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.