Linear Regression Analysis
Find the linear relationship between input factor (X) and output (Y). Used for prediction and parameter optimization. E.g., how much does strength increase per 1°C oven temperature rise?
A quality engineer wants to quantify how reflow oven temperature (X) affects solder pull strength (Y). Linear regression builds a predictive model to set the optimal process parameter window and improve yield. When multiple candidate factors exist, screen significant variables with correlation analysis first, then build the regression model to quantify the relationship between key process variables (KPV) and critical-to-quality characteristics (CTQ).
Collect 20 paired data points (oven temp 200-250°C, pull strength 15-25 N) Regression equation: Y = 0.80 × X - 145.0 R² = 0.87 (model explains 87% of strength variance) Slope p = 0.0001 < 0.05 (statistically significant) → Predicted at 230°C: Y = 0.80 × 230 - 145 = 19 N → Optimal range: set 220-240°C to ensure pull strength ≥ 18 N
FAQFrequently Asked Questions
Related Tools
Correlation Analysis
Before building a regression model, use correlation analysis to confirm a significant linear relationship between X and Y, avoiding modeling unrelated variables.
Open toolOne-Way ANOVA
Regression handles continuous predictors; ANOVA handles categorical factors. They are often combined in DOE to analyze main effects of process factors.
Open toolHistogram
Regression residuals must satisfy the normality assumption. Use a histogram or normality test to check the residual distribution.
Open tool