Compute a linear equation between two or more variables

Are the two variables correlated (no equation)?
Parametric Approach: Pearson's r. Assumes linear relationship. See chap. 8.
Nonparametric Approach. Spearman's rho or Kendall's tau. See chap. 8.

What is the equation when there is one X variable?
Parametric Approach: Linear Regression. Assumes residuals follow a normal distribution. See chapter 9
Nonparametric Approach. Theil-Sen nonparametric line. Assumes linear relationship, but does not require normal residuals. See chapter 10.

What is the equation when there are multiple X variables?
Parametric Approach: Multiple Regression. Assumes residuals follow a normal distribution. See chapter 11
Nonparametric Approach. A two-step process. Compute the residuals of Y from a LOESS surface smoothed versus one or more X variables. In step two, model and test the relationship between the residuals and the primary X variable of interest using the Theil-Sen line. Assumes a linear relationship between residuals and the primary X, but does not require normal residuals. See chapter 12.

Chapter references are to the course textbook Statistical Methods in Water Resources.