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

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

3. 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.

4. 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