Correlation and regression laboratory

Learning objectives

• Calculate correlation and fit a simple linear regression in a free spreadsheet.
• Interpret slope, intercept and R² with units.
• Inspect residuals and avoid extrapolation.

Core idea

Correlation measures linear association. Simple linear regression estimates how the mean of Y changes per unit X and supports prediction inside the studied range only.

Spreadsheet lab

• Scatter Y = seam strength (N) vs X = stitches per inch (SPI).
• r = =CORREL(X,Y); note sign and magnitude.
• Slope b = =SLOPE(Y,X); intercept a = =INTERCEPT(Y,X); R² = =RSQ(Y,X).
• Predict: ŷ = a + b·x for x inside min(X)..max(X).
• Residuals column: =Y - (a + b*X); plot vs X and vs fitted.

Garment-factory example

For 40 knit-polo seams, r = 0.62 between SPI and strength; slope = 3.1 N per SPI, R² = 0.38. A useful positive trend but not a full explanation — fabric weight matters too.

Method

1. Plot before fitting.
2. Report slope with units (Y per X) and R².
3. Check residuals; refit or stratify if patterns appear.

Common mistakes

• Interpreting correlation as causation.
• Extrapolating beyond the sampled X range.
• Ignoring nonlinear or grouped patterns in residuals.