Relationship among variables Click for slide narration Relationship among variables Regression analysis graph equation

Example: a straight-line graph is described by: y = m x + b

Least-squares analysis: method to determine parameters of (any) equation that describes the graph. Let R = Σ (expected value – experimental value)2 = Σ (m xi + b – yi)2 for example in the preceding slide is a minimum, where Solve for m & b in the preceding equations – using calculus.

as R = Σ (m xi + b - yi)2 = m2 Σ xi2 + nb2 - 2b Σ yi + 2mb Σ xi - 2m Σ xi yi Solving for b, Substitue [1] into [2], rearrange, then solve for m