Part 1

Response Surface Curves

Response Surface Methodology or RSM, examines the relationships between several explanatory variables and either one or more response variables. This method is use to determine the design factor settings to improve or optimize the performance or response of your thesis. It combines design of experiments, regression analysis and optimization methodsin order to optimize the expected value of a stochastic response.

In 1951, Box and Wilson published the development and application of this sequential method to chemical process design, in which yields of particular compounds were maximized. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response.

The Response Surface Curve are utilized to visualize the relations between the independent factors and response variables. The response can be represented graphically, either in the three-dimensionalspace or as contour plots that helps visualize the shape of the response surface . Each contour corresponds to a particular height of the responsesurface.

Part 2

Code from the Lab Assignment

I find the graphical respresentation methods provided in the text tp be very efficent functions.


# Assuming the population reaches infinity in 2040

plot(census, ':', label='US Census')
plot(un, '--', label='UN DESA')

e = linspace(1950, 2020)
f = 100 + 220000 / (2040 - e) #  f = a + b / (c - x)
plot(e, f/1000, color='gray', label='model')

decorate(xlim=[1950, 2016], xlabel='Year', 
         ylabel='World population (billions)',
         title='Prehistoric population estimates')

Output