MATH38141 Regression Analysis - Coursework

This coursework accounts for 20% of your overall mark for this course and it may take

up to 10 hours to complete. Please present your solution in the form of a report which

should include:

• Introduction. Briefly describe the problem and the analysis to be undertaken.

• Analyse the data without using R, although R may be used for matrix calculations.

Make sure all parts of the questions are answered, demonstrating knowledge of the

applied methodology. All formulas that are used should be provided in the main

report before the relevant data are substituted in them.

• Analyse the data using R. Compare the results with those you obtained earlier.

Provide your R output as an appendix and reference it in the main part of your

report.

• Conclusions. Provide a summary of the conclusions that you draw from the statis-

tical analysis.

• Appendix.

Most marks will be awarded for correct and accurate calculations and their interpreta-

tion. However, some marks will be awarded for effective presentation of the results, which

should be concise and well structured. Marks will be deducted if any formulas used in

the calculations are missing from the text. Handing a handwritten report is acceptable,

but it should be neatly written.

Hand in your reports at the Teaching and Learning Office (Reception),

Alan Turing Building, by 13:00 on 20 November 2019.

Viscosity of Elastomer Blends

A chemist reports that adding naphthenic oil (phr) and filler (phr) can be used to

control the viscosity (M) of elastomer blends. Data for a particular filler are provided

in the file Viscos.txt available at the course webpage on Blackboard. It is believed that

the viscosity follows a normal distribution with homogenous variance for any oil and

filler level within the design region. Analyse the data as required to answer the following

questions. State all assumptions that you have made.

(A) Fit a regression model that has 4 regressors: a constant term, main effects for naph-

thenic oil and for filler, and an interaction term.

• Write down the first three rows of the X matrix.

• State the fitted model.

• Estimate the variance of the response.

• What is the coefficient of determination for this model? Interpret its value.

• Are the true values of the model parameters likely to be equal to zero?

(7 marks)

(B) Fit a quadratic regression model that can be used to predict the viscosity of elastomer

blends for given oil and filler levels.

• State the fitted model.

• Estimate the variance of the response. Why is the estimate smaller compared

to that when the model in (A) is fitted?

• What is the coefficient of determination for this model? Interpret its value.

• Are the true values of the model parameters likely to be equal to zero?

• How does this model compare to the model that you obtained in (A)? Use your

knowledge based on the material covered up to Page 100 of the lecture notes

to answer this question.

(7 marks)

(C) An elastomer blend with viscosity equal to 21 M is required. A chemist believes that

this can be achieved by using 10 phr oil and 50 phr filler.

• Find the 95% confidence interval for the mean viscosity of elastomer blends

manufactured as suggested by the chemist. Does the setting suggested by the

chemist ensure the required viscosity?

• A quality inspector decides to take a single observation, using the settings

suggested by the chemist. Calculate an interval that will contain the measured

value 95% of the time.

(6 marks)

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