Module 7 — Relationships between scale variables

Question: does blood pressure rise with BMI — and by how much, holding age constant?

Open the sample (Ctrl+Shift+O).

Correlation

Analyze → Correlate → Bivariate…, variables Age, BMI, SystolicBP, HeartRate, Run.

The matrix gives each pair's Pearson r and its p. Expect Age–SystolicBP and BMI–SystolicBP clearly positive, and everything involving HeartRate near zero (the planted null). Remember module 4's scatterplots: r is only trustworthy when the cloud is roughly linear — always look first.

Linear regression

Analyze → Regression → Linear…, dependent SystolicBP, predictors Age and BMI, Run.

How to read the three blocks:

• Model summary — R²: the share of SystolicBP's variance the two predictors explain together.
• ANOVA — whether the model beats no model at all.
• Coefficients — the substance. The BMI coefficient is mmHg per BMI unit, holding Age constant — the "holding constant" is what regression adds over correlation. The constant is the fitted value at Age 0, BMI 0 — outside the data, not meaningful on its own.

Write the fitted equation out once by hand: SystolicBP ≈ b₀ + b₁·Age + b₂·BMI. Predict the SBP of a 50-year-old with BMI 30 and sanity-check it against the Explore output from module 3.

Exercise

1. Add TotalCholesterol_mmolL as a third predictor. Does R² move much? Is its coefficient significant?
2. Correlate PhysicalActivity_minWk with TotalCholesterol_mmolL — the codebook's documented null pair. Report it honestly.
3. Spearman instead of Pearson (the method option): rank-based, robust to outliers and curvature. Do the Age/BMI/SBP conclusions change?

The syntax trail

correlate variables=[Age, BMI, SystolicBP, HeartRate]
linear_regression dependent=SystolicBP, predictors=[Age, BMI]
correlate variables=[PhysicalActivity_minWk, TotalCholesterol_mmolL]