User Tools

Site Tools


gibson:teaching:spring-2018:math445:lecture:loglinear

This is an old revision of the document!


A PCRE internal error occured. This might be caused by a faulty plugin

===== Log-linear relations ===== Logarithmic plots are useful when the data you're plotting varies over many orders of magnitude. Logarithmic plots can also highlight certain functional relationships ^ plot command ^ functional relationship ^ | ''plot(x,y)'' ^ $y = mx + b$ ^ | ''semilogy(x,y)'' | $y = c \: 10^{mx}$ ^ | ''semilogx(x,y)'' | $y = m \log x + b$ ^ | ''loglog(x,y)'' | $y = c \: x^m$ ^ In lecture I will show (1) why each of these functional relationships appears as a straight line in the corresponding plot command and (2) how to estimate the values of the constants from a graph, in order to estimate $y(x)$ as an explicit function, given a few data points. You can derive these formulae from the log-linear relations instead of memorizing them. For example, you can derive $y = c \; 10^{mx}$ by exponentiating both sides of $\log y = m x + b$.

gibson/teaching/spring-2018/math445/lecture/loglinear.1517881381.txt.gz · Last modified: 2018/02/05 17:43 by gibson