5CCM242A / 6CCM242B
Linear Models and Regression Analysis
Coursework
Steven Gilmour
Department of Mathematics
King’s College London
5 March 2018
Please upload a single pdf file to the Turnitin assignment on the Keats page.
Deadline 3.45am 27 March 2018 (Note: there will be no help with technical
problems in Keats or Turnitin for at least 10 hours before this deadline. Submit
early to avoid any risk.)
The file reactor.txt, available on Keats, contains data from an experiment
on a chemical reactor. The file contains the following variables:
X1 the reaction temperature, coded so that X1 = (Temperature - 200)/50,
where Temperature is in degrees Celsius;
X2 the pH of the reaction, coded so that X2 = pH - 5;
X3 the pressure under which the reaction is run, coded so that X3 = (Pres-
sure - 175)/25, where Pressure is measured in kPa;
Y the yield of the reaction as a percentage.
The aim of this project is to recommend settings of temperature, pH and pressure
which will maximise the yield of the reaction.
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Use linear models in R to analyse these data in order to be able to make good
predictions of the yield. You have to decide exactly which analyses to perform,
but things you should consider include:
Is a multiple linear regression model adequate, or should a second (or higher)
order polynomial model be preferred? [Technical note: in R to fit second
or higher order terms using lm we have to write them using I(); for ex-
ample to fit a quadratic regression with one explanatory variable, we use
lm(Y X+I(X^2)).]
More generally, which terms should be included in the model, i.e. what
should the linear predictor be?
Does the model seem to be adequate? Do any of the required assumptions
seem to be contradicted? If so, how can the model be improved?
How can the model be used to estimate the expected yield at different set-
tings of temperature, pH and pressure?
You will be assessed on your answers to the following questions. Give your an-
swers in a single pdf file which should be uploaded to the Turnitin assignment on
the Keats page.
1. State the model you have used to make predictions. It needs to be clearly
written as a formula so that someone else could replicate your analysis.
2. Provide one statistic and one plot from your model which illustrate the ad-
equacy of the model.
3. The standard operating conditions for the reaction are Temperature = 200,
pH = 5 and Pressure = 175. Use your model to estimate the expected yield
that would be obtained from running the reaction at standard operating con-
ditions.
4. Three engineers all agree that the yield can be improved by using pH =
6. However, they disagree about the best settings for the temperature and
pressure. Estimate the expected yield from each of the following settings,
all with pH = 6:
(a) Temperature = 225, Pressure = 200;
(b) Temperature = 250, Pressure = 187.5;
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(c) Temperature = 250, Pressure = 200.
5. At what settings would you recommend the reaction be run in order to max-
imise the yield?