Friday, June 2, 2017

Your data set is [(0,0),(1,2),(2,16),(3,52),(4,118),(5,223)]. Determine the values of a and b rounded to 2 places for the power model, model(x)=ax^b.

We are given the data set (0,0),(1,2),(2,16),(3,52),(4,118),(5,223) and we are asked to fit these in a power model y=ax^b :
(1) The easiest way is to input the data in Excel or a graphing utility and perform a power regression yielding y=2.04x^2.93 with a,b rounded to two decimal places.
(2) To determine if the data set will fit a power model well we can plot (lnx,lny) and determine if the plot is approximately a straight line.
Taking the natural logarithm of the coordinates yields the points (0,.6931),(.6931,2.773),(1.0986,3.9512),(1.3862,4.7707),(1.6094,5.4072). These points appear to lie on a line. Performing linear regression on these points yields the line y=.7146+2.929x
So we have lny=lna+blnx Exponentiating both sides with base e gives us:
y=e^(lna)*e^(blnx)=a*(e^(lnx))^b=ax^b where a=e^(.7146) and b=2.929
So the power model is y~~2.04x^(2.93)
http://mathworld.wolfram.com/LeastSquaresFittingPowerLaw.html

No comments:

Post a Comment

Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...