Analysis of the Regression Line

What it computes

Given a set of (x, y) data points, fits the regression line y = mx + b and reports the slope, y-intercept, x-intercept, correlation coefficient, their standard errors, and confidence limits at the selected level. This is the full diagnostic output for a linear fit; Procedure 3 is a streamlined subset.

Inputs and outputs

When to use it

Whenever the line itself is the result and you need to defend it: reporting a slope with confidence limits, comparing it to another line (Procedure 6 tests two slopes for parallelism), or reading the x-intercept as a meaningful quantity such as a threshold. This is the regression engine that Procedures 6, 7, 14, and 22 lean on.

Reading the results

A high correlation coefficient confirms the points are linear but says nothing about whether the model is appropriate; a curved relationship can still yield a deceptively high r over a narrow range. Check that the slope's confidence limits exclude zero before claiming a real dependence, and expect the x-intercept's limits to be asymmetric when the slope is uncertain.