rate (%)
Example data:
X: 180,40; 190,45; 200,50; 210,55; 220,60
y: 5.2, 4.1, 3.8, 3.5, 3.2
Supply Chain Example
Predict delivery time based on order size and distance.
X: Order Size (units), Distance (miles)
y: Delivery Time (days)
Example data:
X: 100,50; 250,75; 500,100; 750,125; 1000,150
y: 3, 5, 7, 9, 11