Chemistry

# What is Least Square Fitting Equation?

Least square fitting is usually made out to be more difficult than it really is or it is treated as a spreadsheet “black art”. Here briefly explain the fundamentals which are very easy to follow. Typically in a lab experiment we have 3 to 6 data points (xi, yi) and we would like the best straight line through them. As well as the linear function:

y= mc + c

any function f(x) that is capable of being plotted as a linear graph would have the data points fitted by the least squares term; some of the more chemically useful are listed (here, a and b are constants). A log function gives a straight line from a semi-log plot of y against ln(x) with gradient = a and intercept = b.

y =a ln (x) + b

A power function gives a straight line from a log-log plot of ln(y) against ln(x) with gradient = b and intercept = ln(a).

y= ax”

An exponential function gives a straight line from a semi-log plot of ln(y) against x with gradient = ln(b) and intercept = ln(a).

y= ab^x

A reciprocal function gives a straight line from a semi-reciprocal plot of y against 1/x with gradient = b and intercept = a.

y= a + (b/x)