I chose to include:  
Regression, with focus on separating the “pattern” from the “noise.”

Reason for including regression:

1. Desired algebra skills definitely include applications of linear equations.  It is awkward to only include relationships that are exactly linear and completely ignore those which are almost linear.   That leads to linear regression very naturally.
   
2. To deal with measurement issues, students need to believe in measurement noise.   We can approach that by repeated measurements of a single quantity or as variability around a linear model where it seems obvious that y should be very close to a linear function of x.   Many students find the latter more compelling.