Are there differences in the regression lines?

Does each line have the same intercept (one line) or different intercepts (different parallel lines)?**Parametric Approach**: Analysis of Covariance. Requires a linear relationship on partial plots and that residuals follow a normal distribution.**Nonparametric Approach**. A rank-sum test on residuals from a Theil-Sen line of Y vs. X. Requires a linear relationship, but not normality of residuals.

See Helsel & others (2020) Chapters 11 and 12.

Does each line have the same slope? (Are they parallel?)**Parametric Approach**: Analysis of Covariance. Requires a linear relationship on partial plots and that residuals follow a normal distribution.**Nonparametric Approach**. Do confidence intervals on the Theil slope overlap? Requires a linear relationship, but not normality of residuals.

See Helsel & others (2020) Chapters 10 and 11.

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Chapter references are to the 2020 Second Edition of Statistical Methods in Water Resources.