PHARM/PCS V5 · Procedure 4 Dosage and Statistics
Linear Regression II: Lines Through Origin
Fit a straight line forced through zero, for data where theory says zero input must give zero response.
What it computes
Ordinary least-squares fit of y = mx, constraining the line to pass through the origin. Use this when theory requires the intercept to be zero (for example, dose-response curves where zero dose must give zero effect).
Inputs and outputs
You provide
- Paired x and y values, one pair per line
- Optionally, an x value at which to predict y
PHARM/PCS reports
- The slope of the line through the origin
- The predicted y, if you asked for one
- A plot of the data with the fitted line through the origin
When to use it
Only when zero genuinely must give zero: a real physical or theoretical constraint, not just a line that happens to pass near the origin. Several procedures rely on this through-origin fit internally, including first-order decay (Procedure 21) and one method of renal clearance (Procedure 30, Method B).
Reading the results
Forcing the intercept to zero removes a degree of freedom and can distort the slope if the constraint is wrong, so don't impose it just to tidy a fit. If an unconstrained fit (Procedure 3 or 5) shows an intercept clearly different from zero, that's your signal the through-origin model doesn't belong.
Faithful to the original
Output matches the 1986 program to every printed digit. With a single parameter to estimate, it is the simplest regression in the set.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.